Resetting semi-passive stiffness damper, triggering assembly, and method of damping

Abstract

A resetting semi-passive stiffness damper (RSPSD) triggering assembly and a RSPSD and method of use for damping movement of an object. Exemplary embodiments of a RSPSD triggering assembly include, for example, a rotatable disc and a spring-loaded lever arranged between the disc and a slotted channel. A sensor is provided and communicates with a bypass valve on the cylinder. A change in the direction of movement of the disc causes reciprocation of the lever in the channel, which causes the sensor to send open and close signals to the bypass valve. In some embodiments, a single disc may be replaced with two interacting discs. A RSPSD equipped with such a triggering assembly is usable to damp movement of an object of interest.

Claims

1. A triggering assembly for a resetting semi-passive stiffness damper (RSPSD) having a linearly-reciprocatable piston, comprising: a rotatable disc; a displaceable, spring-biased lever having a first end associated with the circumference of the disc and a second end movably arranged in a slotted channel; and a sensor associated with the channel and located to detect the second end of the lever when the lever resides within a sensing range of the sensor, the sensor adapted to send open and close signals to a valve of the RSPSD; wherein, a back-and-forth rotation of the disc will cause the first end of the lever to move along the circumference of the disc and the second end of the lever to reciprocate within the slotted channel.

2. The triggering assembly of claim 1, wherein the slotted channel is mounted to the disc such that rotation of the disc is not transferred to the slotted channel.

3. The triggering assembly of claim 2, wherein: the disc is a first of two discs and is rotatably fixed to one end of a rigid member; a second disc is rotatably fixed to the other end of the rigid member, the second disc being of a smaller diameter than the first disc; and the triggering assembly is mountable to the RSPSD such that the second disc is directly or indirectly rotatable by movement of the RSPSD piston; wherein, a back-and-forth rotation of the second disc will cause a back-and-forth rotation of the first disc.

4. The triggering assembly of claim 3, wherein vertical travel of the lever in the channel per linear travel distance of the RSPSD piston is defined by the formula: $y\left(t\right)=\left[\sqrt{L^2-{\left[R_L\sin \left({}_o-\frac{x_p\left(t\right)}{R_p}\right)\right]}^2}-\left(L-d\right)\right]-[\sqrt{R_L^2-{\left[R_L\sin \left({}_o-\frac{x_p\left(t\right)}{R_p}\right)\right]}^2}-\sqrt{R_L^2-x_o^2}]$ where L is the length of the lever, R.sub.L is the radius of the first disc, .sub.0 is the angle formed between the lever and a radial line of the first disc that extends to the first end of the lever, x.sub.p(t) is the distance of movement of the piston, R.sub.p is the radius of the second disc, d is the total vertical travel distance of the lever within the slotted channel, and x.sub.0 is the distance between the slotted channel and the contact point of the lever with a circumferential flange of the first disc.

5. The triggering assembly of claim 1, wherein the lever and slotted channel are arranged above the disc.

6. The triggering assembly of claim 5, wherein the lever and slotted channel are mounted to an elongate support to which the disc is also rotatably mounted.

7. The triggering assembly of claim 5, wherein: the triggering assembly is mountable to the RSPSD such that the disc is directly or indirectly rotatable by movement of the RSPSD piston; and vertical travel of the lever in the channel is related to the travel distance of the RSPSD piston by the formula: $y\left(t\right)=\left[\sqrt{L^2-{\left[R_L\sin \left({}_o-\frac{x_p\left(t\right)}{R_L}\right)\right]}^2}-\left(L-d\right)\right]+[\sqrt{R_L^2-{\left[R_L\sin \left({}_o-\frac{x_p\left(t\right)}{R_L}\right)\right]}^2}-\sqrt{R_L^2-x_o^2}]$ where L is the length of the lever, R.sub.L is the radius of the disc, .sub.0 is the angle formed between vertical and a radial line extending to the first end of the lever, x.sub.p(t) is the distance of movement of the piston, d is the total vertical travel distance of the lever within the slotted channel, and x.sub.0 is the distance between the slotted channel and the contact point of the lever with the peripheral surface of the disc.

8. The triggering assembly of claim 5, wherein: the disc is a first of two discs and is rotatably fixed to one end of a rigid member; a second disc is rotatably fixed to the other end of the rigid member, the second disc being of a smaller diameter than the first disc; and the triggering assembly is mountable to the RSPSD such that the second disc is directly or indirectly rotatable by movement of the RSPSD piston; wherein, a back-and-forth rotation of the second disc will cause a back-and-forth rotation of the first disc.

9. The triggering assembly of claim 8, wherein vertical travel of the lever in the channel per linear travel distance of the RSPSD piston is defined by the formula: $y\left(t\right)=\left[\sqrt{L^2-{\left[R_L\sin \left({}_o-\frac{x_p\left(t\right)}{R_P}\right)\right]}^2}-\left(L-d\right)\right]+[\sqrt{R_L^2-{\left[R_L\sin \left({}_o-\frac{x_p\left(t\right)}{R_P}\right)\right]}^2}-\sqrt{R_L^2-x_o^2}]$ where L is the length of the lever, R.sub.L is the radius of the larger disc, .sub.0 is the angle formed between vertical and a radial line of the first disc that extends to the first end of the lever, x.sub.p(t) is the distance of movement of the piston, R.sub.p is the radius of the smaller disc, d is the total vertical travel distance of the lever within the slotted channel, and x.sub.0 is the distance between the slotted channel and the contact point of the lever with the peripheral surface of the first disc.

10. The triggering assembly of claim 1, wherein the disc includes an extending circumferential flange upon which the first end of the lever rides.

11. The triggering assembly of claim 1, wherein the sensor and a biasing spring are located in the slotted channel.

12. A resetting semi-passive stiffness damper (RSPSD), comprising: a reciprocatable piston located within a cylinder; an actuator coupled between the piston and an object the movement of which is to be damped, so as to transfer movement of the object to the piston; a bypass valve in communication with the cylinder; a rotatable disc that is directly or indirectly rotatable by linear movement of the piston; and a triggering assembly comprising: a displaceable, spring-biased lever having a first end associated with the circumference of the disc and a second end movably arranged in a slotted channel, and a sensor associated with the channel and located to detect the lever when the second end of the lever resides within a sensing range of the sensor, the sensor configured to send open and close signals to the bypass valve; wherein, reciprocation of the piston will cause a back-and-forth rotation of the disc, which will resultantly cause the first end of the lever to move along the circumference of the disc and the second end of the lever to reciprocate within the slotted channel.

13. The RSPSD of claim 12, wherein the slotted channel is mounted to the disc such that rotation of the disc is not transferred to the slotted channel.

14. The RSPSD of claim 12, wherein the lever and slotted channel are arranged above the disc.

15. The RSPSD of claim 12, wherein: the disc is a first of two discs and is rotatably fixed to one end of a rigid member; and a second disc is rotatably fixed to the other end of the rigid member, the second disc being of a smaller diameter than the first disc and directly or indirectly rotatable by movement of the RSPSD piston; wherein, a back-and-forth rotation of the second disc will cause a back-and-forth rotation of the first disc.

16. The RSPSD of claim 12, wherein the bypass valve is closed while the triggering assembly lever position satisfies the formula y(t)<s, where s is the vertical distance the lever must travel within the slotted channel to be within the sensing range of the sensor.

17. The RSPSD of claim 12, wherein: when the triggering assembly lever reaches a position where sy(t)<d, the bypass valve will open, the pressure in the RSPSD will equalize, and the damper force will drop to zero; where s is the vertical distance the lever must travel within the slotted channel to be within the sensing range of the sensor and where d is the total vertical travel distance of the lever into the slotted channel.

18. The RSPSD of claim 17, wherein the bypass valve will remain open until the lever moves to a position that satisfies the formula y(t)<s.

19. A method of damping the movement of an object, comprising: providing a resetting semi-passive stiffness damper (RSPSD), the RSPSD comprising: a reciprocatable piston located within a cylinder; an actuator for coupling the piston to the object so as to transmit movement of the object to the piston, a bypass valve in communication with the cylinder, a rotatable disc that is directly or indirectly rotatable by linear movement of the piston, a displaceable, spring-biased lever having a first end associated with the circumference of the disc and a second end movably arranged in a slotted channel, and a sensor associated with the channel and located to detect the lever when the second end of the lever resides within a sensing range of the sensor, the sensor configured to send open and close signals to the bypass valve; and coupling the RSPSD piston to the object with the actuator; wherein, movement of the object will cause a reciprocation of the RSPSD piston; and wherein, reciprocation of the piston will cause a back-and-forth rotation of the disc, which will resultantly cause the first end of the lever to move along the circumference of the disc and the second end of the lever to reciprocate within the slotted channel; whereby the sensor will be activated and deactivated in response to movement of the lever, thereby causing the sensor to send open and close signals to the RSPSD bypass valve as required to damp the motion of the object.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) In addition to the features mentioned above, other aspects of the present invention will be readily apparent from the following descriptions of the drawings and exemplary embodiments, wherein like reference numerals across the several views refer to identical or equivalent features, and wherein:

(2) FIG. 1a schematically represents the construction of a typical RSASD;

(3) FIG. 1b depicts the RSASD of FIG. 1a installed in a structure;

(4) FIG. 2 schematically represents an exemplary embodiment of a RSPSD according to the invention;

(5) FIGS. 3a-3b schematically illustrate the position and movement of a lever element of an exemplary RSPSD of the invention before and after displacement of an associated rack element;

(6) FIG. 4a graphically illustrates displacement of the lever element during movement of the rack element;

(7) FIG. 4b graphically illustrates certain design parameters associated with the lever element;

(8) FIGS. 5a-5b graphically represent the movement of a rack element and lever element, respectively, during testing of an exemplary RSPSD;

(9) FIGS. 6a-6b are hysteresis charts illustrating the effects of a change in the sensing distance of a sensor element of an exemplary RSPSD;

(10) FIG. 7 is a table comparing the hysteretic characteristics of an exemplary RSPSD to an exemplary RSASD;

(11) FIGS. 8a-8b graphically depict the controlled vs. uncontrolled displacement and acceleration responses of an exemplary RSPSD during a structural control simulation;

(12) FIGS. 9a-9b graphically depict the controlled vs. uncontrolled displacement and acceleration responses of an exemplary RSASD during a structural control simulation;

(13) FIGS. 10a-10b graphically depict the energy dissipated by the exemplary RSPSD and RSASD corresponding to the graphs of FIGS. 8a-8b and FIGS. 9a-9b, respectively, when subjected to ground motion forces similar to those seen during the Northridge earthquake;

(14) FIG. 11 numerically presents the peak response data associated with the aforementioned exemplary RSPSD and RSASD during the simulation;

(15) FIGS. 12a-12b schematically and respectively illustrate alternative embodiments of amplified and non-amplified triggering lever assemblies that may be used with a RSPSD of the invention;

(16) FIGS. 13a-13b schematically and respectively illustrate further alternative embodiments of amplified and non-amplified triggering lever assemblies that may be used with a RSPSD of the invention;

(17) FIG. 14 graphically compares the vertical displacement of the lever in the channel versus the horizontal displacement of the damper piston for the configurations shown in FIG. 2, FIG. 12a, and FIG. 13a;

(18) FIG. 15 depicts an exemplary scissor-jack mechanism that can be connected to a lever of a RSPSD to provide more flexibility in the design thereof;

(19) FIG. 16 is a plot of the relative horizontal displacement between two joints of the scissor-jack mechanism of FIG. 15 during use;

(20) FIG. 17 schematically illustrates yet another exemplary embodiment of a triggering lever assembly that may be used with a RSPSD of the invention, wherein a single mechanism acts as both the lever and the amplifying component;

(21) FIG. 18 graphically illustrates the vertical displacement of a rod portion in an upper channel portion of the lever assembly of FIG. 17 versus the horizontal displacement of a rack element for different values of the ratio r; and

(22) FIG. 19 schematically illustrates another alternative embodiment of a triggering lever assembly that may be used with a RSPSD of the invention.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENT(S)

(23) Referring again to FIG. 2 and to FIG. 3a, it can be understood that an exemplary embodiment of a RSPSD 5 according to the invention will generally include a piston-containing cylinder 10 that is connected in series with a grooved rack 15. A triggering lever 20, with a length (L), has one end arranged in a slotted channel 25 at a distance (y.sub.0) above the rack 15. The channel may be associated with a vertical column 30, etc. The lever 20 is biased downward by a spring 35 located in the channel 25.

(24) The lever 20 is allowed to move vertically within the channel 25 and to rotate about the end thereof that resides in the channel. The opposite end of the lever 20 rests on the grooves in the rack 15, at a transverse distance (x.sub.0) from the slotted channel 25 and at an initial orientation of (.sub.0) with respect to the rack. A sensor 40, such as a proximity sensor, having a range (r) is located near the end of the channel 25 farthest from the rack 15, and at a distance (h) above the end of the lever that resides in the channel. The lever 20 must travel a selected distance (s) to be within the sensing range of the proximity sensor 40. The proximity sensor 40 communicates with a bypass valve 45 on the cylinder 10.

(25) Referring now to FIGS. 3a-3b, movement of the lever 20 and operation of the RSPSD 5 can be better understood. As shown in FIG. 3a, the rack 15 is initially moving to the left. As long as the rack 15 continues to move in the initial direction, the vertical position of the lever 20 remains unaffected. However, as illustrated in FIG. 3b, when the direction of movement of the rack 15 reverses (as indicated by the arrow), the rack-contacting end of the lever 20 becomes engaged with the grooves of the rack 15. Upon engagement, further movement of the rack 15 in the new direction forces the lever 20 to rotate while simultaneously driving the lever into the slotted channel 25 by some associated distance (y(t)). Vertical movement of the lever also causes a transverse movement of the rack-contacting end thereof, the distance of movement being indicated by (x(t)). The total vertical distance the lever 20 travels is denoted by (d). Using trigonometry, the vertical distance (y(t)) the lever travels as a function of the movement (x(t)) of the rack can be expressed as:
y(t)={square root over (L.sup.2[x.sub.0x(t)].sup.2)}(Ld) (1)
where (y(t)) is valid for 0<x(t)<2.Math.(x.sub.0).

(26) When the lever 20 reaches a predetermined position, it triggers the proximity sensor 40, which then sends a signal to open the bypass valve 45. As the rack 15 continues to move, the lever 20 reaches its maximum vertical position, reverses direction, and is then forced by the return spring 35 back along the channel 25 in a reverse direction. Once the lever 20 leaves the sensing range (r) of the proximity sensor 40, the valve 45 closes. With the rack-contacting end of the lever 20 now oriented in the opposite direction on the rack 15, the above-described movement of the lever and the associated process is repeated when movement of the rack next changes direction.

(27) A plot of (y.sub.t) for 0<x(t)<2.Math.(x.sub.0) is provided in FIG. 4a. Included on the y-axis of the plot are the distance (s) the lever 20 must travel to be within the range (r) of the proximity sensor 40, and the total travel distance (d). For y(t)<s, the lever 20 is engaged but is not within the range of the sensor 40, and the valve 45 on the RSPSD will remain closed. Once (s)y(t)<(d), an electrical signal is sent to the valve 45 and it opens, the pressure in the RSPSD equalizes, and the damper force drops to zero. The valve 45 remains open as the lever 20 reaches (d), changes direction, and begins to move back down the channel 25. Once the lever 20 has moved out of range (r) of the sensor 40 y(t)<s, the voltage drops to zero and the valve 45 closes again. Thus, pressure equalization in the device takes place while 0<x(t)<2.Math.x.sub.0 and (s)y(t)<(d), a condition which was used to model resetting of the device 5 in various numerical simulations.

(28) It is desirable that RSPSDs according of the invention perform similarly to RSASDs, but using less feedback control components so as to simplify device operation and increase reliability. An ideal RSPSD would be able to achieve instantaneous resetting of the control force with each change in direction of the rack. In other words, the valve would open, the force would drop to zero, and the valve would close again at the instant the piston velocity is zero. This operation would guarantee maximum energy dissipation by the RSPSD. Comparable performance is not achievable using a RSASD due to delays in the signal, control logic, and valve operation. In a RSPSD, this is not possible primarily due to limitations of the mechanical components. That is, there is a delay associated with the time it takes the lever to engage and begin moving vertically toward the sensor. This delay is represented by the bottom left hand portion of the curve in FIG. 4a. During this time, the piston has already changed direction, and energy stored in the device is momentarily being transferred back to the structure in which it is installed.

(29) There is a second delay associated with a RSPSD that also prohibits it from achieving ideal performance. More specifically, once the valve is open and the pressure equalizes, the valve will remain open until the lever leaves the sensing range of the proximity sensor, i.e., y(t)<s. This is represented by the top portion of the curve in FIG. 4a. During this time, the stiffness in the device is zero and energy from the structure isn't being stored. The combined time it takes the lever to reach the sensor and then leave the sensor will hereafter be referred to as the resetting delay of the device. Delays due to signal travel time and valve opening/closing are incorporated in the top portion of the curve in FIG. 4a.

(30) In order for a RSPSD to perform similar to a RSASD, both of the RSPSD delays described above should be minimized through the design of the rack-lever mechanism. This can be achieved by reducing the corresponding portions of the curve in FIG. 4a, that is, by reducing (d), (x.sub.0), and (sd). The sensing distance (s) is determined by the location (h) and range (r) of the proximity sensor, while the distances (d) and (x.sub.0) depend on the length (L) and initial orientation (.sub.0) of the lever. As proximity sensors come in a variety of standard ranges (e.g., 2 mm-12 mm), and the height of the sensor above the lever is easily controlled, the primary design considerations are the lever length (L) and initial orientation (.sub.0). FIG. 4b shows the change in (d) and (x.sub.0) for 30<(.sub.0)<60 and (L)=25.4 mm (1 in), and it is apparent that both design parameters decrease with increasing (.sub.0).

(31) Further decreases in (d) and (x.sub.0) can be achieved by reducing the length of the lever (L). Therefore, the rack-lever mechanism can be designed to reduce the resetting delay through the selection of design parameters (L), (.sub.0), (h), and (r). However, consideration must also be given to the practical limits on the minimum size of the rack-lever mechanism components and the minimum time required for pressure equalization of the device. Previous research has shown the time for pressure equalization to be in the range of approximately 20-40 ms for pneumatic valves.

(32) Simulation

(33) In order to demonstrate the feasibility of the rack-lever mechanism and to validate Equation (1), simulations were conducted in Solid Edge, a commercial software package that combines CAD and finite element analysis to aid in the design of complex systems. The rack-lever model consisted of a lever with a length (L)=70 mm (2.75 in) and (.sub.0)=41, resulting in a value of (d)=24.24 mm (1 in) and (x.sub.0)=53 mm (2 in). The rack was driven through a sinusoidal displacement having an amplitude150 mm (6 in) and a frequency of 0.25 Hz, as is shown in FIG. 5a. The vertical displacement of the lever was recorded for analysis. The same system was simulated in Matlab using Equation (1), and the results are presented along with those from Solid Edge in FIG. 5b.

(34) FIGS. 5a-5b demonstrate that each time the rack changes direction (reaches its maximum positive or negative displacement) the lever is engaged and driven vertically to its maximum displacement. The extra hump at the beginning of the Solid Edge curve is due to a combination of the initial orientation of the lever and motion of the rack, resulting in an immediate engagement and vertical (with respect to the drawings herein) displacement of the lever. For the Matlab simulation, it was assumed that the rack moved so that the lever wasn't engaged until the first change in rack direction. In practice, this initial hump would cause the RSPSD to reset at the start of the structure motion. However, no energy is stored in the device at this time, and it is expected that this feature would have little effect on the overall RSPSD performance.

(35) Another observation of FIG. 5b is the small amplitude oscillations of the lever present in the Solid Edge curve as the lever returns to the zero displacement position. These oscillations are attributed to the force from the return spring acting on the lever (see FIG. 2), and damp out over a short period of time. Although the amplitude of these vibrations is small, they could potentially cause unwanted resetting of the device. This can be avoided by designing the sensing distance (s) to be greater than the maximum amplitude of the oscillation, or incorporating a small amount of additional damping in the system. Despite small differences between the two curves, FIG. 5b demonstrates that Equation (1) accurately models the general motion of the rack-lever system.

(36) Hysteresis

(37) Resettable stiffness devices work by storing and dissipating energy from a vibrating structure. The maximum energy dissipated in one cycle of motion is achieved by resetting the device at the instant the piston velocity equals zeroalthough as previously mentioned, this ideal performance is not achievable in practice due to delays in the resetting operation.

(38) The energy dissipation capacity of a resettable device is characterized by the area under its hysteresis curve. To demonstrate the capacity of the RSPSD, simulations were conducted in Matlab based on the setup shown in FIG. 2. In order to reduce the resetting delay while considering practical limitations on the minimum dimensions of the mechanism components, a lever length of (L)=12.7 mm (0.5 in) with initial orientation (.sub.0)=30 was used. The resulting values of (x.sub.0) and (d) were 11 mm (0.5 in) and 6.35 mm (0.25 in) respectively. The height and range of the proximity sensor were varied to yield (s)=2 mm and (s)=6 mm, in order to demonstrate the effect of (s) on the RSPSD performance. The effective stiffness of the pneumatic damper is assumed to be k.sub.d=32.89 kN/mm. For comparison, a hysteresis curve for an ideal RSASD was also computed. For all simulations, the piston of the device was driven through a sinusoidal displacement having an amplitude of 50.8 mm (2 in) and periods of 0.6 s, 1.8 s, and 5.4 s. The hysteresis curves for the RSPSD for T=0.6 s and the two different values of (s) are presented in FIGS. 6a-6b, along with the curve for the ideal RSASD.

(39) A comparison of FIG. 6a and FIG. 6b reveals the effect of the sensing distance (s) on the hysteresis of the device for a given value of (d). For a large sensing distance (s), there is a greater delay in the zeroing of the damper force once the piston has changed direction. This is due to the lever traveling a longer distance prior to being sensed and opening of the valve takes place. As mentioned previously, this would correlate to stored energy being transferred back to the structure, thereby reducing the area under the hysteresis curve compared with the ideal RSASD.

(40) However, a large sensing distance (s) also means that the valve closes quicker due to the reduced time that the lever remains in the proximity of the sensor ((s)y(t)<(d)). As a result, energy begins being stored sooner after the force has zeroed. For a small sensing distance (s), the force drops to zero sooner, and less energy is transferred back to the structure. On the other hand, the lever spends more time in the proximity of the sensor, thereby increasing the time the valve is open and delaying the storage of energy after the force has zeroed. As a result, the amount of energy dissipated by the device is again less than that with the ideal RSASD. In the end, the sensing distance (s) only shifts the hysteresis curve of the RSPSD, the same amount of energy is dissipated for (s)=2 mm and (s)=6 mm, and the energy is always less than that of the RSASD. This is shown in columns 3-4 of Table 1 (FIG. 7), which represents the energies dissipated (E) for both RSPSDs and the ideal RSASD for different input periods.

(41) The results indicate that the sensing distance (s) could be arbitrarily set, as it doesn't affect the energy dissipative characteristics of the device. However, there is still a constraint on the minimum time the lever must remain in the proximity of the sensor so that the pressure has time to equalize during opening of the valve, and this time is directly related to the sensing distance (s) and the total travel distance (d). Previous research has determined this time to be in the range of 20 ms-40 ms depending on the characteristics of the valve.

(42) In order to determine if the RSPSD meets this minimum requirement, the time (t.sub.s) that the lever is in the proximity of the sensor was calculated for each RSPSD and all three input periods. The results of these calculations are presented in Columns 5 and 6 of Table 1, and show that (t.sub.s) is less for smaller periods and larger sensing distances (s). Furthermore, it is observed from Column 6 that (t.sub.s) for the case with T=0.6 s and (s)=6 mm is only 17 ms, and therefore does not meet the minimum requirement of 20 ms-40 ms. Based on the data presented in Table 1, careful consideration should be given to the design of a RSPSD to ensure that sufficient time is allowed for pressure equalization during resetting while simultaneously minimizing the time the valve is open.

(43) Structural Response Mitigation

(44) In order to evaluate the potential of a RSPSD as a structural control device, additional simulations were conducted using a single-degree-of-freedom (SDOF) building adopted from the relevant literature (i.e., Lu and Lin, 2009). The building has a period of T=0.6 s and a damping ratio of 5%. However, to investigate the performance of the RSPSD for SDOF buildings with larger periods, the stiffness of the building was reduced to yield two additional buildings with periods of T=1.8 s and T=5.4 s. The buildings were subjected to ground motion experienced during the Northridge earthquake, with a peak ground acceleration of 0.84 g. For the RSPSD, the same design parameters described in the previous section were used again, including sensing distance values of (s)=2 mm and (s)=6 mm for the sensing distance. For comparison, the uncontrolled response of the building and the response of the building with an ideal RSASD were also obtained.

(45) FIGS. 8a-8b and 9a-9b graphically present the time history displacement and the absolute acceleration responses for the building with T=0.6 s for the RSPSD and RSASD devices. For the RSPSD, the sensing distance (s) was 2 mm. The solid line in each graph represents the controlled response. The graphs indicate that both devices are effective in reducing the displacement response of the building, but less effective in reducing the acceleration response.

(46) FIGS. 10a-10b graphically represent the energy that would be dissipated by each device during the earthquake, and demonstrate that the energy dissipation capacity of a RSPSD is comparable to that of a RSASD.

(47) The responses for the two remaining buildings, and for the RSPSD with sensing distances of (s)=2 mm and (s)=6 mm, are presented in Table 2 (FIG. 11). Columns 2-5 of Table 2 show that the RSPSD is effective in reducing the peak displacement response of all three buildings, and its performance is comparable with that of the RSASD. Meanwhile, columns 6-9 show that the RSPSD with a sensing distance of (s)=2 mm and (s)=6 mm, along with the RSASD, increase the absolute acceleration of the building compared to the uncontrolled case. Furthermore, the performance of the RSPSD is again comparable with that of the RSASD.

(48) It is interesting to note that the displacement response of the RSPSD with a sensing distance (s)=6 mm is slightly smaller than that obtained using (s)=2 mm for the buildings with periods of 1.8 s and 5.4 s. Meanwhile, the RSPSD using a sensing distance (s)=2 mm outperforms the RSPSD using a sensing distance (s)=6 mm with respect to reducing the acceleration response of all three buildings. These results indicate that although the energy dissipated by the RSPSD with a sensing distance (s)=2 mm and (s)=6 mm was the same for the sinusoidal displacement input, the sensing distance does have a small effect on the response of a flexible structure subject to random excitation.

(49) Finally, the time (t.sub.s) for pressure equalization was monitored for the RSPSD for both sensing distance (s) and all three buildings. It was determined that for (s)=6 mm, the value of (t.sub.s) was less than the minimum required for pressure equalization for all three buildings. On the other hand, the minimum value of (t.sub.s) for all three buildings using (s)=2 mm was 42 ms, which is at the high end of the required range.

(50) Amplified and non-amplified alternate embodiments of triggering lever assemblies 50, 85 that may be used with a RSPSD of the invention are schematically illustrated in FIGS. 12a-12b, respectively. Such lever assemblies 50, 85 may be used with the exemplary RSPSD 5 of FIG. 2, or with other alternate embodiments not specifically shown or described herein.

(51) The triggering lever assembly 50 of FIG. 12a is shown to once again include a lever 55 with a length (L) and a second end arranged in a slotted channel 60. The lever 55 is again biased downward by a spring 65 located in the channel 60. In this embodiment, the lever 55 and channel 60 are mounted to a disc 70 in a manner that permits the disc to rotate while the channel and lever remain in the vertical position shown. A proximity sensor 75 having a range (r) is again located near the end of the channel 60 farthest from the disc 70, and at a distance (h) above the end of the lever 55 that resides in the channel.

(52) The disc 70 has a flange 70a around its circumference that provides a contact point for a first end of the lever 55, while the second end of the lever is located in the channel. Rotation of the disc 70 causes the first end of the lever 55 to move along the circumferential flange 70a of the disc, from point A to point A. During this time, the second end of the lever 55 moves up and down within the channel 60 between point B to point B. This movement of the lever 55 within the channel 60 triggers the proximity sensor 75 located at D

(53) For the configuration shown in FIG. 12a, the disc 70 rides on or is mounted on the damper piston 80 of the RSPSD or an element that moves therewith. Consequently, movement of the damper piston 80 or associated element will cause the above-described rotation of the disc 70 and resulting movement of the lever 55.

(54) A primary benefit of the configuration shown in FIG. 12a versus that shown in FIG. 2 is that the entire assembly may be mounted on the damper piston by attaching it directly to the damper cylinder, without the need for the rack 15 and the vertical column 30 of FIG. 2. The main difference between the lever configuration of FIG. 12a and the lever configuration shown in FIG. 2 is that in the configuration of FIG. 12a there is less vertical displacement of the lever in the channel for the same horizontal displacement of the piston damper. Equation (2) below relates the vertical displacement of the lever in the channel to the horizontal displacement of the damper piston for the configuration shown in FIG. 12a.

(55) $\begin{array}{cc}y\left(t\right)=\left[\sqrt{L^2-{\left[x_o-x\left(t\right)\right]}^2}-\left(L-d\right)\right]-\left[\sqrt{R_L^2-{\left[x_o-x\left(t\right)\right]}^2}-\sqrt{R_L^2-x_o^2}\right]x\left(t\right)=x_o-R_L\sin \left({}_o-\left(t\right)\right)\left(t\right)=\frac{x_p\left(t\right)}{R_L}y\left(t\right)=\left[\sqrt{L^2-{\left[R_L\sin \left({}_o-\frac{x_p\left(t\right)}{R_L}\right)\right]}^2}-\left(L-d\right)\right]-[\sqrt{R_L^2-{\left[R_L\sin \left({}_o-\frac{x_p\left(t\right)}{R_L}\right)\right]}^2}-\sqrt{R_L^2-x_o^2}]& \left(2\right)\end{array}$
where L is the length of the lever, R.sub.L is the radius of the disc, .sub.0 is the angle formed between the lever and a radial line extending from the first end of the lever, x.sub.p(t) is the distance of movement of the piston, d is the total vertical travel distance of the lever within the slotted channel, and x.sub.0 is the distance between the slotted channel and the contact point of the lever with the circumferential flange of the disc.

(56) FIG. 12b depicts a variation of the triggering lever assembly 50 of FIG. 12a. The triggering lever assembly 85 of FIG. 12b employs all of the various elements of the triggering lever assembly 50 of FIG. 12a, including the lever 55 with its second end arranged in a slotted channel 60, the lever 55 being biased downward by the spring 65 located in the channel, and the proximity sensor 75 located near the end of the channel 60 farthest from the disc 70. The lever 55 and channel 60 are again mounted to the disc 70 in a manner that permits the disc to rotate while the channel and lever remain in the vertical position shown.

(57) In the triggering lever assembly 85 of FIG. 12b, however, the disc 70 to which the lever and channel are mounted is the larger of two discs present in the assembly. More particularly, in this embodiment, the larger disc 70 is fixed to one end of a rigid shaft 95, while a smaller disc 90 is fixed to the other end of the rigid shaft 95, such that the larger disc 70, the smaller disc 90, and the shaft 95 rotate with the same angular displacement, and the smaller disc 90 rides on or is mounted on the damper piston 80 of the RSPSD or an element that moves therewith. Furthermore, the disc-shaft assembly is mounted in a manner that permits the larger disc 70, the smaller disc 90, and the shaft 95 to rotate while the channel and lever remain substantially in the vertical position shown. Consequently, linear movement of the damper piston 80 or associated element will rotate the smaller disc 90 which will, in turn, cause a rotation of the larger disc 70 and a resulting movement of the lever 55 as described above with respect to the configuration of FIG. 12a.

(58) In the configuration of FIG. 12b, the horizontal displacement/velocity of the damper piston 80 associated with the smaller disc 90 is related to the circumferential displacement/velocity of point A on the larger disc 70 through the ratio of the radii of the two discs. By making the radius of the larger disc 70 greater than the radius of the smaller disc 90, the circumferential displacement/velocity of point A on the larger disc 70 is magnified relative to the horizontal displacement/velocity of the damper piston 80 according to the ratio of the radii of the larger disc 70 to the smaller disc 90.

(59) A benefit of this configuration is more flexibility in the RSPSD design. For example, the radial ratio of the larger disc 70 to the smaller disc 90 may be adjusted so that point A on the larger disc 70 moves through a circumferential velocity that is twice that of the horizontal velocity of the damper piston 80. As a result, the lever 55 will move from point A to point A faster, the lever will spend less time in the sensing range of the sensor 75, and the resetting time will be reduced relative to the configuration shown in FIG. 12a for the same horizontal displacement of the damper piston 80.

(60) The configuration in FIG. 12b may also be used to achieve the same resetting time as the configuration of FIG. 12a, but for a longer lever. Equation (3) below relates the vertical displacement of the lever in the channel to the horizontal displacement of the damper piston for the configuration shown in FIG. 12b.

(61) $\begin{array}{cc}y\left(t\right)=\left[\sqrt{L^2-{\left[x_o-x\left(t\right)\right]}^2}-\left(L-d\right)\right]-\left[\sqrt{R_L^2-{\left[x_o-x\left(t\right)\right]}^2}-\sqrt{R_L^2-x_o^2}\right]x\left(t\right)=x_o-R_L\sin \left({}_o-\left(t\right)\right)\left(t\right)=\frac{x_p\left(t\right)}{R_P}y\left(t\right)=\left[\sqrt{L^2-{\left[R_L\sin \left({}_o-\frac{x_p\left(t\right)}{R_p}\right)\right]}^2}-\left(L-d\right)\right]-[\sqrt{R_L^2-{\left[R_L\sin \left({}_o-\frac{x_p\left(t\right)}{R_p}\right)\right]}^2}-\sqrt{R_L^2-x_o^2}]& \left(3\right)\end{array}$
where L is the length of the lever, R.sub.L is the radius of the larger disc, .sub.0 is the angle formed between the lever and a radial line of the first disc that extends to the first end of the lever, x.sub.p(t) is the distance of movement of the piston, R.sub.p is the radius of the smaller disc, d is the total vertical travel distance of the lever within the slotted channel, and x.sub.0 is the distance between the slotted channel and the contact point of the lever with the circumferential flange of the first disc.

(62) Further alternate embodiments of amplified and non-amplified triggering lever assemblies 100, 140 that may be used with a RSPSD of the invention are schematically illustrated in FIGS. 13a-13b, respectively. Such lever assemblies 100, 140 may be used with the exemplary RSPSD 5 of FIG. 2, or with other alternate embodiments not specifically shown or described herein.

(63) The lever assembly 100 of FIG. 13a is shown to again include a lever 105 with a length (L) and a second end arranged in a slotted channel 110. The lever 105 is again biased downward by a spring 115 located in the channel 110. In this embodiment, the lever 105 and channel 110 are associated with a column 120 or similar element that is in turn mounted to a disc 125 by an axle or in some other manner that permits the disc to rotate while the channel and lever remain in the vertical position shown. A proximity sensor 130 having a range (r) is again located near the end of the channel 110 farthest from the disc 125, and at a distance (h) above the end of the lever 105 that resides in the channel.

(64) In this embodiment, the channel 110 is located on such that the contact point between the lever and the disc 125 occurs along the periphery (circumference) of the disc or a flange 125a attached thereto, while the second end of the lever remains in the channel 110. Rotation of the disc 125 causes the first end of the lever 105 to move along the circumferential flange 125a of the disc 125, from point A to point A. During this time, the second end of the lever 105 moves up and down within the channel 110 between point B to point B. This movement of the lever 105 within the channel 110 triggers the proximity sensor 130 located at D.

(65) For the configuration shown in FIG. 13a, the disc 125 rides on or is mounted on the damper piston 135 or an element that moves therewith. Consequently, movement of the damper piston 135 or associated element will cause the above-described rotation of the disc 125 and resulting movement of the lever 105.

(66) A primary benefit of the configuration shown in FIG. 13a versus the configuration shown in FIG. 2 is that the entire assembly may be mounted on the damper piston by attaching it directly to the damper cylinder, without the need for the rack 15 and the vertical column 30 of FIG. 2. The main difference between the lever configuration of FIG. 13a and the lever configuration shown in FIG. 2 is that in the configuration of FIG. 13a there is more vertical displacement of the lever in the channel for the same horizontal displacement of the piston damper. Equation (4) relates the vertical displacement of the lever in the channel to the horizontal displacement of the damper piston.

(67) $\begin{array}{cc}y\left(t\right)=\left[\sqrt{L^2-{\left[x_o-x\left(t\right)\right]}^2}-\left(L-d\right)\right]+\left[\sqrt{R_L^2-{\left[x_o-x\left(t\right)\right]}^2}-\sqrt{R_L^2-x_o^2}\right]x\left(t\right)=x_o-R_L\sin \left({}_o-\left(t\right)\right)\left(t\right)=\frac{x_p\left(t\right)}{R_L}y\left(t\right)=\left[\sqrt{L^2-{\left[R_L\sin \left({}_o-\frac{x_p\left(t\right)}{R_L}\right)\right]}^2}-\left(L-d\right)\right]+[\sqrt{R_L^2-{\left[R_L\sin \left({}_o-\frac{x_p\left(t\right)}{R_L}\right)\right]}^2}-\sqrt{R_L^2-x_o^2}]& \left(4\right)\end{array}$
where L is the length of the lever, R.sub.L is the radius of the disc, .sub.0 is the angle formed between vertical and a radial line extending to the first end of the lever, x.sub.p(t) is the distance of movement of the piston, d is the total vertical travel distance of the lever within the slotted channel, and x.sub.0 is the distance between the slotted channel and the contact point of the lever with the peripheral surface of the disc.

(68) FIG. 13b depicts a variation of the triggering lever assembly 100 of FIG. 13a. The triggering lever assembly 140 of FIG. 12b employs all of the various elements of the triggering lever assembly 100 of FIG. 13a, including the lever 105 with its second end arranged in a slotted channel 110, the lever 105 being biased downward by the spring 115 located in the channel 110, and the proximity sensor 130 located near the end of the channel 110 farthest from the disc 125. The lever 105 and channel 110 are again mounted to the disc by a column 120 or similar element that is in turn mounted to the disc 125 by an axle or in some other manner that permits the disc to rotate while the channel and lever remain in the vertical position shown.

(69) In the triggering lever assembly 140 of FIG. 13b, however, the disc 125 to which the lever and channel are mounted is the larger of two discs present in the assembly. More particularly, in this embodiment, the larger disc 125 is fixed to one end of a rigid shaft 150, while a smaller disc 145 is fixed to the other end of the rigid shaft 150, such that the larger disc 125, the smaller disc 145, and the rigid shaft 150 rotate with the same angular displacement, and the smaller disc 145 rides on or is mounted on the damper piston 135 of the RSPSD or an element that moves therewith. Furthermore, the disc-shaft assembly is mounted in a manner that permits the larger disc 125, the smaller disc 145, and the shaft 150 to rotate while the channel and lever remain in the vertical position shown. Consequently, linear movement of the damper piston 135 or associated element will rotate the smaller disc 145 which will, in turn, cause a rotation of the larger disc 125 and a resulting movement of the lever 105 as described above with respect to the configuration of FIG. 13a.

(70) In the configuration of FIG. 13b, the horizontal displacement/velocity of the damper piston 135 associated with the smaller disc 145 is related to the circumferential displacement/velocity of point A on the larger disc 125 through the ratio of the radii of the two discs. By making the radius of the larger disc 125 greater than the radius of the smaller disc 145, the circumferential displacement/velocity of point A on the larger disc 125 is magnified relative to the horizontal displacement/velocity of the damper piston 135 according to the ratio of the radii of the larger disc 125 to the smaller disc 145.

(71) A benefit of this configuration is more flexibility in the RSPSD design. For example, the radial ratio of the larger disc 125 to the smaller disc 145 may be adjusted so that point A on the larger disc 145 moves through a circumferential velocity that is twice that of the horizontal velocity of the damper piston 135. As a result, the lever 105 will move from point A to point A faster, the lever will spend less time in the sensing range of the sensor 130, and the resetting time will be reduced relative to the configuration shown in FIG. 13a for the same horizontal displacement of the damper piston 80.

(72) The configuration in FIG. 13b may also be used to achieve the same resetting time as the configuration of FIG. 13a, but for a longer lever. Equation (5) below relates the vertical displacement of the lever in the channel to the horizontal displacement of the damper piston for the configuration shown in FIG. 13b.

(73) $\begin{array}{cc}y\left(t\right)=\left[\sqrt{L^2-{\left[x_o-x\left(t\right)\right]}^2}-\left(L-d\right)\right]+\left[\sqrt{R_L^2-{\left[x_o-x\left(t\right)\right]}^2}-\sqrt{R_L^2-x_o^2}\right]x\left(t\right)=x_o-R_L\sin \left({}_o-\left(t\right)\right)\left(t\right)=\frac{x_p\left(t\right)}{R_P}y\left(t\right)=\left[\sqrt{L^2-{\left[R_L\sin \left({}_o-\frac{x_p\left(t\right)}{R_P}\right)\right]}^2}-\left(L-d\right)\right]+[\sqrt{R_L^2-{\left[R_L\sin \left({}_o-\frac{x_p\left(t\right)}{R_P}\right)\right]}^2}-\sqrt{R_L^2-x_o^2}]& \left(5\right)\end{array}$
where L is the length of the lever, R.sub.L is the radius of the larger disc, .sub.0 is the angle formed between vertical and a radial line of the first disc that extends to the first end of the lever, x.sub.p(t) is the distance of movement of the piston, R.sub.p is the radius of the smaller disc, d is the total vertical travel distance of the lever within the slotted channel, and x.sub.0 is the distance between the slotted channel and the contact point of the lever with the peripheral surface of the first disc.

(74) A comparison of the vertical displacement of the lever in the channel versus the horizontal displacement of the damper piston for the configurations shown in FIG. 2, FIG. 12a, and FIG. 13a is graphically illustrated in FIG. 14. With respect to differentiating the three curves, y represents the vertical displacement of the lever in FIG. 2, y.sub.in represents the vertical displacement of the lever in FIG. 12a, and y.sub.out represents the vertical displacement of the lever in FIG. 13a.

(75) FIG. 14 demonstrates that the effect of mounting the lever-channel on a disc is to increase or decrease the vertical displacement of the lever in the channel relative to a configuration with no disc. For a proximity sensor with sensing distance (s), this either increases or decreases the time that the lever is in the sensing range of the sensor, resulting in an increase or decrease in the resetting time (relative to a configuration with no disc).

(76) An objective of the different RSPSD configurations is to provide for more control over the relationship between the vertical displacement of the lever in the channel and the horizontal displacement of the damper piston, leading to more flexibility in the RSPSD design. With this objective in mind, each of the configurations in FIG. 2, FIG. 12a, and FIG. 13a can be further modified by incorporating a scissor-jack mechanism 200 such as that shown in FIG. 15.

(77) This exemplary scissor-jack mechanism 200 consists of four members of equal length l pinned together at their ends (joints) and initially oriented at an angle .sub.o with respect to the scissor-jack centerline. One end of the scissor-jack is attached to a stationary point D, while the other is attached to the end of the lever B located in the vertical channel. Vertical displacement of the end of the lever in the channel from point B to point B causes horizontal displacement of joint C on the scissor-jack from point C to point C, thereby triggering the proximity sensor located at E.

(78) By incorporating a properly designed scissor-jack, the horizontal displacement of joint C can either be increased or decreased relative to the vertical displacement of the lever in the channel, thereby providing more flexibility in the design of the RSPSD. For the case where the horizontal displacement of joint C is increased relative to the vertical displacement of the lever, the result will be a decrease in the amount of time that the proximity sensor is engaged relative to the case with no scissor-jack, for the same sensing distance s. As a result, the scissor-jack can be used to reduce the resetting time of the RSPSD. For the case when the horizontal displacement of joint C is decreased relative to the vertical displacement of the lever, the opposite is true. Equation (6) below relates the horizontal displacement of joint C on the scissor-jack to the vertical displacement of the lever in the channel.

(79) $\begin{array}{cc}u\left(t\right)=2l\left[\sin \left({\cos }^{-1}\left(\frac{2l\cos {}_o-y\left(t\right)}{2l}\right)\right)-\sin {}_o\right]& \left(6\right)\end{array}$

(80) FIG. 16 is a plot of the horizontal displacement of joint C versus the total vertical lever displacement from point B to point D, as shown in FIG. 15. FIG. 16 demonstrates that for values of the angle .sub.o equal to 10 and 30 degrees, the horizontal displacement of joint C is initially increased relative to the vertical displacement of the lever. However, as the vertical displacement of the lever increases, the amount of relative increase in the horizontal displacement of the lever decreases. Meanwhile, for values of the angle .sub.o equal to 60 degrees, the horizontal displacement of joint C is always less than the vertical displacement of the lever.

(81) Yet another exemplary embodiment of the invention is shown in FIG. 17. In this exemplary embodiment of a RSPSD 250, a single mechanism acts as the lever and amplifying component of the system. In this configuration, the lever 255 is extended so that while one end is in contact with a rack 270 at point A, the other end is pivotally connected to a rod CD at point C such that the lever ABC is free to rotate about rod CD at point C. The extended lever is rotatably connected to a lower channel 260 at point B such that the lever is allowed to move vertically within the lower channel and to rotate about point B thereof that resides in the lower channel. The rod CD is connected to an upper channel 265 at point D such that the rod is allowed to move vertically within the upper channel and to rotate about the end D thereof that resides in the upper channel.

(82) Horizontal displacement of the rack 270 drives the end of the lever in contact with the rack from point A to point A. During this time, lever ABC moves up the lower channel from point B to point B, while simultaneously rotating about point B which resides in the channel. The vertical displacement and rotation of lever ABC is accompanied by vertical displacement and rotation of rod CD, thereby causing the end of rod CD at point D in the upper channel to move from point D to point D, and triggering the proximity sensor located at point E.

(83) In this configuration, the horizontal displacement/velocity of the end of the lever in contact with the rack at A from point A to point A is related to the horizontal displacement/velocity of point C from point C to point C by the ratio of the lever ABC arm lengths r (r=BC/AB). By making the length of arm BC longer than that of arm AB, the horizontal displacement/velocity of point C is magnified relative to the horizontal displacement/velocity of point A according to r. The advantage of this configuration is more flexibility in the RSPSD design. For example, the ratio of the lever arm lengths r may be adjusted so that the horizontal velocity of point C is twice that of the horizontal velocity of point A. If the horizontal displacement of point C is made equal to the rack displacement shown in FIG. 2, the rod will move from point C to point C faster, the lever will spend less time within the sensing range of the sensor, and the resetting time will be reduced (relative to the configuration in shown in FIG. 2).

(84) The configuration of FIG. 17 may also be used to achieve the same resetting time as the configuration of FIG. 2, but for a longer lever. In this regard, equation (7) relates the vertical displacement of rod CD in the upper channel 265 to the horizontal displacement of the rack 270.
y(t)=(1+r)[{square root over (L.sub.1.sup.2[x.sub.ox.sub.p(t)].sup.2)}{square root over (L.sub.1.sup.2x.sub.o.sup.2)}]+[{square root over (L.sub.2.sup.2r.sup.2[x.sub.ox.sub.p(t)].sup.2)}{square root over (L.sub.2.sup.2r.sup.2x.sub.o.sup.2)}](7)

(85) FIG. 18 graphically illustrates the vertical displacement of the rod CD in the upper channel 265 versus the horizontal displacement of the rack 270 for different values of the ratio r, and demonstrates the amplifying effect of the lever ABC in the configuration shown in FIG. 17. It should be noted that the alternate configuration shown in FIG. 17 could also be mounted in the disc configurations shown in FIGS. 12a-12b and 13a-13b.

(86) Another alternate embodiment of a triggering lever assembly 300 that may be used with a RSPSD of the invention is schematically illustrated in FIG. 19. Such a lever assembly 300 may be used with the exemplary RSPSD 5 of FIG. 2, or with other alternate embodiments not specifically shown or described herein. Furthermore, it should be understood that the triggering lever assemblies of FIGS. 3a-3b, 12a-12b, 13a-13b and 17 may be modified to move the proximity sensor to a position like that shown in FIG. 19.

(87) The triggering lever assembly 300 of FIG. 19 is shown to once again include a lever 310 with a length (L) and a first end arranged in a slotted channel 315 at a distance (y0) above a rack 305. The lever 310 is again biased downward by a spring 320 located in the channel 315.

(88) As with previous embodiments, the lever 310 is allowed to move vertically within the channel 315 and to rotate about the end thereof that resides in the channel. The opposite end of the lever 310 rests on grooves in the rack 305, at a transverse distance (x.sub.0) from the slotted channel 315 and at an orientation of () with respect to the rack. As the angle between the lever 310 and the rack 305 is time dependent, the angle is represented in FIG. 19 as (t).

(89) In a manner similar to that of the embodiment shown in FIGS. 3a-3b, when the rack 305 of the assembly 300 of FIG. 19 is moving to the left, the vertical position of the lever 310 remains unaffected. However, when the direction of movement of the rack 305 reverses and moves to the right (as indicated in FIG. 19), the rack-contacting end of the lever 310 becomes engaged with the grooves of the rack 305 and, upon engagement, further movement of the rack in this direction forces the lever to rotate while simultaneously driving the lever into the slotted channel 315 by some associated distance (y(t)). Horizontal movement of the rack 305 also causes a like movement of the rack-contacting end of the lever 310, the distance of movement at any given time being indicated by (x.sub.r(t)).

(90) Like the previously described triggering lever assemblies, this triggering lever assembly 300 also employs a proximity sensor 325 that communicates with a bypass valve 45 on the cylinder 10. However, unlike the previously described exemplary triggering lever assemblies, this variation of the triggering lever assembly 300 employs a proximity sensor 325 that is located outside of the channel 315. More particularly, the proximity sensor 325 is located at a distance (h) below the end of the channel 315 that is closest to the rack 305, and is oriented such that the sensing direction is substantially perpendicular to the plane in which the rack-lever mechanism motion occurs (i.e., the sensing direction extends perpendicularly from the page in FIG. 19).

(91) In the configuration of FIG. 19, a sensing material (not specifically shown) that triggers the proximity sensor 325 may be mounted to the body of the lever 310 rather than the end that resides in the channel 315. Alternatively, the lever 310 itself may trigger the sensor 325. The sensing material (when present) is also located at a height such that it passes over the proximity sensor when the tip of the lever 310 is engaged by the rack 305 and moves through a distance 2(x.sub.o). The sensor 325 is triggered anytime the lever is within the sensing range (s) of the sensor. A benefit of this configuration is that the lever length (L) and the initial lever position (x.sub.o) can be designed so that very small displacements of the rack 305 will trigger the proximity sensor 325 and reset the damper, thereby allowing for energy to be released and then quickly stored again each time the rack changes direction.

(92) While certain exemplary embodiments of the present invention are described in detail above, the scope of the invention is not to be considered limited by such disclosure. Rather, modifications are possible without departing from the spirit of the invention. For example, the grooved or toothed rack elements shown and described herein may be replaced with another type of actuator that simply includes a lever contacting surface of sufficiently high friction to displace the lever as described. Another, non-limiting modification, may include the use of a programmable valve that would remain open for a set amount of time once opened, regardless of vibration characteristics. RSPSD embodiments according to the invention may also have uses outside the field of structural control. For example, such other uses may include, without limitation, vehicle suspensions and aircraft landing gear.