Multi-dimensional vibration control method for the model of strut tail-supported aircraft

Abstract

A multi-dimensional vibration control method based on piezoelectric ceramic actuator applied to wind tunnel test of aircraft model. The pitch and yaw acceleration sensors arranged on the center of mass of the aircraft model are used to measure the two components of the main vibration acceleration of the aircraft model, and the main vibration vector of the aircraft model is obtained and the real-time vibration plane of the strut is determined. Inertia is introduced to solve the dynamic bending moment on the active section of the multi-dimensional vibration damper, and then the stress distribution on the active section is obtained. The multi-dimensional active vibration control system is adopted to improve the stability and reliability of the active vibration control system of wind tunnel model, extend the service life of piezoelectric ceramic actuator, and ensure the quality of wind tunnel test data and the safety of wind tunnel test.

Claims

1. A multi-dimensional vibration control method for a strut tail-supported aircraft model, wherein the method is through the arrangement in the aircraft model on the center of mass of pitch and yaw acceleration sensor measuring aircraft model, the main vibration acceleration of two component, calculate a main vibration vector and determine a strut real-time aircraft model plane, introduction of inertial force to solve a multidimensional active vibration damper on an active section by dynamic bending moment, and then obtain an initiative stress distribution on the active section, through the real-time vibration plane space position relation of multidimensional vibration damper to participate in the work of piezoelectric ceramic actuator serial number; a vibration control force is calculated in real time according to the stress on the active section of a piezoelectric ceramic actuator, and then the dynamic bending moment is generated in the process of a reverse bending moment resisting the vibration of the aircraft model; the multi-dimensional vibration active control system based on the piezoelectric ceramic actuator is adopted to control the multi-dimensional vibration; the specific steps are as follows: step 1: establish an absolute coordinate system of the aircraft model support system the absolute coordinate system OXYZ (E) is established on an aircraft tail strut (4), and the coordinate origin is established in the equilibrium position at the intersection of the active section (F) and the axis of the aircraft tail strut (4), which is defined as O; the direction of the X axis coincides with the balance position of the axis of the aircraft tail strut (4) and points to the aircraft model (5),the direction of the Y axis is that the intersection of the active section (F) and the pitching plane points upward; the Z axis is determined by the right manipulation; a vibration measurement coordinate system O.sub.AX.sub.AY.sub.AZ.sub.A(A) is established on the aircraft model (5), whose origin is established at the intersection of the centroid of the aircraft model (5) and the X axis of the absolute coordinate system OXYZ (E), which is defined as that the direction of the O.sub.A; X.sub.A coordinate axis coincides with the X axis of the absolute coordinate system OXYZ (E), the Y.sub.A coordinate axis and the Y axis of the absolute coordinate system OXYZ (E) point upward, and the Z.sub.A coordinate axis is determined by right manipulation; step 2: obtain the components of the main vibration acceleration in the pitch plane and yaw plane in real time using a pitching accelerometer (6) and a yaw accelerometer (7) at the centroid of the aircraft model (5) to measure the acceleration of the main vibration in the pitch plane and yaw plane perpendicular to each other, the acceleration of the main vibration is fed back to a real-time controller (8) controlled by an upper computer (9), and a plurality of acceleration sampling values of the pitch plane and the yaw plane are collected in each vibration control cycle, the acceleration components of the main vibration acceleration in the pitch direction and yaw direction in a vibration control cycle are calculated by formulas (1) and (2) respectively: $\begin{array}{cc}{a}_{\mathrm{pith}}\left(t\right)=\frac{\underset{i=1}{\overset{N}{.Math.}}{a}_{\mathrm{pithi}}}{N}& \left(1\right)\\ a_{yaw}\left(t\right)=\frac{\underset{i=1}{\overset{N}{.Math.}}{a}_{\mathrm{yawi}}}{N}& \left(2\right)\end{array}$ among them, the acceleration component of the a.sub.pith(t) main vibration acceleration in the pitch direction, the acceleration component of the a.sub.yaw(t) main vibration acceleration in the yaw direction, a.sub.pithi(t) , a.sub.yawi(t) is the acceleration sampling value of the aircraft model (5) in the pitching plane and the yaw plane at the i sampling time, and N is the number of acceleration sampling values in each vibration control cycle, wherein i=1,2. . . N; step 3: solve the main vibration acceleration vector in real time the main vibration acceleration is obtained by combining the acceleration components in the pitching direction and yaw direction; the main vibration acceleration consists of magnitude and direction; the main vibration acceleration vector is constructed by solving the magnitude and direction of the main vibration acceleration vector in each vibration control cycle in real time by using formulas (3) and (4): $\begin{array}{cc}.Math.a\left(t\right).Math.=\sqrt{a_{\mathrm{pith}}^2+a_{\mathrm{yaw}}^2}& \left(3\right)\\ \angle a\left(t\right)=\mathrm{arc}\tan \left(\frac{a_{\mathrm{pith}}\left(t\right)}{a_{\mathrm{yaw}}\left(t\right)}\right),\angle a\left(t\right)\in \left(-\pi ,\pi \right)& \left(4\right)\end{array}$ among them, a(t) is the main vibration acceleration vector, |a(t) | is the magnitude of the a(t) vibration acceleration vector, and ∠a(t) is the main vibration acceleration vector in a(t) directions; step 4: establish a real-time vibration active control coordinate system of the aircraft model and determine the real-time vibration plane of the strut the real-time active vibration control coordinate system O.sub.αX.sub.αY.sub.αZ.sub.α(D) is established on the active section (F), and its origin coincides with the origin O of the absolute coordinate system OXYZ (E); it is defined that the direction of the O.sub.α; X.sub.αaxis coincides with the direction of the X coordinate of the absolute coordinate OXYZ (E), the Y.sub.αaxis coincides with the a(t) direction of the main vibration acceleration vector, and the Z.sub.60 coordinate axis is determined by the right manipulation; plane X.sub.αO.sub.αY.sub.αis the real-time vibration plane X.sub.αO.sub.αY.sub.α(C) of the strut; because of the randomness of the vibration of the aircraft model (5), the real-time active vibration control coordinate system O.sub.αX.sub.αY.sub.αZ.sub.α(D) changes with time, and the real-time vibration plane X.sub.αO.sub.αY.sub.α(C) changes with time; step 5: the real-time inertial force and the stress distribution on the active section of the support system are solved on the real time vibration plane X.sub.αO.sub.αY.sub.α(C) of the aircraft tail strut (4), the inertia force is solved in real time by formula (5)
F.sub.I(t)=−m.sub.eqa(t)  (5) formula (6) was used to calculate the dynamic bending moment on the active section (F) in real time
M(t)=F.sub.I(t).Math.L  (6) a dynamic stress distribution on the active section (F) was solved in real time by formula (7) $\begin{array}{cc}\sigma \left(y_a,z_a,t\right)=\frac{M\left(t\right).Math.y_{\alpha }}{I_{z_{\alpha }}\left(t\right)}& \left(7\right)\end{array}$ among them, m.sub.eq is the equivalent mass of the support system, F.sub.I(t) is the real-time inertia force acting on the aircraft model (5), M(t) is the dynamic bending moment on the active section (F) of the aircraft model (5) during vibration, L is the distance from the centroid of the aircraft model (5) to the active section (F), σ(y.sub.a, z.sub.a, t) is the dynamic stress at the length of the active section (F) inner distance X.sub.αcoordinate axis y.sub.a, and I.sub.z .sub.α(t) is the real time inertia moment of the active section (F) to the Z.sub.αcoordinate axis; step 6: determine the serial number of the piezoelectric ceramic actuator in real time and calculate the vibration control force a number of the piezoelectric ceramic actuators (3-1) are uniformly arranged in the circumferential direction of the multi-dimensional vibration damper (3) at the active section (F), the uniformly distributed circumferential radius is R, and the piezoelectric ceramic which coincides with the Z axis of the absolute coordinate system OXYZ (E) is set as No. 0 piezoelectric ceramic actuator (3-1), the No. 1 piezoelectric ceramic actuator (3-1), the No. 2 piezoelectric ceramic actuator (3-1), . . . , the No. n piezoelectric ceramic actuator (3-1), are arranged in a counterclockwise circular array in turn; the array angle between two adjacent piezoelectric ceramic actuators (3-1) is $\Delta \alpha =\frac{2\pi }{n+1};$ in the real-time active vibration control coordinate system O.sub.αX.sub.αY.sub.αZ.sub.α(D), the piezoelectric ceramic actuator (3-1) above the Z.sub.αaxis participates in the vibration control, and the serial number of the piezoelectric ceramic actuator (3-1) participating in the work is: $\begin{array}{cc}{n}_c\in \left[\mathrm{INT}\left(\frac{\alpha \left(t\right)-\frac{\pi }{2}}{\Delta \alpha }+1\right),\mathrm{INT}\left(\frac{\alpha \left(t\right)+\frac{\pi }{2}}{\Delta \alpha }\right)\right]& \left(8\right)\end{array}$ among them, $\mathrm{INT}\left(\frac{\alpha \left(t\right)-\frac{\pi }{2}}{\Delta \alpha }+1\right)\mathrm{and}\mathrm{INT}\left(\frac{\alpha \left(t\right)+\frac{\pi }{2}}{\Delta \alpha }\right)$ represent the rounding of the calculated values of $\frac{\alpha \left(t\right)-\frac{\pi }{2}}{\Delta \alpha }+1\mathrm{and}\frac{\alpha \left(t\right)+\frac{\pi }{2}}{\Delta \alpha }$ respectively, α(t) is an angle between the main vibration acceleration vector a(t) and the Z axis of the absolute coordinate system OXYZ (E), and then the real-time coordinates of the center of the piezoelectric ceramic actuator (3-1) in the real-time active vibration control coordinate system O.sub.αX.sub.αY.sub.αZ.sub.α(D) are determined as follows: $\begin{array}{cc}\left(z_{\alpha n_c}\left(t\right),y_{\alpha n_c}\left(t\right)\right)=\left(R.Math.\cos \left[{\alpha }_{n_c}-\left(\alpha \left(t\right)-\frac{\pi }{2}\right)\right],R.Math.\sin \left[{\alpha }_{n_c}-\left(\alpha \left(t\right)-\frac{\pi }{2}\right)\right]\right)& \left(9\right)\end{array}$ where, α.sub.n .sub.c, is the angle between participating piezoelectric ceramic actuator (3-1) and the Z axis direction of the absolute coordinate system OXYZ (E), and the resultant force on the active section (F) of the participating piezoelectric ceramic actuator (3-1) is: $\begin{array}{cc}{F}_{n_c}\left(t\right)={\int }_{A_{n_c}}\sigma \left(y_a,z_a,t\right){\mathrm{dA}}_{n_c}& \left(10\right)\end{array}$ where, $A_{n_c}$ is the contact area between no. n.sub.c participating piezoelectric ceramic actuator (3-1) and the active section (F), and resistance required by the no. n.sub.c participating piezoelectric ceramic actuator (3-1) is: $\begin{array}{cc}{F}_{R{n}_c}\left(t\right)=-F_{n_c}\left(t\right)& \left(11\right)\end{array}$ finally, all the participating piezoelectric ceramic actuators (3-1) generate the reverse bending moment M.sub.R (t) to resist the dynamic bending moment M(t) generated during the vibration of the aircraft model (5).

2. The multi-dimensional vibration control method of a strut tail-supported aircraft model according to claim 1, wherein the multi-dimensional vibration control method for the model of the strut tail braced aircraft adopts a multi-dimensional vibration active control system, which is mainly composed of the pitch acceleration sensor (6), the yaw acceleration sensor (7), the real-time controller (8), the upper computer (9), a piezoelectric ceramic actuator power amplifier group (10) and the multi-dimensional vibration damper (3); the pitch acceleration sensor (6) is installed on the centroid of the aircraft model (5) in the pitching plane and is used to measure the vibration acceleration component of the main vibration of the aircraft model (5) in the pitching plane; the yaw acceleration sensor (7) is installed on the centroid of the aircraft model (5) in the yaw plane and is used to measure the vibration acceleration component of the main vibration of the aircraft model (5) in the yaw plane; the multi-dimensional vibration damper (3) includes a plurality of uniformly distributed piezoelectric ceramic actuators (3-1), each of which is pretightened by a pretightening mechanism (3-2), respectively, to ensure a reliable output of the dynamic force of the piezoelectric ceramic actuator (3-1); the multi-dimensional vibration damper (3) is installed in the real-time vibration plane X.sub.αO.sub.αY.sub.α(C) of the aircraft tail strut (4), the real-time controller (8) is connected with the upper computer (9), and the upper computer (9) is used to control the real-time controller (8) and monitor the vibration control process; the real-time controller (8) is connected with the pitch acceleration sensor (6) and the yaw acceleration sensor (7) respectively to obtain the vibration acceleration components in the pitching plane and the yaw plane of the aircraft model (5) in real time; the real-time controller (8) is connected to a piezoelectric ceramic actuator power amplifier group (10), and a plurality of piezoelectric ceramic actuator power amplifiers (10-1) in the piezoelectric ceramic actuator power amplifier group (10) are respectively connected to a plurality of piezoelectric ceramic actuators (3-1) in the multi-dimensional vibration damper (3).

Description

DESCRIPTION OF DRAWINGS

(1) FIG. 1 is the flow chart of the multi-dimensional vibration control method for the model of the supporting strut tail-supported aircraft.

(2) FIG. 2 is the diagram of multi-dimensional vibration active control system based on piezoelectric ceramic actuator. Among them, 1—wind tunnel test section, 2—angle of attack adjustment mechanism, 3—multi-dimensional vibration damper, 3-1 piezoelectric ceramic actuator, 3-2 pretightening mechanism, 4—aircraft tail strut, 5—aircraft model, 6—pitch acceleration sensor, 7—yaw acceleration sensor, 8—real-time controller, 9—upper computer, 10—piezoelectric ceramic actuator power amplifier group, 10-1 piezoelectric ceramic actuator power amplifier.

(3) FIG. 3 is the schematic diagram of random vibration of the aircraft model and the arrangement of coordinates O.sub.AX.sub.AY.sub.AZ.sub.A. Among them, A-aircraft model vibration measurement coordinate system, B-strut real-time vibration deflection, C-strut real-time vibration plane X.sub.αO.sub.αY.sub.α, D-real-time vibration active control coordinate system O.sub.αX.sub.αY.sub.αZ.sub.α, E-absolute coordinate system OXYZ, F-active cross section.

(4) FIG. 4 is the composition of shock absorber.

(5) FIG. 5 is the working principle diagram of shock absorber.

(6) FIG. 6 shows the comparison of pitch acceleration before and after using multi-dimensional vibration control method of strut tail-supported aircraft model when hammering in pitch direction. Abscissa is time, unit s, ordinate is acceleration, unit is g.

(7) FIG. 7 shows the comparison of yaw acceleration before and after using multi-dimensional vibration control method of strut tail-supported aircraft model when hammering in the yaw direction. Abscissa is time, unit s, ordinate is acceleration, unit is g.

(8) FIG. 8 is the comparison diagram of pitch acceleration before and after using multi-dimensional vibration control method for hammer strike in an arbitrary direction.

(9) FIG. 9 is the comparison diagram of yaw acceleration using multi-dimensional vibration control method for hammer strike in an arbitrary direction. Where, the x-coordinate is time, unit s, the y-coordinate is acceleration, unit is g.

DETAILED DESCRIPTION

(10) The specific implementation method of the invention is described in detail below in combination with the technical scheme and the attached drawings.

(11) As shown in FIG. 2 and FIG. 4, the multi-dimensional active vibration control system is mainly composed of the pitch acceleration sensor 6, yaw acceleration sensor 7, real-time controller 8, upper computer 9, piezoelectric ceramic actuator power amplifier group 10 and multi-dimensional vibration damper 3. The pitch acceleration sensor 6 is installed on the centroid of the aircraft model 5 in the pitching plane and is used to measure the vibration acceleration component of the main vibration of the aircraft model 5 in the pitching plane. The yaw acceleration sensor 7 is installed on the centroid of the aircraft model 5 in the yaw plane and is used to measure the vibration acceleration component of the main vibration of the aircraft model 5 in the yaw plane. The multi-dimensional vibration damper 3 contains multiple piezoelectric ceramic actuators 3-1. In this example, 12 piezoelectric ceramic actuators 3-1 are used. Each piezoelectric ceramic actuator 3-1 is pretightened through the pretightening mechanism 3-2 respectively to ensure the reliable output of the piezoelectric ceramic actuator 3-1 dynamic force. The multidimensional vibration damper 3 is installed at the fixed end of the aircraft tail support rod 4, and the real-time controller 8 is connected to the upper computer 9, which is used to control the real-time controller 8 and the vibration control process monitoring. The real-time controller 8 is connected to the pitch acceleration sensor 6 and yaw acceleration sensor 7 respectively to obtain the vibration acceleration components in the pitch plane and yaw plane of the aircraft model 5 in real time. The real-time controller 8 is connected to the piezoelectric ceramic actuator power amplifier set 10, and there are 12 piezoelectric ceramic actuator power amplifiers 10-1 in the piezoelectric ceramic actuator power amplifier set 10, which are connected to 12 piezoelectric ceramic actuator 3-1 in the multi-dimensional vibration damper 3.

(12) FIG. 1 is a flow chart of a multi-dimensional vibration control method for a strut tail-supported aircraft model, which adopts a pitch acceleration sensor 6 and a yaw acceleration sensor 7 arranged at the centroid of the aircraft model 5 to measure the vibration acceleration components a.sub.pith(t) and a.sub.yaw(t) of the main vibration in the mutually perpendicular pitch plane and the yaw plane respectively, and feedback them to the real-time controller 8 controlled by the upper computer 9. The real-time controller 8 calculates the main vibration acceleration vector a(t) in real time and determines the real-time vibration plane X.sub.αO.sub.αY.sub.α C of the supporting rod, calculates the dynamic bending moment M(t) on the active section F of the multi-dimensional vibration damper 3 through the inertia force F.sub.I(t), and then obtains the stress distribution on the active section F. The serial number of the piezoelectric ceramic actuator 3-1 in the multi-dimensional vibration damper 3 is determined through the spatial position relationship of the real-time vibration plane X.sub.αO.sub.αY.sub.α C of the supporting rod, and the vibration control force is calculated in real time according to the stress of the piezoelectric ceramic actuator 3-1 on the active section F, and then the reverse bending moment M.sub.R(t) is generated to resist the dynamic bending moment M(t), produced in the vibration process of aircraft model 5, so as to achieve the effect of vibration reduction. The specific steps of the multi-dimensional vibration control method for the support tail-supported aircraft model are as follows:

(13) Step 1: establish the absolute coordinate system of the aircraft model support system

(14) As shown in FIG. 3, the absolute coordinate system OXYZE is established on the aircraft tail strut 4, and the coordinate origin is established in the equilibrium position at the intersection of the active section F and the axis of the aircraft tail strut 4, which is defined as O; the direction of the X axis coincides with the balance position of the axis of aircraft tail strut 4 and points to the aircraft model 5, the direction of the Y axis is that the intersection of the active section F and the pitching plane points upward; the Z axis is determined by the right manipulation. The vibration measurement coordinate system O.sub.AX.sub.AY.sub.AZ.sub.AA is established on the aircraft model 5, whose origin is established at the intersection of the centroid of the aircraft model 5 and the X axis of the absolute coordinate system OXYZE, which is defined as that the direction of the O.sub.A; X.sub.A coordinate axis coincides with the X axis of the absolute coordinate system OXYZE, the Y.sub.A coordinate axis and the Y axis of the absolute coordinate system OXYZE point upward, and the Z.sub.A coordinate axis is determined by right manipulation.

(15) Step 2: Obtain the components of the main vibration acceleration in the pitch plane and yaw plane in real time

(16) Using the pitching accelerometer 6 and the yaw accelerometer 7 at the centroid of the aircraft model 5 to measure the acceleration of the main vibration in the pitch plane and yaw plane perpendicular to each other, the acceleration of the main vibration is fed back to the real-time controller 8 controlled by the upper computer 9, and a plurality of acceleration sampling values of the pitch plane and the yaw plane are collected in each vibration control cycle, the acceleration components of the main vibration acceleration in the pitch direction and yaw direction in a vibration control cycle are calculated by formulas (1) and (2) respectively:

(17) $\begin{array}{cc}{a}_{\mathrm{pith}}\left(t\right)=\frac{\underset{i=1}{\overset{N}{.Math.}}{a}_{\mathrm{pithi}}}{N}& \left(1\right)\\ a_{\mathrm{yaw}}\left(t\right)=\frac{\underset{i=1}{\overset{N}{.Math.}}{a}_{\mathrm{yawi}}}{N}& \left(2\right)\end{array}$

(18) Among them, the acceleration component of the a.sub.pith(t) main vibration acceleration in the pitch direction, the acceleration component of the a.sub.yaw(t) main vibration acceleration in the yaw direction, a.sub.pithi(t), a.sub.yawi(t) is the acceleration sampling value of the aircraft model 5 in the pitching plane and the yaw plane at the i (i=1, 2, . . . N) sampling time, and N is the number of acceleration sampling values in each vibration control cycle.

(19) Step 3: solve the main vibration acceleration vector in real time

(20) The main vibration acceleration a(t) is obtained by combining the acceleration components in the pitching direction a.sub.pith(t) and yaw direction a.sub.yaw(t). The main vibration acceleration a(t) consists of magnitude and direction. The main vibration acceleration vector a(t) is constructed by solving the magnitude and direction of the main vibration acceleration vector a(t) in each vibration control cycle in real time by using formulas (3) and (4):

(21) $\begin{array}{cc}.Math.a\left(t\right).Math.=\sqrt{a_{\mathrm{pith}}^2+a_{\mathrm{yaw}}^2}& \left(3\right)\\ \angle a\left(t\right)=\arctan \left(\frac{a_{\mathrm{pith}}\left(t\right)}{a_{\mathrm{yaw}}\left(t\right)}\right),\angle a\left(t\right)\in \left(-\pi ,\pi \right)& \left(4\right)\end{array}$

(22) Among them, a(t) is the main vibration acceleration vector, |a(t)| is the magnitude of the vibration acceleration vector a(t), and ∠a(t) is the main vibration acceleration vector a(t) in directions.

(23) Step 4: establish the real-time vibration active control coordinate system of the aircraft model and determine the real-time vibration plane of the strut

(24) The real-time active vibration control coordinate system O.sub.AX.sub.AY.sub.AZ.sub.AD is established on the active section F, and its origin coincides with the origin O of the absolute coordinate system OXYZ E. It is defined that the direction of the O.sub.α. X.sub.α axis coincides with the direction of the X coordinate of the absolute coordinate OXYZ E, the Y.sub.α axis coincides with the a(t) direction of the main vibration acceleration vector, and the Z.sub.α coordinate axis is determined by the right manipulation. Plane X.sub.αO.sub.αY.sub.α is the real-time vibration plane X.sub.αO.sub.αY.sub.αC of the strut. Because of the randomness of the vibration of the aircraft model 5, the real-time active vibration control coordinate system O.sub.αX.sub.αY.sub.αZ.sub.αD changes with time, and the real-time vibration plane X.sub.αO.sub.αY.sub.αC changes with time.

(25) Step 5: the real-time inertial force and the stress distribution on the active cross section of the support system are solved

(26) On the real time vibration plane X.sub.αO.sub.αY.sub.αC of the support bar, the inertia force is solved in real time by formula (5)
F.sub.I(t)=−m.sub.eqa(t)  (5)

(27) Formula (6) was used to calculate the dynamic bending moment on the active section F in real time
M(t)=F.sub.I(t).Math.L  (6)

(28) The dynamic stress distribution on the active cross section F was solved in real time by formula (7)

(29) $\begin{array}{cc}\sigma \left(y_a,z_a,t\right)=\frac{M\left(t\right).Math.y_{\alpha }}{I_{z_{\alpha }}\left(t\right)}& \left(7\right)\end{array}$

(30) Among them, m.sub.eq is the equivalent mass of the support system, F.sub.I(t) is the real-time inertia force acting on the aircraft model 5, M(t) is the dynamic bending moment on the active cross section F of the aircraft model 5 during vibration, L is the distance from the centroid of the aircraft model 5 to the active cross section F, σ(y.sub.a, z.sub.a, t) is the dynamic stress at the length of the active section F inner distance X.sub.α coordinate axis y.sub.a, and I.sub.Z.sub.α(t) is the real time inertia moment of the active cross section F to the 4 coordinate axis.

(31) Step 6: Determine the sequence number of the piezoelectric actuator in real time and calculate the vibration control force

(32) As shown in FIG. 4, in this example a number of piezoelectric ceramic actuators 3-1 are uniformly arranged in the circumferential direction of the multi-dimensional vibration damper 3 at the active section F, the uniformly distributed circumferential radius is R, and the piezoelectric ceramic which coincides with the Z axis of the absolute coordinate system OXYZE is set as No. 0 piezoelectric ceramic actuator 3-1, the No. 1 piezoelectric ceramic actuator 3-1, the No. 2 piezoelectric ceramic actuator 3-1, . . . , the No. n piezoelectric ceramic actuator 3-1, are arranged in a counterclockwise circular array in turn. The array angle between the two adjacent piezoelectric ceramic actuators 3-1 is

(33) $\mathrm{\Delta \alpha }=\frac{2\pi }{n+1}.$
In the real-time active vibration control coordinate system O.sub.αX.sub.αY.sub.αZ.sub.αD, the piezoelectric ceramic actuator 3-1 above the Z.sub.α axis participates in the vibration control, and the serial number of the piezoelectric ceramic actuator 3-1 participating in the work is

(34) $\begin{array}{cc}{n}_c\in \left[\mathrm{INT}\left(\frac{\alpha \left(t\right)-\frac{\pi }{2}}{\Delta \alpha }+1\right),\mathrm{INT}\left(\frac{\alpha \left(t\right)+\frac{\pi }{2}}{\Delta \alpha }\right)\right]& \left(8\right)\end{array}$

(35) Among them,

(36) $\mathrm{INT}\left(\frac{\alpha \left(t\right)-\frac{\pi }{2}}{\Delta \alpha }+1\right)\mathrm{and}\mathrm{INT}\left(\frac{\alpha \left(t\right)+\frac{\pi }{2}}{\Delta \alpha }\right)$
represent the rounding of the calculated values of

(37) $\frac{\alpha \left(t\right)-\frac{\pi }{2}}{\Delta \alpha }+1\mathrm{and}\frac{\alpha \left(t\right)+\frac{\pi }{2}}{\Delta \alpha }$
respectively, α(t) the angle between the main vibration acceleration vector a(t) and the Z axis of the absolute coordinate system OXYZ (E), and then the real-time coordinates of the piezoelectric ceramic actuator 3-1 center in the real-time active vibration control coordinate system O.sub.αX.sub.αY.sub.αZ.sub.αD are determined as follows:

(38) $\begin{array}{cc}\left(z_{\alpha n_c}\left(t\right),y_{\alpha n_c}\left(t\right)\right)=\left(R.Math.\cos \left[{\alpha }_{n_c}-\left(\alpha \left(t\right)-\frac{\pi }{2}\right)\right],R.Math.\sin \left[{\alpha }_{n_c}-\left(\alpha \left(t\right)-\frac{\pi }{2}\right)\right]\right)& \left(9\right)\end{array}$

(39) Where, α.sub.n.sub.c is the Angle between the working piezoelectric actuator 3-1 and the Z axis direction of the absolute coordinate system OXYZE, and the resultant force on the active section F of the working piezoelectric actuator 3-1 is:

(40) 0$\begin{array}{cc}{F}_{n_c}\left(t\right)={\int }_{A_{n_c}}\sigma \left(y_a,z_a,t\right){\mathrm{dA}}_{n_c}& \left(10\right)\end{array}$

(41) Where,

(42) $A_{n_c}$
is the contact area between the no. n.sub.c participating piezoelectric ceramic actuator 3-1 and the active section F, and the resistance required by the no. n.sub.c participating piezoelectric ceramic actuator 3-1 is:

(43) $\begin{array}{cc}{F}_{{\mathrm{Rn}}_c}\left(t\right)=-F_{n_c}\left(t\right)& \left(11\right)\end{array}$

(44) Finally, all the piezoelectric ceramic actuators 3-1 generate a reverse bending moment M.sub.R(t) to resist the dynamic bending moment M(t) generated during the vibration of the aircraft model 5.

(45) The multi-dimensional vibration control method of the strut tail-supported aircraft model is evaluated by the acceleration data measured by the pitch acceleration sensor 6 and the yaw acceleration sensor 7. As shown in FIG. 6, when the pitching direction is hammered, the multi-dimensional vibration control method of the strut tail-supported aircraft model is not used, and the vibration attenuation time of the aircraft model 5 in the pitching direction is 21.49 s. After using the multi-dimensional vibration control method of the strut tail-supported aircraft model, the vibration attenuation time of aircraft model 5 in pitch direction is 1.22 s, and the vibration in pitch direction can be controlled effectively. As shown in FIG. 7, when hammering in the yaw direction, the multi-dimensional vibration control method of the strut tail-supported aircraft model is not used, and the vibration attenuation time of the aircraft model 5 in the yaw direction is 10.45 s. After using the multi-dimensional vibration control method of the strut tail-supported aircraft model, the attenuation time of the yaw direction vibration of the aircraft model 5 is 1.23 s, and the yaw direction vibration can be effectively controlled. As shown in FIGS. 8 and 9, when hammering in any direction, the strut tail-supported aircraft model multi-dimensional vibration control method is not used, the vibration attenuation time of the aircraft model 5 in the pitching direction is 18.85 s, and the yaw direction vibration attenuation time is 11.35 s. After using the multi-dimensional vibration control method of the strut tail-supported aircraft model, the vibration attenuation time of the aircraft model 5 in the pitching direction is 1.03 s, the attenuation time of the yaw vibration is 0.98 s. The results show that the vibration of the aircraft model in any direction can be effectively controlled.