An abstract of the disclosure is submitted herewith in a separate sheet.

Resonating sensors for use in high-pressure and high-temperature environments are provided. In one embodiment, an apparatus includes a sensor with a double-ended tuning fork piezoelectric resonator that includes a first tine and a second tine. These tines are spaced apart from one another so as to form a slot between the first and second tines. The width of the slot from the first tine to the second tine varies along the lengths of the first and second tines. Various other resonators, devices, systems, and methods are also disclosed.

Systems described herein relate to sensing pressure. In one arrangement, a pressure sensor is disclosed. The pressure sensor includes a circuit including a resistor, an inductor, and a capacitor. The circuit generates an electrical resonance. The resistor is an elastomer having a resistance and connected to an outer surface of an inflatable. The pressure sensor also includes a resonator connected to the circuit. The resonator generates a mechanical resonance coupling with the electrical resonance to create a detuning frequency having a sublinear dependence on the resistance of the elastomer. A pressure of the inflatable correlates with the detuning frequency.

A piezoelectric element includes a plurality of vibration regions that are separated from each other by a slit, and the slit is formed to have a tapered portion that is tapered from a first surface of the vibration regions on an opposite side to a support to a second surface opposite to the first surface. An electrode film is positioned inside than the slit when being viewed from a normal direction orthogonal to the first surface, and an angle formed by a side surface of the tapered portion in the vibration region and a surface parallel to the first surface is in a range of 39 to 81 degrees.

A pressure signaling system is provided and includes a container and a signaling device disposed on the container. The signaling device is configured to provide a first demonstrable feedback when an internal pressure of the container is greater than or less than an environmental pressure, and the signaling device is further configured to provide a second demonstrable feedback when a difference between the internal pressure of the container and the environmental pressure is reduced.

A piezoelectric element includes a plurality of vibration regions that are separated from each other by a slit, and the slit is formed to have a tapered portion that is tapered from a first surface of the vibration regions on an opposite side to a support to a second surface opposite to the first surface. An electrode film is positioned inside than the slit when being viewed from a normal direction orthogonal to the first surface, and an angle formed by a side surface of the tapered portion in the vibration region and a surface parallel to the first surface is in a range of 39 to 81 degrees.

System, methods, and other embodiments described herein relate to tuning a mechanical resonator for detecting a significant value using an electrical resonator that enhances sensitivity. In one embodiment, a system includes a mechanical resonator having a beam coupled to a body. The system also includes an electrical resonator coupled through a patch to the mechanical resonator, the electrical resonator operating as a shunt and having an inductor and a resistor (LR) circuit in series. The system also includes the electrical resonator that detects, associated with a perturbation of the body, an exceptional point (EP) of the mechanical resonator by varying the LR circuit according to a model.