Analysis Of Quartz Crystal Resonators Research Articles

High-frequency vibrations of circular and annular plates with the Mindlin plate theory

Circular and annular elastic plates have wide applications as essential elements in various engineering structures and products demanding accurate analysis of their vibrations. At higher frequencies, the analysis of vibrations needs appropriate equations, as shown by the Mindlin plate equations for rectangular plates with tailored applications for the analysis of quartz crystal resonators. Naturally, there are equally strong demands for the equations and applications in circular and annular plates with the consideration of higher-order vibration modes. By following the procedure established by Mindlin based on displacement expansion in the thickness coordinate, a set of higher-order equations of vibrations of circular and annular plates are derived and truncated for comparisons with classical and first-order plate equations of circular plates. By utilizing these equations, coupled thickness-shear and flexural vibrations of circular and annular plates are analyzed for vibration frequencies and mode shapes.

On the interaction between a quartz crystal resonator and an array of micro-beams in thickness-shear vibrations

We studied the coupled dynamic behavior of a quartz-crystal-resonator (QCR)/microbeams system in the thickness-shear motions. Through taking into account the couple stress in the dynamic equations of the quartz plate, both continuous conditions of shear force and bending moment at the resonator/micro-beams interface are realized. Frequency shift of the compound QCR system induced by micro-beams is studied in detail. The obtained results are useful in device design and frequency-stability analysis of quartz crystal resonators.

Acoustic microsensors—the challenge behind microgravimetry

Acoustic microsensors are commonly known as high-resolution mass-sensitive devices. This is a restricted view in many chemical and biosensor applications, especially in liquids. Sensitivity to non-gravimetric effects is a challenging feature of acoustic sensors. In this review we give an overview of recent developments in resonant sensors including micromachined devices and also list recent activity relating to the (bio)chemical interface of acoustic sensors. Major results from theoretical analysis of quartz crystal resonators, descriptive for all acoustic microsensors are summarized, and non-gravimetric contributions to the sensor signal from viscoelasticity and interfacial effects are discussed. We finally conclude with some future perspectives.