Mode coupled vibrations in a thickness-shear (TSh) mode and laterally finite FBAR sensor with one face in contact with Newtonian (linearly viscous and compressional) liquid are investigated. With boundary conditions and interface continuity conditions, exact dispersion curves in FBAR sensor contacting with two kinds of liquids are obtained, and they are compared with the dispersion curves in a bare sensor without liquid contact. Frequency spectra, describing mode couplings between the main TSh modal branch and undesirable modal branches, are calculated by employing weak boundary conditions at lateral free edges constructed based on the variational principle. Mode shapes of mechanical displacements in both the sensor and liquid layer are presented, and mode transformations are observed due to the liquid contact and lateral edge effect. The effect of liquid thickness on frequency spectra is also studied. Numerical results reveal that the generation of shear wave in the liquid layer results in the shifts of spectrum curves along the frequency axis and hence it is the main factor of frequency shifts of FBAR sensors. The compressional wave causes the shifts of spectrum curves along the lateral aspect ratio axis. Then for a given FBAR sensor, the liquid thickness changes could also cause frequency shifts. Therefore, desirable vibration modes should be chosen based on the frequency spectra to avoid strong mode couplings and to eliminate frequency shifts induced by the liquid thickness changes in real applications.

The multimode and dispersion characteristics of Lamb waves make them difficult to apply to nondestructive evaluation. This paper presents a paired configuration of a meander-line coil electromagnetic acoustic transducer (EMAT) to generate a single-mode symmetric and antisymmetric Lamb wave in aluminum plates. In the paired structure, the bias magnetic field of the EMAT that generates symmetric mode Lamb waves is perpendicular to the plate surface, while the bias magnetic field of the EMAT that generates antisymmetric Lamb waves is parallel to the plate surface. The symmetric and antisymmetric exciting forces generated by these two EMATs are consistent with the dispersion equations of single symmetric and antisymmetric Lamb wave modes, respectively. The numerical simulations and experiments verified that the presented paired configurations of meander-line coil EMATs can effectively control the generation of single-mode Lamb waves at low frequencies.

Using plates of weak piezoeletcric crystal (quartz) loaded with various liquids, it is shown that along with common modes, whose sensitivity towards different liquid parameters comparable with each other, there are some uncommon modes, whose amplitude responses towards viscosity η are much larger than towards temperature T and electric conductivity σ. The search of the modes with the selective properties is accomplished by varying plate thickness h, crystal orientation, wave length λ, and mode order n. It is found that all modes possessing the property are characterized by small surface-normal displacement, avoiding wave radiation into adjacent liquid, large in-plane displacements, enhancing viscous coupling the modes and liquids, and small electro-mechanical constant, reducing electro-acoustic interaction. Basing on the modes, the sensor prototypes with selective operation are developed and tested for η from 1 to 1500 cP, σ from 0 to 1.2 S/m, and t from 0 to 55 °C. Because of operation at ultrasonic frequency (tens MHz) the prototypes have different sensitivities in various η-ranges: 0.3 dB/cP for 1–20 cP, 0.12 dB/cP for 20–100 cP, and 0.015 dB/cP for 100–1500 cP. Viscosity responses of the prototypes become comparable with their electric outputs only for η < 2 cP. Temperature responses are almost zero in air, but when plate is coated with liquid they increase depending on liquid properties, allowing measurements of the temperature dependence of the liquid viscosity.

Vibration frequencies and modes for the thickness-shear vibrations of infinite partially-electroded circular AT-cut quartz plates are obtained by solving the two-dimensional (2D) scalar differential equation derived by Tiersten and Smythe. The Mathieu and modified Mathieu equations are derived from the governing equation using the coordinate transform and the collocation method is used to deal with the boundary conditions. Solutions of the resonant frequencies and trapped modes are validated by those results obtained from COMSOL software. The current study provides a theoretical way for figuring out the vibration analysis of circular quartz resonators.

The paper proposes an inverse reconstruction method for inner cavities in a 2D plate using guided SH-waves. When a pure incident wave mode is sent toward the flaw area, reflected waves are observed at the far field due to mode conversion. From wave scattering theory, the reflected wave field is expressed by an integral over the unknown flaw surface concerning the total wave field. By the introduction of Born approximation and far-field expressions of Green’s function, it is found that the reflection coefficient for the mode of the same order as that of the incident mode is related to the unknown shape of the cavity by Fourier transform relations. By mathematical deduction, we show that if the basic (0th-order) symmetric and the 1st-order antisymmetric modes are used as incident waves, the locations and shapes of upper and lower boundaries of the cavity can be reconstructed. Numerical examples are illustrated in the paper, and a proper condition for applying this method is discussed. The research can act as a basis of nondestructive inspection for latent flaws within more complicated structures.