We study stress-induced frequency shifts in a rotated Y-cut quartz resonator (theta = 23.7 degrees ) with degenerate fundamental thickness-shear modes when the biasing stress is not present. Using the recently derived perturbation procedure for degenerate frequencies in crystal resonators, we show that when a planar stress system is applied, the degenerate frequency splits into two. This phenomenon is expected to be typical for degenerate frequencies in crystal resonators and may be responsible in part for the jump discontinuities in frequency temperature curves and other frequency jump phenomena.

In this paper, we report on our study of stress-induced effects on thickness vibrations of a langasite plate. The plate is assumed to be doubly-rotated, specified by angles /spl phi/ and /spl theta/. The stresses are assumed to be uniform and planar. The first-order perturbation integral as developed by Tiersten for frequency shifts in resonators is used. The dependence of frequency shifts on /spl phi/ and /spl theta/ is calculated and examined, and loci of stress-compensation are determined. The analysis makes use of the third-order material constants that are available for langasite but not for its isomorphs.

A set of two-dimensional nonlinear equations for thin electroelastic shells in vibrations with moderately large thickness-shear deformations are obtained from the variational formulation of the three-dimensional equations of nonlinear electroelasticity by expanding the mechanical displacement vector and the electric potential into power series in the shell thickness coordinate and retaining lower order terms. As an example, the equations are used to study nonlinear thickness-shear vibrations of a circular cylindrical shell driven by an electric voltage. Nonlinear amplitude-frequency behavior of electric current near strong resonance is obtained.

We study the effects of a small curvature of the middle plane of a thickness-shear mode crystal plate resonator on its vibration frequencies, modes and acceleration sensitivity. Two-dimensional equations for coupled thickness-shear, flexural and extensional vibrations of a shallow shell are used. The equations are simplified to a single equation for thickness-shear, and two equations for coupled thickness-shear and extension. Equations with different levels of coupling are used to study vibrations of rotated Y-cut quartz and langasite resonators. The influence of the middle plane curvature and coupling to extension is examined. The effect of middle plane curvature on normal acceleration sensitivity is also studied. It is shown that the middle plane curvature causes a frequency shift as large as 10−8 g−1 under a normal acceleration. These results have practical implications for the design of concave–convex and plano-convex resonators.

The bending mode effect on sensitivity of pressure sensors operating with surface acoustic waves (SAW) propagating over the surface of a plate is analyzed using Tiersten's perturbation integral for frequency shifts in a piezoelectric resonator due to the presence of initial fields. For a plate subjected to nonpure bending, the SAW speed, whose shift in response to pressure determines the sensitivity, can be defined locally through the local variations of the effective material constants. Three common bending modes of pure bending, bending under a concentrate load, and bending under a uniformly load are analyzed and compared.

Two-dimensional equations for multilayered shells of piezoelectric semiconductors are derived. The equations are used to analyze the propagation of torsional waves in a single-layered circular cylindrical shell of a piezoelectric semiconductor, and in a multilayered shell of nonconducting piezoelectrics and nonpiezoelectric semiconductors. Dispersion and dissipation due to semiconduction as well as wave amplification by a biasing DC electric field are discussed.

We study frequency shifts in crystal resonators due to intrinsic stresses from electrodes with different thickness. The first-order perturbation integral, as developed by Tiersten for frequency shifts in resonators, is used. Frequency shifts in rotated Y-cut quartz thickness-shear resonators are calculated. The effect of asymmetric electrodes is examined.

We study electromechanical fields in the anti-plane deformation of an infinite medium of piezoelectric materials of 6 mm symmetry with a circular cylindrical hole. The theory of electroelastic dielectrics with electric field gradient in the constitutive relations is used. Special attention is paid to the fields near the surface of the hole.

The equations of elastic dielectrics with electric field gradient effects are specialized to the case of anti-plane motions of polarized ceramics. A general solution is obtained in polar coordinates. Analytical solutions to the static problems of the potential field of a line source, the capacitance of a circular cylindrical ceramic shell, and the dynamic problem of the dispersion relation of plane waves are obtained to examine the electric field gradient effect. Special attention is paid to the case when the shell is thin and the waves are short.

The authors perform sensitivity analysis theoretically on three surface acoustic wave (SAW) pressure sensor structures and two material selections. The analyses take into consideration the effects of mounting structures, ways of transferring pressure to the sensing element, and various physical and geometrical parameters. It is shown that pressure-induced bending produces a larger change of wave speed than pressure-induced extension. A proposed shallow shell structure is demonstrated to increase the sensitivity of SAW pressure sensors, and for this structure, Si SAW exhibits a slightly higher sensitivity than Ge SAW.

Frequency shifts in crystal resonators under relatively large biasing fields are studied from a perturbation procedure based on the equations for small fields superposed on finite biasing fields in an anisotropic elastic body. A general expression for second-order frequency shifts is obtained. Estimates are made on the order of magnitude of second-order frequency shifts in a quartz resonator due to relatively large normal acceleration.