The Mindlin plate equations have been widely used in the analysis of high-frequency vibrations quartz crystal resonators with accurate solutions, as demonstrated by design procedure based on analytical results terms frequency, mode shapes, and optimal parameters for AT-cut plate, which is core element a resonator structure. Earlier studies focused (which one type rotated Y-cut) plates because it produced has relatively simple couplings vibration modes at thickness-shear frequencies...

We investigated the nonlinear vibrations of coupled thickness-shear and flexural modes quartz crystal plates with Mindlin plate equations, taking into consideration kinematic material nonlinearities. The equations for strongly thickness- shear have been established by following constitutive relations approximation procedures. Based on long wave aided corresponding linear solutions, equation has solved combination Galerkin homotopy analysis methods. amplitudefrequency relation we obtained...

In this paper, the thickness-extension vibration of a layered piezoelectric plate is investigated. The deformation consists symmetric and asymmetric deformation. Thicknesses adhered layers will influence frequency amplitude ratio between significantly.

The nonlinear effects of material constants and initial stresses strains in quartz crystal resonators is well known f on the frequency-temperature curves, drive-level dependency, acceleration sensitivity, stress compensation. Consequently, accurate predictions resonator behavior their electrical circuit parameters require use vibration equations solutions. effectiveness analyses has been shown by a few researchers with finite element perturbation methods. Mindlin plate theory, which used...

At high strain rates, the dynamic response of cement mortar, a heterogeneous material with damage, was experimentally studied under three different stress states: (1) one-dimensional state by using SHPB technique, (2) at pressures from 1 to 5 GPa one-stage gas gun, and (3) quasi an improved passive confining technique. The experimental results indicate that mortar is kind nonlinear rate-dependent internal damage evolution, pressure greatly influences its ductility strength. main are given discussed.

Mindlin plate theory has been the choice for analysis of high frequency vibrations piezoelectric quartz crystal resonators, which utilize electroded plates vibrating at thickness-shear and overtone modes to achieve generation functions applications. For this purpose, equations have simplified, modified, corrected accommodate actual geometry, structural complications, practical boundary conditions, various bias fields such as temperature change initial stresses. Accordingly, correction should...

Mindlin plate equations have wide applications in engineering fields with piezoelectric crystal resonators particular due to its accurate prediction of high frequency vibrations plates the vicinity thickness-shear mode. As a linear theory based on assumption infinitesimal deformation, been limited mainly vibration analysis. Many important properties quartz such as electrical circuit parameters, and nonlinear phenomena drive-level dependence (DLD), be studied consideration higher-order...

Mindlin plate theory was first developed to provide accurate solutions for vibrations of thickness-shear mode, which has a much higher frequency than usual flexure vibrations. It been widely used in the analysis high quartz crystal plates, are core resonators. The vibration obtained with proven closer exact solutions. However, due truncation and approximation, equations need be corrected, as compared three-dimensional elasticity This done high-order without electrodes AT-cut correction...

Quartz crystal resonator design achieves frequency targets through the choice of thickness quartz blank and vibration modes overtone. The overtone types resonators have been widely available to meet ever increasing needs high resonators. Earlier studies on analysis concentrated vibrations fundamental thickness-shear mode for solutions displacements which are essential in initial subsequent calculation electrical parameters. We now stage analyze provide frequency, electrodes, displacements,...

The behavior of anisotropic functionally graded piezoelectric beams subject to sinusoidal transverse loads is investigated based on the equations for a generalized plane stress problem. Both function and electric displacement are assumed consist two parts. One corresponds product trigonometric longitudinal coordinate (x) an undetermined thickness (z). other represented by linear polynomial x with unknown coefficients also depending z. governing these z-dependent functions presented....

As demands for high frequency quartz crystal resonators rise, we are prompted to design and make overtone devices with the same material, process, technology. Indeed, high-order have been widely utilized in many applications further precision products also growing. The of improvement existing ones meet requirements largely based on empirical approaches, but found that technique can be polished theoretical analytical efforts as examine Mindlin plate theory analysis fundamental type. Through...

With higher frequency and miniaturization of piezoelectric resonators, many nonlinear phenomena such as derive level dependency (DLD) activity dip have emerged needed to be systematically studied. Our earlier studies shown neither kinematic nor material nonlinearities are the main factors shifts performance fluctuation quartz crystal resonator. consideration nonlinearities, a system two-dimensional equations for coupled thickness-shear flexural vibrations plates is established by expanding...

Finite element method has been applied to quartz crystal resonator engineers due its long history in research based on Mindlin plate and three-dimensional approaches for piezoelectric plates with considerations of complication factors such as electrodes, thermal effect, mounting, packaging, among others. The earlier efforts have dampened, however, by the fact that high vibration frequency thickness-shear mode caused significant increase problem size terms number equations, or total degree...

Two-dimensional equations for flexural motions of a lithium niobate piezoelectric plate are derived from three-dimensional equations. The has ferroelectric inversion layer where the constants reverse signs. show an unconventional behavior that uniform electric field along thickness can produce bending. This offers many possibilities new designs devices. Waves in unbounded plates examined accuracy A energy harvester based on such is analyzed as example application vibrations finite plates.

Since resonators are climbing to higher frequency and shrinking smaller size, the software needs be parallelized with new algorithms libraries for large size problems. The 2D program is implemented higher-order Mindlin plate theory integrating thermal piezoelectric effect into analysis. standard finite element formulation procedure demonstrated, but we highlight distributed parallel algorithms, which include eigensolver combined PARPACK, SuperLU_DIST, Aztec ParMetis, linear equation solver...