Thickness-stretch Vibrations Research Articles

Thickness-Stretch Vibration of an Infinite Piezoelectric Plate with Flexoelectricity

In this paper, the thickness-stretch vibration of an infinite piezoelectric plate is studied, with consideration of the flexoelectric effect. The theoretical model developed herein is based on a one-dimensional formulation, with the assumption that the displacement and electric potential vary through the thickness. The Gibbs energy density function and variational principle are adopted to derive the constitutive equation with flexoelectricity, governing equations, and boundary conditions. For the effect of flexoelectricity, the coupling between the strain gradient through the thickness and the electric field is considered. Two electric boundary conditions are used in this work and the corresponding frequency shift due to the flexoelectricity is calculated. The present results demonstrate that the flexoelectric effect decreases the fundamental frequency of the thickness-stretch vibration and has a significant effect on the vibrational frequencies of the thickness-stretch mode of a thin piezoelectric plate. The results also show that the flexoelectric effect has a significant size dependency, and should be taken into consideration for the design and development of next-generation high-precision and high-frequency piezoelectric transducers and resonators in the future.

Performance Enhancement of an Ultrasonic Power Transfer System Through a Tightly Coupled Solid Media Using a KLM Model.

Contactless ultrasonic power transmission (UPT) through a metal barrier has become an exciting field of research, as metal barriers prevent the use of electromagnetic wireless power transfer due to Faraday shielding effects. In this paper, we demonstrate power transfer through a metal wall with the use of ultrasonic waves generated from a piezoelectric transducer. Accurate characterization and modeling of the transducer and investigation of the influence of the acoustic properties of the transmitting medium are instrumental for the performance prediction and optimal design of an ultrasonic power link. In this work, we applied the KLM model for the emitting and receiving transducers, with respect to the transmitting medium and model for both the emission and reception function. A practical UPT system was built by mechanically coupling and co-axially aligning two composite transducers on opposite sides of a transmitting medium wall. The optimal transmission performance of the ultrasonic power link through thickness-stretch vibrations of the wall together with two piezoelectric transducers working in TE mode was determined. Eventually, the operating frequency and ohmic loading condition for maximum power transmission were obtained for two different media, aluminium and polyoxymethylene (POM), with contrasting specific acoustic impedances. The results showed that the measured optimal electric loads and operating frequency for maximum power transfer agreed well with the theoretical predictions.

Dynamic modeling of 1–3 piezoelectric composite hydrophone and its experimental validation

Conventional hydrophones are usually used below their resonance frequency over a wide frequency band. Resent study showed that the hydrophones operated around the resonance frequency had potential applications in weak signal diagnosis for improving the sensitivity or resolution. However, the conventional hydrostatic model based on off-resonance hydrophone design is incapable of analyzing the hydrophones operated around the resonance frequencies, where the electromechanical response is changed sharply with frequencies. To expand the operating limits of the hydrostatic model, a dynamic model of fluid–structure interaction for analyzing the 1–3 piezoelectric composite hydrophones is presented. An analytical solution for output voltage of the hydrophone operated in thickness-stretch vibration is derived. This dynamic model is sufficient to analyze the 1–3 piezoelectric composite hydrophones over the entire frequency range, especially around the resonance. In addition, the output voltage obtained by dynamic model in the off-resonance range agrees well with those obtained by hydrostatic model. To verify the theoretical analysis, we fabricated a 1–3 piezoelectric composite hydrophone and experimentally measured the output voltage. Experimental results around the resonance show good agreement with the dynamic theory. The output voltage which peaks at the anti-resonance frequency as expected is of three orders of magnitude higher than that of conventional off-resonance hydrophones.

Nonlinear thickness-stretch vibration of thin-film acoustic wave resonators

We perform a theoretical analysis on nonlinear thickness-stretch free vibration of thin-film acoustic wave resonators made from AlN and ZnO. The third-order or cubic nonlinear theory by Tiersten is employed. Using Green’s identify, under the usual approximation of neglecting higher time harmonics, a perturbation analysis is performed from which the resonator frequency-amplitude relation is obtained. Numerical calculations are made. The relation can be used to determine the linear operating range of these resonators. It can also be used to compare with future experimental results to determine the relevant thirdand/or fourth-order nonlinear elastic constants.

Modeling of 1-3 piezoelectric composites operating in thickness-stretch vibration mode

For bulk piezoelectric ceramics plates, the fundamental thickness-stretch (TSt) waves are always coupled to the in-plane extension waves and the symmetric thickness-shear waves. The occurrence of these spurious modes in bulk piezoelectric ceramics plates is undesirable as it may interfere with the operation of transducers. 1–3 piezoelectric composites are promising candidates to suppress the spurious modes mentioned above. However, theoretical modelling of multiphase ceramic composite objects is very complex. In this study, a simple analytical TSt vibration model is constructed from three-dimensional equations of linear piezoelectricity. The mechanical damping is considered in the model by introducing a complex elastic constant. The performance of 1–3 piezoelectric composites is analysed and the electrical impedance results from theoretical and experimental analysis are compared. The results show that there is excellent agreement between the experimental electrical impedance and that obtained by the theoretical TSt vibration analysis. This indicates that 1–3 piezoelectric composites can be operated in a nearly pure TSt vibration mode near the fundamental resonance. The analytical model we present is valid for analysing 1–3 piezoelectric composites plates with large aspect ratios quickly and efficiently.

Thickness-stretch vibration of a crystal plate carrying a micro-rod array

We analyze thickness-stretch vibrations of a plate of hexagonal crystal carrying an array of micro-rods with their bottoms fixed to the top surface of the plate. The rods undergo longitudinal vibrations when the crystal plate is in thickness-stretch motion. The plate is modeled by the theory of anisotropic elasticity. The rods are modeled by the one-dimensional structural theory for extensional vibration of rods. A frequency equation is obtained and solved using perturbation method. The effect of the rod array on the resonant frequencies of the crystal plate is examined. The results are potentially useful for using thickness-stretch modes of crystal plates to measure the mechanical properties of microrod arrays.

Power transmission through a hollow cylinder by acoustic waves and piezoelectric transducers with radial polarization

Transmission of electric energy through an elastic hollow cylinder by acoustic waves is investigated using the linear theories of piezoelectricity and elasticity. The elastic cylinder is between two perfectly bonded piezoelectric layers of piezoelectric ceramics with radial polarization. Power transmission is achieved through the electrical excitation of axisymmetric thickness-stretch vibrations. An exact solution is obtained which is validated by comparison with a solution from the state space method (SSM). Numerical results are presented for the transmitted voltage, power, efficiency, input admittance, and the radial distributions of displacement and stress. The effects of the load impedance and driving frequency are examined.

Nonlinear coupling between thickness- shear and thickness-stretch modes in a rotated y-cut quartz resonator

We point out an implication of the Poynting effect in nonlinear elasticity. It is shown that, due to the Poynting effect, thickness-stretch vibration can be induced in a plate thickness-shear mode resonator of rotated Y-cut quartz when the thickness-shear deformation is no longer infinitesimal. This nonlinear coupling is particularly strong when the frequency of the thickness-stretch mode is twice the frequency of the thickness-shear mode. The induced thickness-stretch vibration affects the operating thickness-shear mode through Mathieu's equation.

Performance of a piezoelectric harvester in thickness-stretch mode of a plate

We studied mechanical-to-electrical power conversion of a piezoelectric plate driven mechanically into thickness-stretch vibrations. We have derived an analytical solution from the three-dimensional equations of linear piezoelectricity that shows the role of each of the physical parameters in determining the performance of such a piezoelectric device, usually measured by the output power density, the power efficiency, or both. Numerical results are included for illustrating the dependence of the device performance upon these physical parameters.

Analytical and Experimental Study of Free Vibration Response of Soft-core Sandwich Beams

The natural frequencies and corresponding vibration modes of a cantilever sandwich beam with a soft polymer foam core are predicted using the higher-order theory for sandwich panels (HSAPT), a two-dimensional finite element analysis, and classical sandwich theory. The predictions of the higher-order theory are shown to be in good agreement with experimental measurements made with a simple experimental setup, as well as with finite element analysis. Experimental observations and analytical predictions show that the classical sandwich theory is not capable of accurately predicting the free vibration response of soft-core sandwich beams. It is shown that the vibration response of the cantilever soft-core sandwich beam consists of a group of five lower frequency shear (antisymmetric) modes that are followed by a group of four thickness-stretch (symmetric) modes. For the higher frequency range, the vibration modes alternate between groups of one-two antisymmetric and symmetric modes. For very high frequencies, interactive vibration response is observed. Experiments show that the damping properties of the foam core are manifest most noticeably in the case of thickness-stretch vibration modes, whereas the influence of damping on the anti-symmetric modes is insignificant.

Piezoelectric ceramic disks with thickness-graded material properties

A system of two-dimensional, first-order equations for electroded piezoelectric crystal plates with general symmetry and thickness-graded material properties recently was deduced from the three-dimensional equations of linear piezoelectricity. These equations are simplified for the two limiting cases of thickness-graded piezoelectric properties, i.e., the homogeneous plate and bimorph of piezoelectric ceramics. Closed-form solutions are obtained from these reduced equations for the flexural and thickness-shear vibrations and static response of bimorph disks as well as for the extensional and thickness-stretch vibrations of homogeneous disks. Frequency spectra and modes are computed and examined. Resonance frequencies for both homogeneous and bimorph disks of PZT-857 are computed and measured. The comparison of the results shows that the agreement is close.

A forced vibration problem involving time derivatives in the boundary conditions

Three methods for solving boundary-value problems that have both time derivatives of the dependent variable and known time-dependent functions in the boundary conditions are discussed. In each procedure the time-dependence is removed from the boundary conditions by decomposing the solution into a quasi-static part and a dynamic part. Special requirements are imposed on the quasi-static portion of the complete solution, thereby assuring that the boundary conditions containing the time derivatives of the dependent variable are satisfied identically. Forced thickness-stretch vibrations of a plated elastic plate are considered as a specific example. Plots of displacement and stress vs. time are given.