This work, part of a two-volume set, applies the material developed in the Volume One to various boundary value problems (reflection and refraction at plane surfaces, composite media, waveguides and resonators). The text also covers topics such as perturbation and variational methods.

Acoustic Fields and Waves in Solids

A finite element formulation which includes the piezoelectric or electroelastic effect is given. A strong analogy is exhibited between electric and elastic variables, and a ‘stiffness’ finite element method is deduced. The dynamical matrix equation of electroelasticity is formulated and found to be reducible in form to the well-known equation of structural dynamics, A tetrahedral finite element is presented, implementing the theorem for application to problems of three-dimensional electroelasticity.

Finite element method for piezoelectric vibration

General electromechanical reciprocity relations applied to the calculation of elastic wave scattering coefficients

Ahrroct-A method of analysis which uses a combination of analytical and numerical techniques has been developed to obtain an accurate solution to the coupled electromagnetic and acoustic fields set up by an interdigital transducer on the surface of a piezoelectric substrate. Full account is taken of the coupling to bulk modes as well as surface modes, and the solution for the charge on the electrodes includes both electrostatic charge and piezoelectrically regenerated charge. Programs have been written for interdigital arrays with uniform aperture but varying electrode width and pitch and arbitrary electrical connections. The theory is also valid for arbitrary crystal orientations. Generation and detection may be analyzed separately with information being provided on the partition of power into the various acoustic modes and the external load impedance, and the bulk wave radiation patterns are also computed. The program may also be used to find the insertion loss of a pair of transducers. Results are presented for the BleusteinGulyaev orientation of PZT-4 ceramic and the YZ and 41” rotated YX orientations of lithium niobate.

Analysis of Generation and Detection of Surface and Bulk Acoustic Waves by Interdigital Transducers

The calculus of variations is applied to the analy- sis of the short-circuit resonant properties of piezoelectric vib- rators. A stationary expression is derived from the equations of motion for such vibrations. This stationary expression is used to develop a approximation technique for detennin- ing the short-circuit resonant frequencies and the corresponding mechanical displacements and electric potentials. The technique is used to analyze the short-circuit resonant properties of fully electroded piezoelectric ceramic discs with comparable diameter and thickness dimensions. Agreement of the barium titanate resonant frequency calculations with Shaw's published experimental frequency spectrum is better than three percent for the lowest eight resonances. Also, exact solutions have been obtained for the equivoluminal modes supported in isotropic elastic discs of certain diameter-to-thickness ratios. The application of the elastic portion of the present electroelastic approxi- mation to such discs produced frequency values for these modes which agree with the exact values to better than 0.3 percent. In the present paper, a stmatiormy expression describing the steady-state vihrations of n piezoelectric insulat,ing solid with N short-circuit,ed clectrodcs on its surface is derived from the steady-stale equations of motion. The stat'iorltlry property of this cspression is used to develop a variational approsirnation technjque for short-c-ircuit elec- troelastic vibration anxlyscs. The technique is applied to the short-circuit vibrations of fully-electroded piczoelec- tric ceramic discs mit.11 comparable diameter and thickness dimensions. Agreeenlent between the BaTi03 calculations and Slmv's cxpcrinlental data(61 proves to be considerably better than that obt,ained with past npproximntion tech- niques. (" The accuracy of the technique is investigated further by comparing calculations for isotropic elastic discs with some exact equivoluminal modes of such discs. C;\r,cur~cs OF Ii.i~~.\~~~~~ IS ELECTROELASTIC ~TI13R.4TIOXS

Variational Method for Electroelastic Vibration Analysis

In the present paper general formulas for the electrical admittance of a piezoelectric crystal, in terms of its resonant frequencies and static and motional capacitances, are derived and applied to the investigation of the effect of electrode shape on the spectrum of resonances and the capacitance ratio of the crystal. Particular attention is given in two cases of practical importance, namely, small piezoelectric coupling and thin crystal plates.

http://ieeexplore.ieee.org/iel7/6731005/6769307/06769309.pdf

J. A. Lewis

Papers

The effect of driving electrode shape on the electrical properties of piezoelectric crystals