THERMOELASTIC LAMB WAVES IN ELECTRICALLY SHORTED TRANSVERSELY ISOTROPIC PIEZOELECTRIC PLATE

Abstract

The propagation of Lamb waves in a homogeneous, transversely isotropic, piezothermoelastic plate, which is stress free, electrically shorted, and thermally insulated (or isothermal), is investigated. Secular equations for the plate in closed form and isolated mathematical conditions for symmetric and antisymmetric wave mode propagation are derived in completely separate terms. It is shown that the motion of the purely transverse shear horizontal (SH) mode gets decoupled from the rest of the motion and remains unaffected due to piezoelectric, pyroelectric, and thermal effects. The secular equations for stress-free piezoelectric, thermoelastic, and elastic plates are deduced as special cases in the current analysis. At short wavelength limits the secular equations for symmetric and skew symmetric modes reduce to Rayleigh surface wave frequency equation, because a finite-thickness plate in such a situation behaves like a semi-infinite medium. The amplitudes of dilatation, electrical potential, and temperature change are also computed during the symmetric and skew symmetric motion of the plate. Finally, numerical solutions of various secular equations and other relevant relations are carried out for cadmium selenide (6 mm class) material. The dispersion curves, attenuation coefficients and amplitudes of dilatation, temperature change, and electrical potential for symmetric and antisymmetric wave modes are presented graphically to illustrate and compare the analytical results. The theory and numerical computations are found to be in close agreement. The coupling between the thermal/electric/elastic fields in piezoelectric materials provides a mechanism for sensing thermomechanical disturbances from measurements of induced electric potentials and for altering structural responses via applied electric fields. Therefore, the analysis will be useful in the design and construction of Lamb wave sensors, temperature sensors, and surface acoustic wave filter devices.