Propagation of Lamb waves in a transversely isotropic piezothermoelastic plate

The propagation of Lamb waves in a homogeneous, transversely isotropic, piezothermoelastic plate subjected to charge- and stress-free, thermally insulated or isothermal boundary conditions, is investigated. Secular equations for the plate in closed form and isolated mathematical conditions for symmetric and antisymmetric wave mode propagation in completely separate terms are derived. It is shown that motion of purely transverse (SH) mode gets decoupled from rest of the motion and remains unaffected due to piezoelectric, pyroelectric and thermal effects. At short wavelength limits, the secular equations for symmetric and skew symmetric waves reduce to Rayleigh surface wave frequency equation, because a finite plate in such situation behaves like a semi-infinite medium. The amplitudes of dilatation, temperature change and electrical potential have also been computed during the symmetric and skew symmetric mode of vibrations of the plate. Finally, numerical solution of various secular equations and other relevant relations is 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 in order to illustrate and compare the analytical results. The theory and numerical computations are found to be in close agreement. The various wave characteristics are found to be more stable and realistic in the presence of piezoelectric and pyroelectric effects than in the absence of such effects, thereby making such materials more viable for practical applications and use.