Straight and Circular Crested Lamb Waves in Generalized Piezothermoelastic Plates

Abstract

This paper concentrates on the study of propagation of straight and circularly crested Lamb waves in homogeneous, transversely isotropic, piezothermoelastic plates subjected to: stress- and charge-free, thermally insulated/isothermal and stress free, thermally insulated/isothermaland electrically shorted boundary conditions in the context of generalized theories of thermoelasticity. The motion of purely transverse shear horizontal (SH) modes get decoupled from rest of the motion and do not interact with other fields. Secular equations for wave propagation modes in the plate are derived from a coupled system of governing partial differential equations of linear piezothermoelasticity. It is shown that the Rayleigh–Lamb secular equation also governs circular crested piezothermoelastic waves in a plate. Although the frequency wave number relationship holds whether the waves are straight or circularly crested the displacement, stress, electric and temperature fields vary according to Bessel functions rather than trigonometric one as far as the radial coordinate is concerned. At short wavelength limits, the secular equations reduce to Rayleigh surface wave frequency equation. The amplitudes of displacements, temperature change and electrical potential during vibrations of the plate have also been obtained. Finally, in order to illustrate and verify the analytical developments numerical solution of secular equations corresponding to stressfree, thermally insulated, open and closed circuit piezoelectric plates is carried out for cadmium-selenide (6 mm class) material. After obtaining the complex characteristic roots with the help of DesCartes' algorithm, the transcendental secular equations have been solved by functional iteration numerical technique to compute dispersion curves and attenuation coefficients. These are then presented graphically in order to illustrate and compare the results in the context of coupled and generalized theories of thermoelasticity.