Axisymmetric free vibrations in a microstretch thermoelastic homogeneous isotropic plate

The propagation of axisymmetric free vibrations in a microstretch thermoelastic homogeneous isotropic plate subjected to stress free thermally insulated and isothermal conditions is investigated in the context of the conventional coupled thermoelasticity (CT) and Lord and Shulman (L-S) theories of thermoelasticity. The generalized theory of elasticity developed by Lord and Shulman is employed by assuming the mechanical behaviour as dynamic to study the problem. Mathematical modeling of the problem of obtaining dispersion curves for microstretch isotropic thermally conducting elastic plates leads to coupled differential equations. The model has been simplified by using the Helmholtz decomposition technique and the resulting equations have been solved by using the variable separable method to obtain the secular equations in isolated mathematical conditions for the plates with a stress free thermally insulated and isothermal boundary surface. The secular equations for both the symmetric and skew-symmetric wave mode propagation have been obtained. Thin plate results have also been deduced. These vibration modes are found to be dispersive and dissipated in character. At short wavelength limits, the secular equations for symmetric and skew-symmetric modes reduce to the Rayleigh surface wave frequency equation. The dispersion curves, attenuation coefficients and amplitudes of dilatation, microrotation, microstretch and temperature distribution for the symmetric and skew-symmetric wave modes are computed analytically and presented graphically for the Lord and Shulman theory of elasticity. The theoretical and numerical computations are found to be in close aggrement.