SomeConsiderations on the Rayleigh–Lamb Wave Propagation in Visco-thermoelastic Plates

Abstract

The aim of present paper is to study the thermoelastic interaction in an infinite Kelvin–Voigt-type viscoelastic, thermally conducting plate. The upper and lower surfaces of the plate are subjected to stress-free/rigidly fixed, thermally insulated or isothermal boundary conditions. Coupled dynamical thermoelasticity is employed to study the problem. We derive complex secular equations for the plate in closed from and isolated mathematical conditions for symmetric and skew-symmetric wave mode propagation in completely separate terms. The results for coupled and uncoupled theories of thermoelasticity have been obtained as particular cases from the derived secular equations. In general, the obtained secular equations are complex each of these on separating real and imaginary parts leads to two real frequency equations. These equations contain complete information regarding wavenumber, phase velocity, group velocity and attenuation coefficients of different propagating modes. The regions and the corresponding forms of Rayleigh–Lamb-type secular equations have been obtained and discussed in addition to Lame modes, decoupled shear horizontal modes and thin plate results. At short wavelength limits, the secular equations for symmetric and skew-symmetric waves in stress-free insulated and stress-free isothermal plate reduce to Rayleigh surface wave frequency equations. The amplitudes of temperature and displacement components during symmetric and skew-symmetric motion of the plate have been computed and discussed. In order to illustrate and compare the theoretical results, the numerical solution is carried out for copper material by using the functional iteration method. The dispersion curves, attenuation coefficients, amplitudes of temperature change, and displacements in case of symmetric and skew-symmetric wave modes are presented graphically.