Wave propagation in a generalized thermoelastic plate using eigenvalue approach

In the present work, we obtain a dispersion relation for Rayleigh–Lamb wave propagation in a plate of thermoelastic material. For this aim, we consider the theory of generalized thermoelasticity with one relaxation time. The thickness of the plate is taken to be finite and the faces of the plate are assumed to be isothermal and free from stresses. We obtain the analytical solution for the temperature, displacement components, and stresses using an eigenvalue approach. Finally, we derive a dispersion relation for the plate in closed form taking into account isothermal boundary conditions for wave mode propagation. To obtain the phase velocity and attenuation coefficients of propagating wave mode, we use the function iteration numerical scheme to solve the complex dispersion relation. The phase velocity and attenuation coefficients for the first five modes of waves are represented graphically for Lord–Shulman and classical coupled dynamical theories.