Propagation of Lamb wave in the plate of microstretch thermoelastic diffusion materials

The present paper investigates the three thermoelastic theories on the propagation of Lamb wave in a linearly isotropic microstretch diffusion plate subjected to the thermally insulated/impermeable and isothermal/isoconcentrated boundary conditions. The secular equations of the Lamb wave are obtained for both symmetric and anti-symmetric modes of vibration. The secular equations for Rayleigh surface wave at short wavelength and plate wave at longer wavelength are obtained for both the boundary conditions from symmetric vibration. We also obtain the secular equation of flexural wave from the anti-symmetric vibration at the longer wavelength compared with the thickness of the plates. The phase velocity and attenuation are computed numerically for a particular model, and these results are compared for the coupled themoelasticity(CT), Lord–Shulman ( \(L-S\) $L-S$ ) and Green–Lindsay ( \(G-L\) $G-L$ ) theories. There are three modes of dispersion and attenuation for each symmetric and anti-symmetric vibration. The dispersion curves of the Lamb wave increase from first to third mode of symmetric vibration in both thermally insulated/impermeable and isothermal/isoconcentrated plates. Certain special cases are reduced from the current formulation.