Mathematical Modelling and Analysis of Lamb Waves in Elasto-Thermodiffusive Plates

Abstract

The propagation characteristics of elasto-thermodiffusive Lamb waves in a homogenous isotropic, thermodiffusive, elastic plate have been investigated in the context of linear theory of generalized thermodiffusion. After developing the formal solution of the mathematical model consisting of partial differential equations, the secular equations have been derived by using relevant boundary conditions prevailing at the surfaces of the plate for symmetric and asymmetric wave modes in completely separate terms. The secular equations for long wavelength and short wavelength waves have also been deduced and discussed. The amplitudes of displacement components, temperature change and mass concentration under the Lamb wave propagation conditions have also been obtained. The complex transcendental secular equations have been solved by using a hybrid numerical technique consisting of irreducible Cardano method along with function iteration technique after splitting these in a system of real transcendental equations. The numerically simulated results in respect of phase velocity, attenuation coefficient, specific loss factor and relative frequency shift of thermoelastic diffusive waves have been presented graphically in the case of brass material.