Mathematical Modelling and Analysis of Lamb Waves in a Elastothermodiffusive Material Plates
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.
