Mathematical Modelling and Analysis of Lamb Waves in Elasto-Thermodiffusive Plates (Advances in Applied Mathematics and Mechanics, 2010)
The propagation characteristics of elasto-thermodiffusive Lamb waves in a homogenousisotropic, thermodiffusive, elastic plate have been investigated in the context oflinear theory of generalized thermodiffusion. After developing the formal solutionof the mathematical model consisting of partial differential equations, the secularequations have been derived by using relevant boundary conditions prevailing at thesurfaces of the plate for symmetric and asymmetric wave modes in completely separateterms. The secular equations for long wavelength and short wavelength waves have alsobeen deduced and discussed. The amplitudes of displacement components, temperaturechange and mass concentration under the Lamb wave propagation conditions have alsobeen obtained. The complex transcendental secular equations have been solved byusing a hybrid numerical technique consisting of irreducible Cardano method alongwith function iteration technique after splitting these in a system of realtranscendental equations. The numerically simulated results in respect ofphase velocity, attenuation coefficient, specific loss factor and relativefrequency shift of thermoelastic diffusive waves have been presented graphicallyin the case of brass material.