Rayleigh–Lamb waves in magneto-thermoelastic homogeneous isotropic plate

Abstract

The propagation of magnetic-thermoelastic plane wave in an initially unstressed, homogeneous isotropic, conducting plate under uniform static magnetic field has been investigated. The generalized theory of thermoelasticity is employed, by assuming electrical behaviour as quasi-static and the mechanical behaviour as dynamic, to study the problem. The secular equations for both symmetric and skew-symmetric waves have been obtained. The magneto-elastic shear horizontal (SH) mode of wave propagation gets decoupled from rest of the motion and it is not influenced by thermal variations and thermal relaxation times. At short wavelength limits, the secular equations for symmetric and skew-symmetric modes reduce to Rayleigh surface wave frequency equation, because a finite thickness plate in such a situation behaves like a semi-infinite medium. Thin plate results are also deduced at the end. Dispersion curves are represented graphically for various modes of wave propagation in different theories of thermoelasticity. The amplitudes of displacement, perturbed magnetic field and temperature change are also obtained analytically and computed numerically. The result in case of elastokinetics, magneto-elasticity and coupled magneto-elasticity has also been deduced as special cases at appropriate stages of this work.