Wave propagation in thermo‐elastic plate of arbitrary cross‐sections

Abstract

PurposeThe purpose of this paper is to study the wave propagation in a homogeneous isotropic, thermo‐elastic plate of arbitrary cross‐sections using the two‐dimensional theory of thermo‐elasticity.Design/methodology/approachA mathematical model is developed to study the wave propagation in an arbitrary cross‐sectional thermo‐elastic plate by using two‐dimensional theory of thermo‐elasticity. After developing the formal solution of the mathematical model consisting of partial differential equations, the frequency equations have been derived by using the boundary conditions prevailing at the arbitrary cross‐sectional surface of the plate for symmetric and antisymmetrical modes in completely separate forms using Fourier expansion collocation method. The roots of the frequency equation are obtained by using the secant method, applicable for complex roots.FindingsThe computed non‐dimensional frequencies are compared with those results available in the literature in the case of elliptic cross‐sectional solid plate with clamped edges without thermal field and this result is coincide with the results of Nagaya. The computed non‐dimensional frequencies are plotted in the form of dispersion curves for longitudinal and flexural (symmetric and antisymmetric) modes of vibrations for the material copper.Originality/valueThe wave propagation in a plate of arbitrary cross‐sections with the stress free (unclamped) and rigidly fixed (clamped) edges are analyzed with and without thermal field.