Circumferential Waves in Transradially Isotropic Thermoelastic Spherical Curved Plates

Abstract

This paper presents the propagation of thermoelastic waves along circumferential direction in homogeneous, transradially isotropic spherical curved plates. Mathematical modeling of the problem to obtain dispersion curves for transversely isotropic thermally conducting spherically curved elastic plates leads to coupled differential equations. The coupled differential equations of motion and heat conductions equation in conjunction with stress free, rigidly fixed thermal boundary conditions on the inner and outer surfaces of a spherical curved plate are solved with matrix Frobenius method. In order to illustrate theoretical development, numerical solutions are obtained and presented graphically for a zinc, cobalt and silicon nitride plate. The graphical results are compared with the available literature. Thermal variations for the non-axially symmetric case of plane strain vibrations, these modes remain coupled and are affected by temperature change. Moreover, these vibration modes are found to be dispersive in nature.