Analysis of Free Vibrations in Homogeneous Isotropic Rigidly Fixed Thermoelastic Circumferential Spherical Curved Plates

Abstract

The 1st and 2nd class vibrations of rigidly fixed thermoelastic spherical curved plates have been presented in this article. After mathematical modeling, the obtained equations have been solved by applying normal mode analysis. The uncoupled equation has been considered as 1st class vibrations named toroidal vibrations, remains independent of temperature variations. The coupled system of equations which is considered as 2nd class vibrations named spheroidal vibrations. The series solution of matrix Fröbenius method has been applied to coupled system of ordinary differential equations to obtain potentials and temperature. Fixed point iteration numerical technique has been applied to analytical results with the assistance of MATLAB software tools. Computational techniques have been applied to analytical results and numerically generated data has been represented graphically for frequencies, dissipation factor, displacements and temperature. HIGHLIGHTS The 1st and 2nd class vibrations of rigidly fixed thermoelastic spherical curved plates have been presented in this article The uncoupled equation has been considered as 1st class vibrations named toroidal vibrations, remains independent of temperature variations The coupled system of equations which is considered as 2nd class vibrations named spheroidal vibrations The series solution of matrix Fröbenius method has been applied to couple system of ordinary differential equations to obtain potentials and temperature Computational techniques have been applied to analytical results and numerically generated data has been represented graphically for frequencies, dissipation factor, displacements and temperature GRAPHICAL ABSTRACT