Vibration analysis of axisymmetric functionally graded viscothermoelastic spheres

摘要

The present study focuses on the analysis of free vibrations of axisymmetric functionally graded hollow spheres.The material is assumed to be graded in radial direction with a simple power law.Matrix Fro¨benious method of extended power series is employed to derive the analytical solutions for displacement,temperature,and stresses.The dispersion relations for the existence of various types of possible modes of vibrations in the considered hollow sphere are derived in a compact form.In order to explore the characteristics of vibrations,the secular equations are further solved by using fixed point iteration numerical technique with the help of MATLAB software.The numerical results have been presented graphically for polymethyl methecrylate materials in respect of natural frequencies,frequency shift,inverse quality factor,displacement,temperature change,and radial stress.