On Problem of the Radial Vibrations in Non-Homogeneous Orthotropic Hollow Sphere Subject to the Initial Stress and Rotation

Abstract

In the present article, the effect of the initial stress, rotation and non-homogeneity on the radial vibrations in orthotropic material is investigated. The elastodynamic equation is solved in terms of displacement. Three different boundary condition, namely the free surface is considered. The determination is concerned with the eigenvalues of the fundamental frequency of the radial vibrations. Numerical results are given and illustrated graphically for each case considered. Comparisons are made with the results in the absence of initial stress, rotation and non-homogeneity.

Approximate solution of nonlinear ordinary differential equation for Cauchy problem based on linearization

“…In this paper the estimation of proximities of that desired solution to its linearized counterpart, depending on the deviation of the linearized solution from the value at initial point were obtained. This mater have many applications and attracted the attention of many researchers such as [1][2][3]. Lions [4] investigated some methods for the solution of nonlinear boundry problems.…”