Natural vibration of the three-layered solid sphere with middle layer made of FGM: three-dimensional approach


AKBAROV S. , Guliyev H. H. , YAHNİOĞLU N.

STRUCTURAL ENGINEERING AND MECHANICS, vol.57, no.2, pp.239-263, 2016 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 57 Issue: 2
  • Publication Date: 2016
  • Doi Number: 10.12989/sem.2016.57.2.239
  • Title of Journal : STRUCTURAL ENGINEERING AND MECHANICS
  • Page Numbers: pp.239-263
  • Keywords: functionally graded material, three-layered solid sphere, natural vibration, natural frequencies, torsional oscillation, spheroidal oscillation, SHELL-THEORY ANALYSIS, HOLLOW SPHERES, ELASTIC-WAVES, FREQUENCIES

Abstract

The paper studies the natural oscillation of the three-layered solid sphere with a middle layer made of Functionally Graded Material (FGM). It is assumed that the materials of the core and outer layer of the sphere are homogeneous and isotropic elastic. The three-dimensional exact equations and relations of linear elastodynamics are employed for the investigations. The discrete-analytical method proposed by the first author in his earlier works is applied for solution of the corresponding eigenvalue problem. It is assumed that the modulus of elasticity, Poisson's ratio and density of the middle-layer material vary continuously through the inward radial direction according to power law distribution. Numerical results on the natural frequencies related to the torsional and spheroidal oscillation modes are presented and discussed. In particular, it is established that the increase of the modulus of elasticity (mass density) in the inward radial direction causes an increase (a decrease) in the values of the natural frequencies.