Frequency of Thick FGM Spherical Shells with TSDT Under Thermal Environment

Functionally graded material (FGM) is usually used in high temperature environment. Thick FGM spherical shells usually rarely consider the shear deformation effect of thickness. So the purpose of this study was to investigate the natural frequency directly from the homogeneous matrix under free vibration, in which elements contain the third-order shear deformation theory (TSDT) effect.

This study was based on the formulations containing temperature-dependent FGM properties, nonlinear displacements, dynamic equations of motion and fully homogeneous equation. Thus the determinant of fully homogeneous coefficient matrix in sinusoidal oscillations can be used to calculate the numerical data of natural frequencies.

The numerical results of natural frequencies for SUS304/Si3N₄ constituent materials were obtained. These results include the effects of stiffness integrals, c₁ term, density integrals, temperature-dependent properties and power law index of FGMs on the vibrations of flexural, shear and twist modes. Some non-dimensional frequency parameters were also compared with published literature.

Usually the values of dimensional first natural frequency are greater in value with c₁=0 than that with c₁=0.925925/mm2, including the TSDT effect, for a given meridional angle in thick FGM spherical shells.