Free vibration frequency of thick FGM spherical shells with simply homogeneous equation by using TSDT

Abstract

The effects of third-order shear deformation theory (TSDT) and varied shear correction coefficient on the free vibration frequency of thick functionally graded material (FGM) spherical shells are investigated with simply homogeneous equation under thermal environment. The nonlinear coefficient term of displacement field of TSDT is included to derive the simply homogeneous equation with the assumed reasonable simplifications in the elements of homogeneous matrix under free vibration of thick FGM spherical shells. The determinant of the coefficient matrix in dynamic equilibrium differential equations under free vibration can be represented into the simply five-degree polynomial equation; thus, the natural frequency can be obtained. For the preliminary FGM spherical shell study, the effects of nonlinear coefficient term and meridional angle on the varied shear correction coefficient calculation are not considered. The calculated values of shear correction coefficient are increasing with the increase in power law index. Three parametric effects of nonlinear coefficient term, environment temperature and power law index on the frequency of thick FGM spherical shells are computed and investigated for a given meridional angle in the spherical shells. Data in underestimated or overestimated are also investigated in the frequency parameters under free vibration with and without the effects of nonlinear coefficient term, respectively.