Advanced Frequency of Thick FGM Spherical Shells by Nonlinear Shear and TSDT

An advanced frequency study in thick-walled functionally graded material (FGM) spherical shells is investigated with advanced shear correction. The values of advanced shear correction can be greater than one, be a negative value, and be affected by a nonlinear term of third-order shear deformation theory (TSDT) of displacements, FGM power law index, and temperature. It is novel and interesting to consider using TSDT and advanced shear correction to derive a simple homogeneous equation with reasonable simplifications into a symmetrical sparse matrix subjected to free vibration. The zero determinant of the symmetrical sparse matrix can be expressed to calculate the natural frequency by Newton’s method. The parameter effects of advanced shear correction, a nonlinear TSDT term, temperature, and the FGM power-law index on the natural frequencies of thick-walled FGM spherical shells are presented. The natural-frequency data for the axial and circumferential mode shapes are obtained. This is a new finding, as the assumed simplification in a sparse matrix causes a numerical truncation error; the natural-frequency values of the presented sparse matrix are much greater than those in a full matrix for thick-walled FGM spherical shells.