Free vibration analysis of uniform thickness and stepped P-FGM plates: A FSDT-based dynamic stiffness approach

Abstract

In this article, the dynamic stiffness method (DSM) is implemented to analyze the out-of-plane free vibration behavior of uniform thickness and stepped functionally graded plates with power-law material property variation (P-FGM) along the thickness direction. The P-FGM plate is discretized suitably in a number of segments, and for each segment the dynamic stiffness (DS) matrix is formulated. The displacement field is defined with respect to the physical neutral surface of the plate based on the first-order shear deformation theory (FSDT). Assuming Levy-type plate boundary conditions, the governing differential equations are solved exactly to obtain the DS matrix pertaining to a plate segment. Finally, the eigenvalues and eigenvectors of the assembled global DS matrix are computed using the Wittrick–Williams algorithm to obtain the natural frequencies and mode shapes of various P-FGM plate configurations. It is shown that the frequency results obtained using DSM are very accurate as the method utilizes the exact solution of the governing differential equations. It is emphasized that FSDT-based frequency results for stepped P-FGM plates are reported, for the first time, in this article, and these results can be used as benchmark solutions for comparison purposes.

Keywords:

• Functionally graded material
• stepped plate
• transverse vibration
• dynamic stiffness method
• first-order shear deformation theory
• physical neutral surface

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work presented in this article was not funded by any funding agency.