Development of the Dynamic Stiffness Method for the Out-of-Plane Natural Vibration of an Orthotropic Plate

Abstract

In this present paper, the dynamic stiffness method (DSM) was formulated to investigate the out-of-plane natural vibration of a thin orthotropic plate using the classical plate theory (CPT). Hamilton’s principle was implemented to derive the governing differential equation of motion for free vibration of the orthotropic plate for Levy-type boundary conditions. The Wittrick–Williams (W–W) algorithm was used as a solution technique to compute the natural frequencies of a thin orthotropic plate for different boundary conditions, aspect ratios, thickness ratios, and modulus ratios. The obtained results are compared with the results by the finite element method using commercial software (ANSYS and those available) in the published literature. The presented results by the dynamic stiffness method can be used as a benchmark solution to compare the natural frequencies of orthotropic plates.

Keywords

• natural vibration
• orthotropic plate
• dynamic stiffness method
• Wittrick–Williams algorithm