Application of the finite element method to analyze the natural vibration of variable thickness plates

Abstract

This article examines the free vibration behavior of plates with different thicknesses that are supported by a two-coefficient elastic foundation. The analysis is conducted using a quadrilateral element consisting of four nodes, each with five degrees of freedom. The fundamental basis for the calculation formulas is in Mindlin's firstorder shear deformation theory. The thickness of a plate is subject to vary in accordance with a certain law. The validity of the calculation theory is evaluated through a comparative analysis with previously published findings. This work also investigates the influence of different characteristics, such as plate thickness, boundary conditions, and elastic foundation rigidity, on the specific vibration response of plates of increasing thicknesses.

Keywords: Variable thickness; finite element method; naturalvibration; elastic foundation.