Hybrid finite element theory in dynamic analysis of an imperfect plate

Abstract

This paper presents a comprehensive vibrational analysis of geometrically imperfect plate under various boundary conditions. To achieve this, an approach combining the finite element method and Sanders’ shell theory is adopted to develop a mathematical model the plate, considering the displacements in form of polynomial functions. The elementary mass and stiffness matrices required for the finite element method are obtained by analytical integration for a single element, thereby enabling the dynamic equations for an entire homogeneous flat plate without needing to determine all the matrices for each individual element of the plate. The modal study specifically focuses on a thin, isotropic, elastic, and homogeneous plate. This study includes the numerical examples to evaluate the accuracy and convergence characteristics of the proposed finite element model. The analysis examines the influence of various parameters such as mechanical properties, boundary conditions, and different imperfection amplitude on the free vibration characteristics of the plate. The comparison between the experimental and theoretical results reveals a significant agreement. Furthermore, the results highlight an increase in the natural frequencies of the structure due to the presence of initial imperfections. Additionally, the theory accurately describes the dynamic behavior of the plate when the imperfection amplitude is less than, equal to or greater than the thickness of the plate.