BENDING AND FORCED VIBRATION RESPONSE OF A CLAMPED ORTHOTROPIC THICK PLATE AND SANDWICH PANEL

Abstract

A closed-form solution for the forced response of an orthotropic thick plate and sandwich panel has been developed and is presented in this paper. The paper outlines the methodology and develops the formulation to enable the solution to be derived. A novel truss-core sandwich panel is introduced and a method is outlined in which the panel is represented as an equivalent homogeneous orthotropic thick plate continuum. The 3-D dynamic finite element method is one of the most versatile developments of the 20th century. However, the software is not as accessible or as user-friendly for engineers who are not trained in such analytical tools. Therefore, alternative methods of analysis must be found, especially in the dynamic assessment of thin-walled truss-core sandwich panels. One way is to transform the sandwich structure into an equivalent homogeneous orthotropic thick plate continuum and to conduct the analysis on the equivalent model. The authors have derived the necessary elastic constants to hasten this transformation. In this paper, the derived elastic constants are used with closed-form solution to determine the bending and forced vibration response of a clamped truss-core sandwich panel, represented as a homogeneous orthotropic thick plate continuum. The Rayleigh–Ritz method is employed for the closed-form solution and the forced response is determined using Duhamel's integral. Admissible functions are taken as a series of products of beam mode-shape functions in the two orthogonal directions. The beam function in either direction is derived from the corresponding beam eigenvalue problem. Numerical examples, which include the influence of transverse shear on the response, show that the closed-form solution agrees with analytical and numerical data available in the literature and also with 3-D finite element results.