Free vibration of unidirectional sandwich panels, Part I: Compressible core

Abstract

The free vibration response of a unidirectional sandwich panel with a compressible and incompressible core using the various computational models is presented and compared with closed-form elasticity solutions and finite element results. The mathematical formulations for various models along with the numerical investigation are presented in two parts. In the first part compressible core are considered using the elasticity closed-form solution and various high-order computational models such as the high-order sandwich panel theory (HSAPT) and the extended HSAPT model (EHSAPT). The second part is dedicated to incompressible cores and includes classical models, first-order and high-order shear deformable models, and zig-zag displacement pattern model, ordinary sandwich panel theory. The elasticity-based model serving as the benchmark solution (in first part) assumes isotropic, orthotropic, as well as layered core types. The mathematical formulation utilizes Hamilton’s principle to derive the general equations of motion. A closed-form solution of the elasticity model is available only for a simply-supported panel and it is compared with all various models numerically. The numerical investigation includes: eigenfrequencies, displacement modes along the length and through the depth of panel, as well as stress modes through the depth of panel. The results of the various models are compared with the 2D elasticity solution and finite element results of ADINA. In general, the lower mode correlates well for all models while for the higher modes only the EHSAPT and the HSAPT with displacement formulation compared well.