Analysis of Linear and Nonlinear Vibrations of Composite Rectangular Sandwich Plates with Lattice Cores

Abstract

For the first time, the linear and nonlinear vibrations of composite rectangular sandwich plates with various geometric patterns of lattice core have been analytically examined in this work. The plate comprises a lattice core located in the middle and several homogeneous orthotropic layers that are symmetrical relative to it. For this purpose, the partial differential equations of motion have been derived based on the first-order shear deformation theory, employing Hamilton’s principle and Von Kármán’s nonlinear displacement-strain relations. Then, the nonlinear partial differential equations of the plate are converted into a time-dependent nonlinear ordinary differential equation (Duffing equation) by applying the Galerkin method. From the solution of this equation, the natural frequencies are extracted. Then, to calculate the non-linear frequencies of the plate, the non-linear equation of the plate has been solved analytically using the method of multiple scales. Finally, the effect of some critical parameters of the system, such as the thickness, height, and different angles of the stiffeners on the linear and nonlinear frequencies, has been analyzed in detail. To confirm the solution method, the results of this research have been compared with the reported results in the literature and finite elements in ABAQUS, and a perfect match is observed. The results reveal that the geometry and configuration of core ribs strongly affect the natural frequencies of the plate.