Stability and vibrations of a metal seven-layer rectangular plate with trapezoidal corrugated cores

The paper is devoted to mathematical modelling of multi-layered structures. The case of a metal seven-layer rectangular plate is considered. The plate is composed of a trapezoidal corrugated main core, two inner flat sheets, two trapezoidal corrugated cores of the faces and two outer flat sheets. The direction of the corrugation of the main core is orthogonal to the one of the face cores corrugations. The hypothesis of deformation of normal to middle surface of the plate after bending and the field of displacements and stresses is formulated. The plate is simply supported and subjected to a uniformly distributed compressive loads applied to the edges. Equations of motion are derived based on the Hamilton's principle. These equations are analytically solved for static or pulsating loads. The influence of the trapezoidal corrugation pitch of the cores on the critical loads and natural frequency of the plates is analysed. The results obtained form the analytical solution are compared with the results given by the proposed finite element model.