Stability and free vibrations of the three layer beam with two binding layers

The paper is devoted to the stability analysis of a simply supported three layer beam. The sandwich beam consists of two metal facings, a metal foam core and two binding layers between the faces and the core. In consequence, the beam is a five layer beam. The main goal of the study is to elaborate a mathematical model of the beam, analytical description and solution of the stability problem. The beam is subjected to an axial compression and, in particular, a pulsating compression. The nonlinear hypothesis of deformation of the cross section of the beam is formulated. Based on the Hamilton's principle the system of four stability equations is derived. The system is reduced to one equation of motion (Mathieu's equation) serving as a basis for determining the critical loads, free vibrations and unstable regions. The influence of the binding layers is considered. The results of solutions of the vibration problem analysis are shown in tables and figures. The analytical model is verified numerically with the use of Finite Element Analysis.