Static and dynamic stability of an axially compressed five-layer sandwich beam

• The field of displacement of the cross section of sandwich beam is formulated.
• The stability problem of a compressed beam is mathematically described.
• The static and dynamic equilibrium paths, and the critical load are determined.
• The natural frequencies of the beam and two unstable regions are determined.
• The influence of binding layers is considered.

The paper is devoted to the stability analysis of a five layer sandwich beam. The goal is to elaborate a mathematical model of this beam and to check the influence of the binding glue layers on the stability of this structure. The simply supported sandwich beam consists of five layers which are two metal faces, the metal foam core and two binding layers (the glue) between faces and the core. The mechanical properties vary through the thickness of the beam and depend on the material of each layer. The field of displacement for the flat cross section of the beam is defined. Based on Hamilton׳s principle the system of three partial differential equations of motion is obtained. This system is approximately solved. The forms of unknown functions are assumed and the system of equations is reduced to a single ordinary differential equation of motion. The equation is then numerically processed. The results of solutions of the vibration problem analysis are shown in graphs and figures.