Thermal post-buckling and vibration analysis of a symmetric sandwich beam with clamped and simply supported boundary conditions

Sandwich structures are widely used in aerospace, marine and other engineering industries. This paper is focused on the post-buckling and free vibration of the sandwich beam theoretically in thermal environments with simply supported and clamped boundary conditions. Firstly, nonlinear governing equations of the sandwich beam are obtained based on the principle of virtual work and natural frequencies are derived by linear equations. Secondly, buckling temperatures together with corresponding modes are addressed. Thirdly, the new equilibrium position of the sandwich beam is obtained after it loses the stability. Finally, free vibration analysis of a post-buckling sandwich beam is derived when the temperature exceeds the critical temperature. It is observed that the maximum deformation of the sandwich beam suddenly increases sharply once it loses the stability. The natural frequencies of a sandwich beam decrease with the increment of temperature, but the first-order natural frequency increases as the temperature rises once the temperature exceeds the critical buckling temperature. The theory of this paper will provide a theoretical support for the numerical method and engineering design.