Dynamic Buckling of a FGM Euler-Bernoulli Beam under Thermal Shock via Symplectic Method

Based on Euler-Bernoulli beam theory, the dynamic buckling of a functionally graded beam subjected to thermal shock is investigated in the Symplectic space. The boundaries of the FGM beam are simply supported at one end, and the other is clamped. The dynamic buckling problem is reduced to zero-eigenvalue problem. The buckling mode and critical thermal axial forces can be obtained through bifurcation condition, and the critical temperature rise of the functionally graded beam is obtained by inverse solution.