Energy Method on Dynamic Buckling of Elastic Bar with Clamped-Free boundary Condition subjected to Impact of Rigid Mass

Abstract

Abstract Considering the effect of stress wave, the dynamic buckling problem of elastic bar with clamped-free boundary condition subjected to impact of rigid mass is studied using the energy method. The Lagrange function is built. Both of the trial function that satisfy the boundary conditions and the Lagrange function are substituted into the second Lagrange equation. After that an analytical expression of critical impact velocity can be deduced. By the analytical expression, it is obtained that the critical impact velocity is related to the impact mass of rigid block, the critical length and the inertia radius of the bar. The result show that the critical velocity decreases by increasing the impact mass and critical length, while increases by the increasing of inertia radius.