THE STUDY OF DYNAMIC RESPONSE ANALYSIS OF BEAM-ROD SYSTEM CONSIDERING SECOND-ORDER EFFECTS

Based on the dynamic stiffness method and finite element method, a new method for calculating the dynamic response of a beam-rod system considering the second-order effect is proposed. By solving the differential equation of the free vibration for an axially loaded Bernoulli-Euler beam and the displacement boundary conditions used to get the undetermined coefficient, the dynamic exact shape function is obtained. The mass matrix and stiffness matrix considering the second-order effect are deduced by a classic finite element method, each element of the mass matrix and stiffness matrix is transcendental functions of the axial force and circular frequency. The dynamic equilibrium equation to analyze the transient dynamic response of a beam-rod system is established, and a stable and efficient solution scheme is proposed to solve the equations. The proposed method are used to analyze various typical numerical examples and compared with that of ANSYS. The results show that the new method for calculating the dynamic response of a beam-rod system has a high computational accuracy and efficiency, especially for the impact of an axial force to the dynamic response of beam structures accurately.