Dynamic Stability of Thin-Walled Members

Publisher Summary This chapter explores the dynamic stability of thin-walled structures subjected to periodically alternating axial forces. A thin-walled member subjected to periodically alternating axial force is essentially variation stiffness. Linear stiffness matrix of thin-walled member remains constant, while nonlinear geometry stiffness matrix changes with periodically alternating axial force. A system of second-order differential equations with period coefficients of the Mathieu type describes the dynamic stability of thin-walled members without damping. The problem discussed is of dynamic stability of variation stiffness thin-walled member. Dynamic stability is one of the three criteria to dynamic design of structures. To solve the problem, the finite element method is applied that can greatly reduce the process of simplification. Using MATLAB package, a computer program is developed to calculate the region of dynamic instability without damping corresponding to bending vibration, torsion, and warping coupling vibration. The results prove to be more efficient and credible if compared with other calculation methods.