Non-linear dynamic instability analysis of thin-walled stiffener beam subjected to uniform harmonic in-plane loading

Present analysis deals with nonlinear flexural-torsional vibration and dynamic instability of thin-walled stiffener beam with open section subjected to harmonic in-plane loading. The static and dynamic components of the applied harmonic in-plane loading are assumed to vary uniformly. A set of nonlinear partial differential equations (PDEs) describing the vibration of system is derived. Using Galerkin's method, these partial differential equations are reduced into coupled Mathieu equations. The steady state response of the system is determined by solving the condition for a non-trivial solution. The principal regions of parametric resonance are determined using the method suggested by Bolotin. The numerical results are presented to investigate the effect of aspect ratios, boundary conditions and static load factor on the frequency-amplitude responses and instability regions.