Large amplitude forced vibration analysis of cross-beam system through energy method

Abstract

Large amplitude forced vibration behaviour of cross-beam system under harmonic excitation is studied, incorporating the effect of geometric non-linearity. The forced vibration analysis is carried out in an indirect way, in which the dynamic system is assumed to satisfy the force equilibrium condition at peak load value, thus reducing the problem to an equivalent static case. The two beams of the system are solved individually either by a direct substitution method employing successive relaxation technique or a multi-dimensional secant method, known as Broyden’s method. An iterative scheme, based on the reaction force between the two beams of the system and equality of vibration amplitude at the contact of two beams, is developed to obtain the response of the system under external harmonic excitation. The present method is validated through results generated in ANSYS 11.0. The system response is studied for various loading type and contact location of the beams. The results are presented in terms of plots of vibration amplitude of the contact point versus frequency of forcing excitation in dimensional plane. Keywords: Cross-beam, Forced vibration, Geometric non-linearity, Variational methods, Harmonic excitation