Abstract

This paper describes a new reduction principle which can be used to solve singular perturbation problems arising from the nonlinear dynamics of spinning rectangular beams which are much suffer in one of the transverse directions. With this approach, the vibration in the suffer direction is considered as a singular perturbation to that in the less stiff direction. The reduction principle enables the outer solution (the long term behaviour) of the equations of motion to be obtained easily without the “stiffness” often associated with singular perturbation problems. The reduction in dimension from a four-dimensional to a two-dimensional vector field also facilitates the use of analytical tools like Mel’nikov’s method for predicting the onset of chaos for beams with von Karman nonlinearity. Examples involving simply-supported spinning rectangular beams under external periodic excitation, parametric excitation and quasi-periodic excitation are used to demonstrate the effectiveness of the reduction principle and the corresponding dimension reduction.

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