Abstract
The method of multiple scales is applied to the analysis of the coupled torsional-axial oscillations of a torsional spring mass oscillator consisting of a neo-Hookean bar fixed at one end and with a heavy disc attached to the other end. This coupling is due to the Poynting effect. Numerical results obtained from the method of multiple scales are compared with those obtained from numerical integration of the system of two second order non-linear governing equations of the system. Two different cases are considered which are termed the non-resonant and near resonant cases and the method of multiple scales requires some modification for the near resonant case.
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