Approximate solutions of the equation of motion’s of the rigid rod which rocks on the circular surface without slipping

In this paper, a modified harmonic balance method based an analytical technique has been developed to determine approximate solutions for a strongly nonlinear oscillator with a discontinuous term which is arising from the motion of rigid rod on the surface without slipping. Usually, a set of nonlinear algebraic equations is solved in this method. However, analytical solutions of these algebraic equations are not always possible, especially in the case of a large oscillation. We have been compared the solution results of this method with the numerical solution in order to validate the approach and assess the accuracy of the solutions has been demonstrated and discussed. We found that, a second order modified harmonic balance method works very well for the whole range of initial amplitudes. The advantage of the using method is its simple procedure and gives almost similar results in comparison with the exact solution.