RESEARCH ON NONLINEAR FREE VIBRATIONS USING HOMOTOPY ANALYSIS METHOD

Abstract

This paper applies the homotopy analysis method to study nonlinear free vibrations. The paper has used the homotopy analysis method to find analytical solutions of a nonlinear two-degree-of-freedom system. Analytical results have found the natural oscillation frequencies, the displacement formula of the system are approximately calculated at the 10th order. Research to find analytical solutions only receives positive results when selecting the auxiliary parameter  is the deciding factor in the values of the solution. Compared with the results calculated by numerical methods, using calculations by homotopy analysis method is an advantage to find solutions to the nonlinear vibration problem. From calculating results, in case of auxiliary parameter , those results are matched very well when analyzed by the numerical methods. In additionally, to evaluate the reliability of the homotopy analysis method, this paper has determined that when the time variable is in the range t = [ ], the displacemental results are compared by calculated by the homotopy method with the numerical method would be confidence interval.