Analytical solutions to nonlinear conservative oscillator with fifth-order nonlinearity

This paper describes analytical and numerical methods to analyze the steady state periodic response of an oscillator with symmetric elastic and inertia nonlinearity. A new implementation of the homotopy perturbation method (HPM) and an ancient Chinese method called the max-min approach are presented to obtain an approximate solution. The major concern is to assess the accuracy of these approximate methods in predicting the system response within a certain range of system parameters by examining their ability to establish an actual (numerical) solution. Therefore, the analytical results are compared with the numerical results to illustrate the effectiveness and convenience of the proposed methods.