Power Series Solution for Strongly Non-linear Conservative Oscillators

This paper compares the accuracy of the power series approach with that of the modified Lindstedt-Poincare method for strongly nonlinear vibration. The free vibration of an undampedDuffing oscillator is considered because it has an exact solution. In the power series approach, the time variable is transformed into an “oscillating time” which reduces the governing equation to a form well-conditioned by the power series method.The results show that the power series approach provides extremely accurate vibration frequencies, even at large values of the nonlinear parameter, compared with errors of up tonine percent for the modified Lindstedt-Poincare method.