LARGE-AMPLITUDE FREE VIBRATION OF A CONSERVATIVE SYSTEM WITH INERTIA AND STATIC NON-LINEARITY

A power-series solution is presented for the free vibrations of a conservative oscillator having inertia and static non-linearities. The periodic vibrations of the oscillator are captured by the power-series method upon transforming the time variable into a harmonically oscillating time. A recursive relation is established between the solution coefficients which depend on initial conditions and oscillating time frequency. Rayleighʹs energy principle is then used to determine the oscillating time frequency. The results show excellent agreement for the vibration frequency with numerical solutions even for relatively large-vibration amplitudes