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 conservat ive oscillator having inertia and static non-linearities. The periodic vibr ations of the oscillator are captured by the power-series method upon trans forming 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. Rayleigh's energy princi ple is then used to determine the oscillating time frequency. The results s how excellent agreement for the vibration frequency with numerical solution s even for relatively large-vibration amplitudes (C) 2001 Academic Press.