A power series solution for the non-linear vibration of beams

A power series solution is presented for the non-linear free vibration of beams with restrained ends. The analysis is based on transforming the time variable into an oscillating time which allows the motion of the beam, assumed to be periodic, to be expressed as a double power series that is convergent for all time. A recurrence relation is used to determine the series coefficients, with the initial movement satisfying the boundary conditions as its basis. Results are obtained for simply supported and clamped beams and compared with available solutions. (C) 1997 Academic Press Limited.