Large amplitude free vibrations of beams - an energy approach

The conservation of energy principle, which says that the total energy of a vibrating system, at any given instant of time is constant, is used to evaluate the large amplitude free vibration behaviour of beams with immovable ends. With an assumed space mode, which satisfies the geometric boundary conditions, the final governing equation is obtained. This equation is solved by a numerical integration scheme to obtain the ratio of frequencies of nonlinear to linear systems. Comparison of the present results with those of other researchers on this topic and a Galerkin approximation is also included.