Basic Investigation on Nonlinear Vibration of Beam

The nonlinear free vibrations of beams and nonlinear responses to pulse excitations are discussed by using finite difference method in this paper. The nonlinearity is attributed to the axial tensile force due to lateral deflection. The explicit formula of finite difference method is applied to solve approximately the governing nonlinear partial differential equations. At first, nonlinear free vibrations of beams whose ends are binged or clamped are analyzed and compared with previous solutions. Finally, nonlinear responseo to pulse exitations such as exponentially decaying pulse and step function are presented and compared with other solution which is obtained by using a single mode approximations