Free vibration analysis of a rotating beam with nonlinear spring and mass system

Free, out of plane vibration of a rotating beam with nonlinear spring–mass system has been investigated. The nonlinear constraint is connected to the beam between two points on the beam through a rigid rod. Formulation of the equation of motion is obtained starting from transverse/axial coupling through axial strain. Solution is obtained by applying method of multiple time scale directly to the nonlinear partial differential equations and the boundary conditions. The results of the linear frequencies match well with those obtained in open literature. Subsequent nonlinear study indicates that there is a pronounced effect of spring and its mass. The influence of rigid rod location on frequencies is also investigated on nonlinear frequencies of rotating beam.