Nonlinear free vibration analysis of rotating composite Timoshenko beams

Linear and nonlinear free vibrations of rotating composite Timoshenko beams are investigated in this paper. The formulation is based on the assumptions of Timoshenko beam theory and the nonlinear von-Karman strain–displacement relationships. The updated equations of motion about the prestressed configuration are obtained from the three-coupled partial differential equations of motion. The differential transform method is implemented to find the prestressed configuration due to centrifugal forces. The Galerkin discretization approach is applied to the linearized updated equations of motion to determine the linear normal modes and the associated natural frequencies of the rotating composite Timoshenko beam. The rotation speed and number of layers variation effects on the flapping natural frequencies are studied and the necessity of employing the Timoshenko beam model for the composite beams is illustrated. The direct multiple scales method is applied to the three-coupled nonlinear updated partial differential equations for the nonlinear vibration study especially on the flapping backbone curves. The number of layers variation effects is investigated on the three lowest flapping backbone curves. The present results are validated with the previous literature results.