Nonlinear vibration analysis of Timoshenko beams using the differential quadrature method

This paper addresses the large-amplitude free vibration of simply supported Timoshenko beams with immovable ends. Various nonlinear effects are taken into account in the present formulation and the governing differential equations are established based on the Hamilton Principle. The differential quadrature method (DQM) is employed to solve the nonlinear differential equations. The effects of nonlinear terms on the frequency of the Timoshenko beams are discussed in detail. Comparison is made with other available results of the Bernoulli-Euler beams and Timoshenko beams. It is concluded that the nonlinear term of the axial force is the dominant factor in the nonlinear vibration of Timoshenko beams and the nonlinear shear deformation term cannot be neglected for short beams, especially for large-amplitude vibrations.