Affiliations: State Key Laboratory for Disaster Reduction in Civil
Engineering, Tongji University, Shanghai 200092, P.R. China | Civil Engineering Institute, Guangxi University,
Nanning 530004, P.R. China | Department of Civil, Architectural, and Environmental
Engineering, University of Missouri-Rolla, Rolla, MO 65409, USA
Abstract: Timoshenko beams have been widely used in structural and mechanical
systems. Under dynamic loading, the analytical solution of a Timoshenko beam is
often difficult to obtain due to the complexity involved in the equation of
motion. In this paper, a modal perturbation method is introduced to
approximately determine the dynamic characteristics of a Timoshenko beam. In
this approach, the differential equation of motion describing the dynamic
behavior of the Timoshenko beam can be transformed into a set of nonlinear
algebraic equations. Therefore, the solution process can be simplified
significantly for the Timoshenko beam with arbitrary boundaries. Several
examples are given to illustrate the application of the proposed method.
Numerical results have shown that the modal perturbation method is effective in
determining the modal characteristics of Timoshenko beams with high accuracy.
The effects of shear distortion and moment of inertia on the natural
frequencies of Timoshenko beams are discussed in detail.
