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.


Civil, Architectural and Environmental Engineering

Keywords and Phrases

Timoshenko Beams; Modal Characteristics; Modal Perturbation Method

International Standard Serial Number (ISSN)

1070-9622; 1875-9203

Document Type

Article - Journal

Document Version

Final Version

File Type





© 2005 IOS Press, All rights reserved.

Publication Date

01 Jan 2005