A modified modal perturbation method for vibration characteristics of non-prismatic Timoshenko beams

Danguang Pan, Genda Chen and Menglin Lou

Abstract

A new perturbation method is introduced to study the undamped free vibration of a nonprismatic Timoshenko beam for its natural frequencies and vibration modes. For simplicity, the natural modes of vibration of its corresponding prismatic Euler-Bernoulli beam with the same length and boundary conditions are used as Ritz base functions with necessary modifications to account for shear strain in the Timoshenko beam. The new method can transform two coupled partial differential equations governing the transverse vibration of the non-prismatic Timoshenko beam into a set of nonlinear algebraic equations. It significantly simplifies the solution process and is applicable to non-prismatic beams with various boundary conditions. Three examples indicated that the new method is more accurate than the previous perturbation methods. It successfully takes into account the effect of shear deformation of Timoshenko beams particularly at the free end of cantilever structures.

Key Words

Timoshenko beams; Euler-Bernoulli beams; perturbation; eigenvalue; natural mode; vibration

Address

Danguang Pan: Department of Civil Engineering, University of Science and Technology Beijing, Beijing, 100083, P. R. China; Department of Civil, Architectural, and Environmental Engineering, Missouri University of Science and Technology, Rolla, MO, 65409, USA Genda Chen: Department of Civil, Architectural, and Environmental Engineering, Missouri University of Science and Technology, Rolla, MO, 65409, USA Menglin Lou: State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, Shanghai, 200092, P. R. China

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