A Modified Modal Perturbation Method for Vibration Characteristics of Non-Prismatic Timoshenko Beams


A new perturbation method is introduced to study the undamped free vibration of a non-prismatic 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.


Civil, Architectural and Environmental Engineering

Keywords and Phrases

Eigenvalue; Euler-Bernoulli Beams; Natural Mode; Timoshenko Beams; Vibration; Algebra; Boundary Conditions; Eigenvalues And Eigenfunctions; Nonlinear Equations; Partial Differential Equations; Particle Beams; Shear Flow; Shear Strain; Perturbation Techniques

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Article - Journal

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© 2011 Techno Press, All rights reserved.

Publication Date

01 Jan 2011