Free Vibration of Non uniform Timoshenko Cantilever Beams
PAN Dan guang,WU Shun chuan and ZHANG Wei
DOI:10.11835/j.issn.1674-4764.2009.03.006
Received February 02, 2009,Revised , Accepted , Available online July 01, 2015
Volume ,2009,Pages 25-28
- Abstract
In order to consider the effect of shearing deformation and rotating inertia, an approximate method, which is based on modal perturbation method, is proposed for the free vibration analysis of non uniform Timoshenko cantilever beams. With the eigenvalues and eigenvectors of uniform Euler beams, a set of partial differential characteristic equations of non uniform Timoshenko beams is transformed into a set of algebraic equations for solutions of non uniform Timoshenko beams. The method can solve the dynamic characteristics of beams with complicated cross section, whether the cross section variation is continuous or discontinuous. At the end, two types of beams, namely (a) discontinuous variation of thickness and (b) continuous and linear variation, are analyzed and shown that the method is simple, practicable and owns good precision.