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 nonuniform Timoshenko cantilever beams. With the eigenvalues and eigenvectors of uniform Euler beams, a set of partial differential characteristic equations of nonuniform Timoshenko beams is transformed into a set of algebraic equations for solutions of nonuniform Timoshenko beams. The method can solve the dynamic characteristics of beams with complicated crosssection, whether the crosssection 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.