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.