Free vibration analysis of non-uniform timoshenko beams using differentialtransform

This study introduces using differential transform to solve the free vibrat ion problems of a general elastically end restrained non-uniform Timoshenko beam. First, differential transform is briefly introduced. Second, taking differential transform of a non-uniform Timoshenko beam vibration problem, a set of difference equations is derived. Doing some simple algebraic opera tions on these equations, we can determine any i-th natural frequency, the closed form series solution of any i-th normalized mode shape. Finally, thr ee examples are given to illustrate the accuracy and efficiency of the pres ent method.