SEMI-ANALYTIC SOLUTION OF DYNAMIC CHARACTERISTICS OF NON-PRISMATIC TIMOSHENKO SIMPLY SUPPORTED BEAMS

Based on modal perturbation method, a novel approach is presented to analyze the free vibration of non-prismatic Timoshenko beams．In the method, the dynamic characteristics of non-prismatic Timoshenko beams are calculated approximately in the modal subspace spanned by several lower models of equivalent prismatic Euler-Bernoulli beams. As a result, the set of characteristic equations of non- prismatic Timoshenko beams is transformed into a set of algebraic equations. For prismatic Timoshenko simply supported beams, the exact eigenvalues and eigenfunctions can be obtained by using the method. For non- prismatic ones, the results of numerical examples show that the method is simple, practicable and accurate.