Abstract
In this paper, an analytic solution for free and forced vibrations of stepped Timoshenko beams is presented and used for the approximate analysis of generally non-uniform Timoshenko beams. In the case of free vibrations, the frequency equation is expressed in terms of some initial parameters at one end of the beam; while in the case of forced vibrations, the solution may be obtained by solving a set of algebraic equations with only two unknowns. Several examples are presented to illustrate the validity and accuracy of the analysis.
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