| Summary: | 碩士 === 國立成功大學 === 工程科學系碩博士班 === 93 === In this thesis, the free vibration of stepped beams is investigated. The Timoshenko beam model is considered. The beam structure has one segment
of sandwich beam. The displacement fields are set up. The strains, stresses, stress resultants and stress-couple resultants, kinetic energy and strain energy of the entire beam are derived. The governing equations are formulated via the Hamilton’s principle.
An analytical method is presented to obtain the modal frequencies and the corresponding sets of mode shape functions of the stepped beam. Further, the shape functions of an element of core and an element of sandwich beam are derived, respectively. Then, the technique of finite element is employed to compute the modal frequencies of the entire beam.
The effects of length and location of the sandwich beam segment on the modal frequencies of the entire beam are studied. Further, the efficiency of the presented finite element computation also is investigated.
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