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A Study on the Solving Natural Frequencies and Mode Shapesof Multi-Span Beams with Springs and Masses

Abstract
The purpose of this study is to determine the exact natural frequencies and mode shapes of multi-span uniform and multi-step Euler-Bernoulli beams with various concentrated elements (such as point masses, rotary inertias, linear springs, rotational springs, spring-mass systems, etc.) by using the matrix assembly method (MAM). To this end, the coefficient matrices for an intermediate pinned support, an intermediate concentrated elements, left-end support and right-end support of a beam are derived, first. Next, the overall coefficient matrix for the whole structural system is obtained by using the assembly technique of the finite element method. Finally, the natural frequencies and the associated mode shapes of the vibrating system are determined by equating the determinant of the last overall coefficient matrix to zero and substituting the corresponding values of integration constants into the associated eigenfunctions respectively. The effects of in-span pinned supports and various concentrated elements on the free vibration characteristics of the beam are also studied.

Identiferoai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0511106-055414
Date11 May 2006
CreatorsLin, Hsien-yuan
ContributorsChao-kuang Chen, Ying-Chien Tsai, Cheng-Kuo Sung, Jong-Shyong Wu
PublisherNSYSU
Source SetsNSYSU Electronic Thesis and Dissertation Archive
LanguageCholon
Detected LanguageEnglish
Typetext
Formatapplication/pdf
Sourcehttp://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0511106-055414
Rightsunrestricted, Copyright information available at source archive

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