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http://dx.doi.org/10.12989/sem.2008.29.5.531

On the natural frequencies and mode shapes of a multi-span and multi-step beam carrying a number of concentrated elements  

Lin, Hsien-Yuan (Department of Mechanical Engineering, Cheng Shiu University)
Publication Information
Structural Engineering and Mechanics / v.29, no.5, 2008 , pp. 531-550 More about this Journal
Abstract
This paper adopts the numerical assembly method (NAM) to determine the exact solutions of natural frequencies and mode shapes of a multi-span and multi-step beam carrying a number of various concentrated elements including point masses, rotary inertias, linear springs, rotational springs and springmass systems. First, the coefficient matrix for an intermediate station with various concentrated elements, cross-section change and/or pinned support and the ones for the left-end and right-end supports of a beam are derived. Next, the overall coefficient matrix for the entire beam is obtained using the numerical assembly technique of the conventional finite element method (FEM). Finally, the exact solutions for the natural frequencies of the vibrating system are determined by equating the determinant of the last overall coefficient matrix to zero and the associated mode shapes are obtained by substituting the corresponding values of integration constants into the associated eigenfunctions.
Keywords
multi-step beam; exact solution; natural frequency; mode shape;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
Times Cited By Web Of Science : 2  (Related Records In Web of Science)
Times Cited By SCOPUS : 1
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