Technical Briefs

Free Vibration Analysis of Frames Using the Transfer Dynamic Stiffness Matrix Method

[+] Author and Article Information
Tsung-Hsien Tu

Institute of Mechanical and Electrical Engineering,  National Taipei University of Technology, Taiwan

Jen-Fang Yu

Graduate Institute of Medical Mechatronics, Chang Gung Universityjfyu@mail.cgu.edu.tw

Hsin-Chung Lien

Department of Mechanical Engineering, Northern Taiwan Institute of Science and Technology

Go-Long Tsai

Department of Vehicle Engineering,  National Taipei University of Technology, Taiwan

B. P. Wang

Department of Mechanical and Aerospace Engineering,  University of Texas at Arlington, Arlington, TX 76019

J. Vib. Acoust 130(2), 024501 (Jan 30, 2008) (3 pages) doi:10.1115/1.2827366 History: Received May 11, 2004; Revised October 06, 2007; Published January 30, 2008

A method for free vibration of 3D space frame structures employing transfer dynamic stiffness matrix (TDSM) method based on Euler–Bernoulli beam theory is developed in this paper. The exact TDSM of each member is assembled to obtain the system matrix that is frequency dependent. All free vibration eigensolutions including coincident roots for the characteristic equation can be obtained to any desired accuracy using the algorithm developed by Wittrick and Williams (1971, “A General Algorithm for Computing Natural Frequencies of Elastic Structures  ,” Q. J. Mech. Appl. Math., 24, pp. 263–284). Exact eigenfunction of structures can then be computed using the dynamic shape function and the corresponding eigenvector. The results showed good agreement with those computed by finite element method.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

End forces (a) and displacements (b).

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Figure 2

Three-story space structure

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Figure 3

First mode shape of three-story space structure by (a) FEM and (b) exact dynamic shape function



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