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TECHNICAL BRIEFS

Exact Solutions for Longitudinal Vibration of Multi-Step Bars with Varying Cross-Section

[+] Author and Article Information
Q. S. Li

Department of Building and Construction, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong

J. Vib. Acoust 122(2), 183-187 (Nov 01, 1999) (5 pages) doi:10.1115/1.568459 History: Received November 01, 1999
Copyright © 2000 by ASME
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References

Timoshenko, S. P., Young, D. H., and Weaver, Jr., W., 1974, Vibration Problems in Engineering, McGraw Hill, New York.
Meirovitch, L., 1967, Analytical Methods in Vibration, MacMillan, New York.
Ward,  P. F., 1913, “Transverse Vibration of Bars of Varying Cross Section,” Philos. Mag., 25, pp. 86–106.
Conway,  H. D., Becker,  E. C. H., and Dubil,  J. F., 1964, “Vibration Frequencies of Tapered Bars and Circular Plates,” ASME J. Appl. Mech., 31, pp. 329–331.
Wang, G. Y., 1978, Vibration of Building and Structures, Science and Technology Press, Beijing.
Bapat,  C. N., 1995, “Vibration of Rods with Uniformly Tapered Sections,” J. Sound Vib., 185, pp. 185–189.
Eisenberger,  M., 1991, “Exact Longitudinal Vibration Frequencies of a Variable Cross-Section Rod,” Appl. Acoust. 34, pp. 123–130.
Lau,  J. H., 1984, “Vibration Frequencies for a Non-Uniformed Beam with End Mass,” J. Sound Vib., 97, No. 3, pp. 513–521.
Abrate,  S., 1995, “Vibration of Non-Uniform Rods and Beams,” J. Sound Vib., 185, pp. 703–716.
Kumar,  B. M., and Sujith,  R. I., 1997, “Exact Solutions for the Longitudinal Vibration of Non-Uniform Rods,” J. Sound Vib., 207, No. 5, pp. 721–729.
Li,  Q. S., Cao,  H., and Li,  G., 1994, “Analysis of Free Vibrations of Tall Buildings,” ASCE J. Eng. Mech., 120, No. 9, pp. 1861–1876.
Li,  Q. S., Cao,  H., and Li,  G., 1996, “Static and Dynamic Analysis of Straight Bars with Variable Cross-Section,” International Journal of Computers & Structures, 59, No. 6, pp. 1185–1191.
Yong,  Y., and Lin,  Y. K., 1989, “Propagation of Decaying Waves in Periodic and Piecewise Periodic Structures of Finite Lengths,” J. Sound Vib., 129, No. 2, pp. 99–118.
Li,  Q. S., Cao,  H., and Li,  G., 1995, “Calculation of Free Vibration of High-Rise Structures,” Asian J. Structural Eng., 1, No. 1, pp. 17–25.

Figures

Grahic Jump Location
A multi-step bar with lumped masses
Grahic Jump Location
A multi-step bar with varying cross-section
Grahic Jump Location
A cantilever bar with varying cross-section

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