Vibration Analysis of One-Dimensional Structures with Discontinuities Using the Acoustical Wave Propagator Technique

[+] Author and Article Information
S. Z. Peng

School of Mechanical Engineering, The University of Western Australia, Crawley, WA6009, Australiaspeng@mech.uwa.edu.au

J. Vib. Acoust 127(6), 604-607 (Dec 13, 2004) (4 pages) doi:10.1115/1.2013298 History: Received December 03, 2003; Revised December 08, 2004; Accepted December 13, 2004

A numerical technique, named the acoustical wave propagator technique, is introduced to describe the dynamic characteristics of one-dimensional structures with discontinuities. A scheme combining Chebyshev polynomial expansion and fast Fourier transforms is introduced in detail. Comparison between exact analytical solutions and predicted results obtained by the acoustical wave propagator technique shows that this scheme has highly accurate and computationally efficient. Furthermore, this technique is extended to investigate the wave propagation and reflection of elastic waves in beams at the location of a sudden change in cross section.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 1

Schematic of a stepped beam

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Figure 2

Comparison of the results predicted by the Chebyshev-Fourier scheme and Euler scheme with the exact analytical solution when t=0.034s

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Figure 3

Predicted results of the displacement y(x,t) at different instants

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Figure 4

Predicted results of the bending moment M at different instants

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Figure 5

Effect of material properties on the displacement y(x,t) at different instants



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