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.
Vibration Analysis of One-Dimensional Structures with Discontinuities Using the Acoustical Wave Propagator Technique
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Peng, S. Z. (December 13, 2004). "Vibration Analysis of One-Dimensional Structures with Discontinuities Using the Acoustical Wave Propagator Technique." ASME. J. Vib. Acoust. December 2005; 127(6): 604–607. https://doi.org/10.1115/1.2013298
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