This paper studies wave propagation in strings with rigid bodies using the method of transfer matrices. The transmission property of a single rigid body is investigated. It is found that when the size of a rigid body is included, a symmetrically defined rigid body will transmit wave energy completely at a non-zero frequency defined by the tension, the length of the body, the mass of the string replaced by the body, and the mass of the body. Using the concept of impedance matching, the effect of a discontinuity on wave transmission in an infinite string system is revealed. The same idea is extended to the study of wave propagation in a string with multiple, equally-spaced rigid bodies (a periodic structure). The input impedance of such a system and the conditions of complete transmission are expressed in terms of the transfer matrix. The input impedance is used to identify the frequencies at which there is complete wave transmission. These frequencies are related to the natural frequencies of the corresponding finite system and constitute the so-called propagation zones. The results of this work may be applied to the propagation of vibration in complex cable systems such as oceanographic moorings.
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October 1995
Research Papers
Wave Propagation in Strings with Rigid Bodies
Li Li,
Li Li
Department of Ocean Engineering, Massacthusetts Institute of Technology, Room 5-222, Cambridge, MA 02139
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J. Kim Vandiver
J. Kim Vandiver
Department of Ocean Engineering, Massacthusetts Institute of Technology, Room 5-222, Cambridge, MA 02139
Search for other works by this author on:
Li Li
Department of Ocean Engineering, Massacthusetts Institute of Technology, Room 5-222, Cambridge, MA 02139
J. Kim Vandiver
Department of Ocean Engineering, Massacthusetts Institute of Technology, Room 5-222, Cambridge, MA 02139
J. Vib. Acoust. Oct 1995, 117(4): 493-500 (8 pages)
Published Online: October 1, 1995
Article history
Received:
September 1, 1993
Online:
February 26, 2008
Citation
Li, L., and Vandiver, J. K. (October 1, 1995). "Wave Propagation in Strings with Rigid Bodies." ASME. J. Vib. Acoust. October 1995; 117(4): 493–500. https://doi.org/10.1115/1.2874489
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