Vibrations of One-Dimensional Structure with Arbitrary Constraints
Publication: Journal of Engineering Mechanics
Volume 121, Issue 6
Abstract
An analytical scheme is developed for the free and forced vibrations of a one-dimensional structure with arbitrary intermediate constraints and boundaries. Upon applying eigenanalysis to governing differential equations for a continuous medium or a conventional transfer matrix for a discrete medium, the vibration motion is interpreted as a wave motion. The structure is treated accordingly as a waveguide, composed of side-by-side subwaveguides including intermediate constraints, boundaries, and uniform sections without apparent constraints. Reflection and transmission matrices are derived to characterize wave scattering phenomena for individual subwaveguides. Similar matrices for a union of multiple subwaveguides are obtained through a composition rule. The quantitative descriptions of a wave-scattering mechanism make it possible to effectively determine the characteristic equation for the free-vibration and response solutions for the forced vibration. Because the subwaveguides are treated equally in this approach, their numbers and change patterns from one section to the other are immaterial in the analysis.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bapat, A. V., and Suryanarayan, S.(1990). “A new approach for the continuum representation of point supports in vibration analysis of beams.”J. Sound and Vibration, 143(2), 199–219.
2.
Dowell, E. H. (1979). “On some general properties of combined dynamic systems.”J. Appl. Mech., Vol. 46, 206–209.
3.
Lin, Y. K., and McDaniel, T. J. (1969). “Dynamics of beam-type periodic structures.”J. Engrg. for Industry, Vol. 91, 1133–1141.
4.
Lin, Y. K., and Donaldson, B. K. (1969). “A brief survey of transfer matrix techniques with special reference to the analysis of aircraft panels.”J. Sound and Vibration, Vol. 10, 103–143.
5.
Mace, B. R. (1984). “Wave reflection and transmission in beams.”J. Sound and Vibration, Vol. 97, 237–246.
6.
McDaniel, T. J., and Eversole, K. B. (1977). “A combined finite element–transfer matrix structural analysis method.”J. Sound and Vibration, Vol. 51, 157–169.
7.
Mead, D. J., and Yaman, Y.(1990). “This harmonic response of uniform beams on multiple linear supports: a flexural wave analysis.”J. Sound and Vibration, 141(3), 465–484.
8.
Pestel, E. C., and Leckie, F. A. (1963). Matrix methods in elasto-mechanics . McGraw-Hill Book Co., New York, N.Y.
9.
von Flotow, A. H. (1986). “Disturbance propagation in structural networks.”J. Sound and Vibration, Vol. 106, 433–450.
10.
Yang, B.(1992). “Transfer functions of constrained/combined one-dimensional continuous dynamic systems.”J. Sound and Vibration, 156(3), 425–443.
11.
Yong, Y. (1991). “Vibration of Euler-Bernoulli beams with arbitrary boundaries and intermediate constraints.”Proc., ASME 13th Biennial Conf. on Mech. Vibration and Noise, Am. Soc. of Mech. Engrs. (ASME), New York, N.Y., DE-Vol. 36, 119–128.
12.
Yong, Y., and Lin, Y. K.(1989). “Propagation of decaying waves in periodic and piecewise periodic structures of finite length.”J. Sound and Vibration, 129(2), 99–118.
13.
Yong, Y., and Lin, Y. K. (1992). “Dynamic response analysis of truss-type structural networks: a wave propagation approach.”J. Sound and Vibration, Vol. 156, 27–45.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 121 • Issue 6 • June 1995
Pages: 730 - 736
Copyright
Copyright © 1995 American Society of Civil Engineers.
History
Published online: Jun 1, 1995
Published in print: Jun 1995
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.