Response of Elastic Continuum Carrying Multiple Moving Oscillators
Publication: Journal of Engineering Mechanics
Volume 127, Issue 3
Abstract
The problem of calculating the dynamic response of a one-dimensional distributed parameter system carrying multiple moving oscillators is examined. A solution procedure is suggested that reduces the problem to the integration of a system of linear ordinary differential equations governing the time-dependent coefficients of the series expansion of the response in terms of the eigenfunctions of the continuous structure. The program implementation of the solution procedure is discussed and numerical results are presented. Numerical illustrations clearly demonstrate that the incorporation of even one additional oscillator into the model makes the dynamics of the system vibration considerably more complicated.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Adams, G. G. ( 1995). “Critical speeds and the response of a tensioned beam on an elastic foundation to repetitive moving loads.” Int. J. Mech. Sci., 37(7), 773–781.
2.
Chen, C. H., and Wang, K. W. ( 1994). “An integrated approach toward the modeling and dynamic analysis of high-speed spindles. II: Dynamics under moving end load.” J. Vibration and Acoustics, 116, 514–522.
3.
Delgado, R. M., and S. M. dos Santos, R. C. ( 1997). “Modeling of railway bridge-vehicle interaction in high speed tracks.” Comp. and Struct., 63(3), 511–523.
4.
Diana, G., and Cheli, F. ( 1989). “Dynamic interaction of railway systems with large bridges.” Vehicle Syst. Dyn., 18, 71–106.
5.
Henchi, K., Fafard, M., Talbot, M., and Dhatt, G. ( 1998). “An efficient algorithm for dynamic analysis of bridges under moving vehicles using a coupled modal and physical components approach.” J. Sound and Vibration, 212(4), 663–683.
6.
Hwang, E. S., and Nowak, A. S. (1991). “Simulation of dynamic load for bridges.”J. Struct. Engrg., ASCE, 117(5), 1413–1434.
7.
Iwan, W. D., and Moeller, T. L. ( 1976). “The stability of a spinning elastic disk with a transverse load system.” J. Appl. Mech., 43(3), 485–490.
8.
Iwankiewicz, R., and niady, P. ( 1984). “Vibration of a beam under a random stream of forces.” J. Struct. Mech., 12, 13–26.
9.
Jeffcott, H. H. ( 1929). “On the vibrations of beams under the action of moving loads.” Philosophical Mag., 7(8), 66–97.
10.
Li, J., and Su, M. ( 1999). “The resonant vibration for a simply supported girder bridge under high-speed trains.” J. Sound and Vibration, 224(5), 897–915.
11.
Mote, C. D., Jr. ( 1970). “Stability of circular plates subjected to moving loads.” J. Franklin Inst., 290(4), 329–344.
12.
Pesterev, A. V., and Bergman, L. A. (1997a). “Response of elastic continuum carrying moving linear oscillator.”J. Engrg. Mech., ASCE, 123(8), 878–884.
13.
Pesterev, A. V., and Bergman, L. A. (1997b). “Vibration of elastic continuum carrying accelerating oscillator.”J. Engrg. Mech., ASCE, 123(8), 886–889.
14.
Pesterev, A. V., and Bergman, L. A. ( 1998). “Response of a nonconservative continuous system to a moving concentrated load.” J. Appl. Mech., 65, 436–444.
15.
Pesterev, A. V., and Bergman, L. A. ( 2000). “An improved series expansion of the solution to the moving oscillator problem.” J. Vibration and Acoustics, 122, in press.
16.
Sadiku, S., and Leipholz, H. H. E. ( 1987). “On the dynamics of elastic systems with moving concentrated masses.” Ingenieur-Archiv, 57, 223–242.
17.
niady, P. ( 1989). “Dynamic response of linear structures to a random stream of pulses.” J. Sound and Vibration, 131, 91–102.
18.
Staniić, M. M. ( 1985). “On a new theory of the dynamic behavior of the structures carrying moving masses.” Ingenieur-Archiv, 55, 176–185.
19.
Taheri, M. R., Ting, E. C., and Kukreti, A. R. ( 1990). “Vehicle-guideway interactions: a literature review.” Shock and Vibration Dig., 22, 3–9.
20.
Ting, E. C., and Yener, M. ( 1983). “Vehicle-structure interactions in bridge dynamics.” Shock and Vibration Dig., 15(2), 3–9.
21.
Yang, B. ( 1996). “Integral formulas for non-self-adjoint distributed dynamic systems.” AIAA J., 34, 2132–2139.
22.
Yang, B., Tan, C. A., and Bergman, L. A. ( 1998). “On the problem of a distributed parameter system carrying a moving oscillator.” Dynamics and control of distributed systems, H. Tzou and L. Bergman, eds., Cambridge University Press, New York, 69–94.
23.
Yang, Y. B., and Lin, B. H. (1995). “Vehicle-bridge interaction analysis by dynamic condensation method.”J. Struct. Engrg., ASCE, 121(11), 1636–1643.
24.
Yang, Y. B., and Yau, J. D. (1997). “Vehicle-bridge interaction element for dynamic analysis.”J. Struct. Engrg., ASCE, 123(11), 1512–1518.
25.
Zhu, W. D., and Mote, C. D., Jr. ( 1994). “Free and forced response of an axially moving string transporting a damped linear oscillator.” J. Sound and Vibration, 177(5), 591–610.
Information & Authors
Information
Published In
History
Received: Dec 20, 1999
Published online: Mar 1, 2001
Published in print: Mar 2001
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.