TECHNICAL PAPERS
Aug 1, 1997

Response of Elastic Continuum Carrying Moving Linear Oscillator

Publication: Journal of Engineering Mechanics
Volume 123, Issue 8

Abstract

This paper presents a method for solving the problem of the dynamic response of a continuous elastic structure carrying a moving linear oscillator. The method 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 method is simple and elegant and can be applied to any conservative spatially one-dimensional continuum with arbitrary boundary conditions.

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References

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Azarov, V. L., Lupichev, L. N., and Tavrizov, G. A. (1975). Mathematical methods for investigation of complex physical systems. Nauka, Moscow, Russia (in Russian).
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Bogacz, R., and Szolc, T. (1993). “On dynamic interaction between the moving oscillator and a discrete-continuous system.”ZAMM, 73(4–5), T195.
3.
Fryba, L. (1972). Vibration of solids and structures under moving loads. Noordhoff International Publishing, Groningen, The Netherlands.
4.
Lyusternik, L. A., and Sobolev, V. I. (1974). Elements of functional analysis, 3rd Ed. John Wiley & Sons, Inc., New York, N.Y.
5.
Pesterev, A. V., and Bergman, L. A.(1997). “Vibration of elastic continuum carrying accelerating oscillator.”J. Engrg. Mech., ASCE, 123(8), 886–889.
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Pesterev, A. V., and Tavrizov, G. A.(1994a). “Vibrations of beams with oscillators. I: Structural analysis method for solving the spectral problem.”J. Sound and Vibration, 170(4), 521–536.
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Pesterev, A. V., and Tavrizov, G. A. (1994b). “On inversion of some meromorphic matrices.”Linear Algebra and Its Applications, 212/213, 505–521.
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Sadiku, S., and Leipholz, H. H. E.(1987). “On the dynamics of elastic systems with moving concentrated masses.”Ingenieur-Archiv, 57, 223–242.
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Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 123Issue 8August 1997
Pages: 878 - 884

History

Published online: Aug 1, 1997
Published in print: Aug 1997

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Authors

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Alexander V. Pesterev
Inst. for System Analysis, Russian Academy of Sciences, pr. 60-letiya, Oktyabrya 9, Moscow, 117312 Russia.
Lawrence A. Bergman, Member, ASCE
Prof., Aeronautical and Astronautical Engrg. Dept., Univ. of Illinois, 104 South Wright St., Urbana, IL 61801.

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