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New feature of the solution of a Timoshenko beam carrying the moving mass particle

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Języki publikacji
EN
Abstrakty
EN
The paper deals with the problem of vibrations of a Timoshenko beam loaded by a travelling mass particle. Such problems occur in a vehicle/track interaction or a power collector in railways. Increasing speed involves wave phenomena with significant increase of amplitudes. The travelling speed approaches critical values. The moving point mass attached to a structure in some cases can exceed the mass of the structure, i.e. a string or a beam, locally engaged in vibrations. In the literature, the travelling inertial load is often replaced by massless forces or oscillators. Classical solution of the motion equation may involve discussion concerning the contribution of the Dirac delta term, multiplied by the acceleration of the beam in a moving point in the differential equation. Although the solution scheme is classical and successfully applied to numerous problems, in the paper the Lagrange equation of the second kind applied to the problem allows us to obtain the final solution with new features, not reported in the literature. In the case of a string or the Timoshenko beam, the inertial particle trajectory exhibits discontinuity and this phenomenon can be demonstrated or proved mathematically in a particular case. In practice, large jumps of the travelling inertial load is observed.
Rocznik
Strony
327--341
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
autor
autor
  • Institute of Fundamental Technological Research Polish Academy of Sciences Pawińskiego 5b 02-106 Warszawa, Poland, bdynie@ippt.gov.pl
Bibliografia
  • 1. M. Olsson, On the fundamental moving load problem, Journal of Sound and Vibration, 154, 2, 299–307, 1991.
  • 2. L. Fryba, Vibrations of solids and structures under moving loads, Thomas Telford House, 1999.
  • 3. A.V. Pesterev, L.A. Bergman, C.A. Tan, T.-C. Tsao, B. Yang, On asymptotics of the solution of the moving oscillator problem, J. Sound and Vibr., 260, 519–536, 2003.
  • 4. W.W. Bolotin, On the influence of moving load on bridges [in Russian], Reports of Moscow University of Railway Transport MIIT, 74, 269–296, 1950.
  • 5. G. Michaltsos, D. Sophianopoulos, A.N. Kounadis, The effect of a moving mass and other parameters on the dynamic response of a simply supported beam, J. Sound Vibr., 191, 357–362, 1996. New feature of the solution of a Timoshenko beam. . . 341
  • 6. E.C. Ting, J. Genin, J.H. Ginsberg, A general algorithm for moving mass problems, J. Sound Vib., 33, 1, 49–58, 1974.
  • 7. S. Mackertich, Response of a beam to a moving mass, J. Acoust. Soc. Am., 92, 1766–1769, 1992.
  • 8. U. Lee, Separation between the flexible structure and the moving mass sliding on it, J. Sound Vibr., 209, 5, 867–877, 1998.
  • 9. S. Sadiku, H.H.E. Leipholtz, On the dynamics of elastic systems with moving concentrated masses, Ingenieur-Archiv, 57, 223–242, 1987.
  • 10. M.A. Foda, Z. Abduljabbar, A dynamic Green function formulation for the response of a beam structure to a moving mass, J. Sound Vibr., 210, 295–306, 1998.
  • 11. M. Ichikawa, Y. Miyakawa, A. Matsuda, Vibration analysis of the continuous beam subjected to a moving mass, J. Sound Vibr., 230, 493–506, 2000.
  • 12. A.V. Kononov, R. de Borst, Instability analysis of vibrations of a uniformly moving mass in one and two-dimensional elastic systems, European J. Mech., 21, 151–165, 2002.
  • 13. C.E. Smith, Motion of a stretched string carrying a moving mass particle, J. Appl. Mech., 31, 1, 29–37, 1964.
  • 14. B. Dyniewicz, C.I. Bajer, Paradox of the particle’s trajectory moving on a string, Arch. Appl. Mech., 79, 3, 213–223, 2009.
  • 15. P. Antosik, J. Mikusiński, R. Sikorski, Theory of distributions. The sequential approach, Elsevier-PWN, Amsterdam-Warsaw 1973.
  • 16. L. Schwartz, Theory of distributions I [in French], Paris 1950.
  • 17. A. H. Zemanian, Distribution Theory and Transform Analysis: An Introduction to Generalized Functions, with Applications, Dover Publications, 1987.
  • 18. W. Flügge, E.E. Zajac, Bending impact waves in beams, Ingenieur-Archiv, 28, 2, 59–70, 1959.
  • 19. C.I. Bajer, B. Dyniewicz, Space-time approach to numerical analysis of a string with a moving mass, Int. J. Numer. Meth. Engng., 76, 10, 1528–1543, 2008.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT4-0010-0001
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