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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.
Słowa kluczowe
Czasopismo
Rocznik
Tom
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
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- 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.
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- 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.
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- 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