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Stationary Action Principle for Vehicle System with Damping

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EN
Abstrakty
EN
The aim of this note is to show possible consequences of the principle of stationary action formulated for nonconservative sys tems. As an example, linear models of vibratory system with damping and with one and two degrees of freedom are considered. This kind of models are frequently used to describe road and rail vehicles. There are vibrations induced by road profile. The appropriate action functional is proposed with the Lagrangian density containing: the kinetic and potential energies as well as dissipative one. Possible variations of generalized coordinates are introduced together with a noncommutative rule between operations of taking variations of the coordinates and their time derivatives. The stationarity of the action functional leads to the EulerLagrange equations.
Rocznik
Strony
23--26
Opis fizyczny
Bibliogr. 17 poz., Wykr.
Twórcy
autor
autor
  • PolishJapanese Institute of Information Technology, Computer Science Department, ul. Koszykowa 86, 02008 Warsaw, Poland, wkos@pjwstk.edu.pl
Bibliografia
  • 1. Biot M. A. (1970), Variational principles in heat transfer, Oxford Mathematical Monographs, Oxford Univ.
  • 2. Chambers I. G. (1956), A variational principle for the conduction of heat., Q. J. Mech. Appl. Math., IX (2), 234–235.
  • 3. Grochowicz B., Kosiński W. (2011), Lagrange’s method for derivation of long line equations, Acta Technica, 56 (1), 331–341.
  • 4. Grzyb A. (2012), Optimal parameters selection of vibration dampers of dynamic vehicles system, Polioptymization and computer aided design (in Polish), Mielno, Kiczkowiak T., Tarnowski W. (red.), Wydaw. Uczelniane Politechniki Koszalińskiej, Koszalin, 20–31.
  • 5. Kosiński W., Perzyna P. (2012), On consequences of the principle of stationary action for dissipative bodies, Arch. Mech., 64 (1), 95–106.
  • 6. Kotowski R. (1989), On the Lagrange functional for dissipative processes, Arch. Mech., 41 (4), 571–587.
  • 7. Kotowski R. (1992), Hamilton’s principle in thermodynamics, Arch. Mech., 44 (2), 203–215.
  • 8. Lebon G., Lambermont J. (1973), Generalization of Hamilton’s principle to continuous dissipative systems, J. Chem. Phys., 59, 2929–2936.
  • 9. Marsden J. E., Hughes T. J. R. (1983), Mathematical Theory of Elasticity, Prentice-Hall, Englewood Cliffs, New York,
  • 10. Prigogine I., Glansdorff P. (1965), Variational properties and fluctuation theory, Physica, 31 (8), 1242–1256.
  • 11. Rosen P. (1954), Use of restricted variational principles for the solution of differential equations, J. Appl. Phys., 25, 336–338.
  • 12. Schechter R. S. (1967), The Variational Methods in Engineering, McGraw-Hill, New York.
  • 13. Vujanović B. (1971), An approach to linear and non-linear heat transfer problem using a Lagrangian, A. I. A. A. Journal, 9(1), 131–134.
  • 14. Vujanović B. (1974), On one variational principle for irreversible phenomena, Acta Mechanica, 19, 259–275.
  • 15. Vujanović B. (1975), A variational principle for nonconservative dynamical systems, ZAMM – Zeitschrift f¨ur Angewandte Mathematik und Mechanik, 55(6), 321–331.
  • 16. Vujanović B., Djukiić D. (1972), On one variational principle of Hamilton’s type for nonlinear heat transfer problem, International Journal of Heat and Mass Transfer, 15, 1111–1123.
  • 17. Yang Q. (2010), Hamilton’s principle for Green-inelastic bodies, Mechanical Research Communications, 37, 696–699.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB2-0073-0005
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