Dynamic stability of an infinite Euler's beam resting on a three-parameter inertial Vlasov foundation

• Autorzy: Szcześniak W.

Warianty tytułu

PL

Stateczność dynamiczna nieskończonej belki Eulera spoczywającej na trójparametrowym podłożu Własowa

• Języki publikacji: EN

Abstrakty

EN

The paper deals with dynamic stability of an infinite Euler's beam subjected to an infinitely long, inertial, uniformly distributed continuous moving load of constant intensity. The beam rests on a three-parameter unidirectional inertial one- or two-layer foundation of the Vlasov type. A new method of taking into account the offset of the ballast in the transverse sections of the beam is put forward. A critical force has been evaluated. This force depends not only upon the parameters of the moving load, i.e. its mass mp and velocity v , but also upon the three parameters of the inertial foundation: k0 , c0 and m0 .

PL

Przedmiotem rozważań jest stateczność dynamiczna nieskończonej belki Eulera spoczywającej na trójparametrowym inercyjnym podłożu Własowa. Nieskończenie długi ruchome, inercyjne obciążenie ciągłe porusza się po belce ze stałą prędkością. Po rozwiązaniu zadania metodą analityczną wyznaczono prędkość i dynamiczną siłę krytyczną zależną od masy belki, masy podłoża, masy ruchomego obciążenia i od parametrów mechanicznych belki i podłoża. Zadanie ma zastosowanie praktyczne w kolejnictwie i drogownictwie.

Słowa kluczowe

EN

dynamic stability; Euler's beam

PL

stateczność dynamiczna; belka Eulera

• Wydawca: Wydawnictwo Politechniki Świętokrzyskiej
• Czasopismo: Zeszyty Naukowe Politechniki Świętokrzyskiej. Nauki Techniczne
• Rocznik: 2007
• Tom: Z. 6
• Strony: 165--178
• Opis fizyczny: Bibliogr. 26 poz., rys., wzory

Twórcy

autor

Szcześniak W.

• Warsaw University of Technology, Faculty of Civil Engineering, Institute of Structural Mechanics, Armii Ludowej Street 16, 00-637, Poland

Bibliografia

• 1. VlasovV.Z. Beams, plates and shells on elastic foundation(in Russian) GIF-ML, Moscow 1960
• 2. Wieghardt K. Über den Balken auf nachgiebiger Unterlage, ZAMM, Vol.2, 3, (1922), pp. 165-184
• 3. Pasternak P.L. On a new method of analysis of foundations lying on elastic subsoil, with the help of two interaction coefficients. (in Russian) Moscow-Leningrad Gos. Izdat. Literatury po Stroitelstvu i Arkhitekture. 1954
• 4. Pasternak P.L. On a new method of analysis of rigid and flexible foundations on an elastic subsoil. (in Russian) Sbornik Trudov MISI No 14, 1956, pp.116-144
• 5. Filonenko-Borodich M.M. Selected approximate theories of an elastic foundation (in Russian). Uchenye Zapiski MGU, issue 46, 1940, pp. 3-18
• 6. Winkler E. Die Lehre von der Elasticitaet und Festigkeit, Prag, Dominicus, 1867
• 7. Meshcheryakov Yu M. Survey of Soviet papers on plates and beams on a compressive foundation (review for years 1917-1967) (in Russian). Osnovanii i Podzemnykh Sooruzhenii 1967
• 8. Lvovskii V.M. Three-dimensional vibrations of an infinite beam lying on an inertial elastic foundation, subject to a continuously distributed moving load (in Russian). Izv.Visshikh Uchebnykh Zavedenii, Lesnoi Zhurnal No 5,1963, pp. 56-67
• 9. Lvovskii V.M. On uniform motion of a point load along an infinite beam lying on an inertial elastic two-layer foundation.(in Russian) No 2, 1964,pp.81-88
• 10. Lvovskii V.M. Vibrations of a beam-like plate lying on a nonlinear inertial elastic foundation subject to a moving load. (in Russian) Izv. VUZ, Stroitelstvo i Arkhitektura No 9, 1970, pp. 37-45
• 11. Lvovskii V.M, Lvovskii B.V. A contact problem for a circular punch on a two-layer foundation.(in Russian) Soprotivlenie Materialov i Teoria Sooruzhenii, issue No 38, Kiev.1976, pp. 34-41
• 12. DanovichV.D. Vibrations of an infinite beam on an elastic foundation with a varying coefficient of damping of displacements (in Russian) Mezhvuzovskii Sbornik Nauchnykh Trudov, issue 204/21, pp. 77-88, Dniepropetrovsk 1979.
• 13. DanovichV.D. Vibrations of a beam of infinite length lying on an elastic two-parameter foundation, subject to a moving harmonic load. (in Russian) In: “Strength and Stability of Complex Mechanical Systems”. Kiev 1979, Naukova Dumka, pp.135-141
• 14. Lazaryan V.A., DanovichV.D. Differential equations of plane vibrations of a train moving on an inertial railroad. (in Russian) In: “Selected Problems of Mechanics of Fast Transport”. Naukova Dumka, Kiev 1970, pp.142-148
• 15. Lazaryan V.A., Litvin I.A. Differential equations of plane vibrations of a train moving on an inertial railroad (in Russian). In: “Selected problems of Mechanics of Fast Transport”. Naukova Dumka, Kiev 1970, pp. 61-73
• 16. Szczesniak W. Effect of axial forces and shear of the foundation on amplitudes of vibrations of an infinite beam under a moving load. (in Polish) Prace Naukowe Politechniki Warszawskiej, Budownictwo Nr 56, 1977, pp. 19-36
• 17. Jemielita G, Szczesniak W. Methods of modelling foundations of structures. (in Polish) Prace Naukowe Politechniki Warszawskiej, Budownictwo Nr 120, 1993, pp. 1-62
• 18. Newland D.E. Instability of an elastically supported beam under a travelling inertial load, J. Mech. Eng. Sci., Vol. 12, No.5, 1970, pp. 373-374
• 19. Valsangkar R., Pradhanang R. Vibrations of beam-columns on two-parameter elastic foundations, Earthquake Eng. Struct. Dyn., 16, 1988, pp. 1103-1114
• 20. Szczesniak W. Dynamic stability of Euler's and Timoshenko's beams subject to moving inertial loadings. (in Polish), Prace Naukowe Politechniki Warszawskiej, Budownictwo, vol. 129, 1995, cf. also Proceedings of the Polish-Russian Seminar: Theoretical Foundations of Civil Engineering. Moscow, 1994, pp. 94-105
• 21. Kerr A.D. Étude relative a la stabilité de voie ferée dans le plan vertical, Rail International, Fév. 1974, pp. 169-183
• 22. Kerr A.D. (ed.) Railroad track mechanics and technology, Pergamon Press, 1975
• 23. Saito H., Murakami T. Vibrations of an infinite beam on elastic foundation with consideration of mass of a foundation for moving loads, Bult. JSME, Vol. 12, No.50, 1969, pp. 200-205
• 24. Saito H., Terasawa T. Steady-state vibrations of a beam on a Pasternak foundation for moving loads, J. Appl. Mech., Vol. 47,4, 1980, pp. 879-883
• 25. Holder B.W., Michalopoulos C.D. Response of a beam on an inertial foundation to a travelling load, AIAA Journal, Vol. 15,8, 1977, pp. 1111-1115
• 26. Jaiswal O.R., Iyengar R.N. Dynamic response of a beam on elastic foundation of finite depth under a moving force, Acta Mechanica 96, 1993, pp. 67-83