Analysis of Dynamic Interaction Between the Continuous String and Moving Oscillator
The paper presents the analysis of dynamic interaction between a discrete oscillator of two degrees of freedom and a finite continuous string suspended on rigid and visco-elastic concentrated supports. This oscillator moves along the string with a constant sub-critical or super-critical speed. Dynamic transverse displacements of the string as well as the contact force between the oscillator and the string are determined using the d'Alembert solutions of the wave motion equations. Such approach leads to a system of algebraic and ordinary differential equations with a "shifted" argument which are solved numerically in an appropriate sequence. From the performed comparison of numerical results for the sub-critical oscillator speeds with analogous results obtained by means of the finite element method it follows, that the method based on the d'Alembert solutions in the form of travelling waves seems to be more accurate. Moreover, the approach proposed in the paper is numerically very efficient which makes it advantageous for investigations of more complex systems.
L.FRYBA, Vibrations of solids and structures under moving loads, Academia/Groningen: Noordhoff International Publishing, Prague 1972.
S.KALISKI, Vibrations and waves in solids [in Polish], PWN Warszawa 1966.
S.CHONAN, Moving harmonic load on an elastically supported Timoshenko beam, Z. Angew. Math. Mech., 58, pp. 9-15, 1978.
R.BOGACZ, On self-excitation of moving oscillator interacting at two points with a continuous system, Nonlinear Vibration Problems, 16, pp, 239-250, 1979.
M.RIEMER, Anwendung des Prinzips von Hamilton auf die mit konstanter Geschwindigkeit bewegte Saite, Z. Angew. Math. Mech., 66, 4, T78-T80, 1986.
R.BOGACZ, T.KRZYŻYŃSKI, K.POPP, On generalization of Mathew's problem of the vibration of beam on elastic foundation, Z. Angew. Math. Mech., 69, pp. 243-252, 1989.
R.BOGACZ, T.SZOLC, On methods of solution for the discrete-continuous system under moving load, Z. Angew. Math. Mech., 72, 4, T16-T19, 1992.
M.LINK, B.NOWAK, Zur dynamischen Analyse des Systems Stromabnehmer und Fahrleitung, dargestellt am Beispiel des Intercity-Experimental [in German], Proc. of the Conference on "Dynamik Fortschrittlicher Bahnsysteme", VDI Berichte, 635, 1987.
B.NOWAK, M.LINK, Zur Optimierung der dynamischen Parameter des ICE-Stromabnehmers durch Simulation der Fahrdynamik [in German], VDI Berichte, Nr. 635, pp. 147-166, 1987.
A.RENGER, Dynamical analysis of pantograph and catenary system, Proc. of the 16th Int. Conf. on Dynamics of Machines, Stupava, Czechoslovakia, Vol. II, pp. 46-53, 1989.
R.MEISINGER, Dynamic analysis of active and passive ICE pantographs, Proc. of the 5th Symposium on Dynamic Problems of Mechanics "Diname'93", Santo Amaro da lmperatriz, Santa Catarina, Brasilia, pp. 256-258, March 1993.
Copyright © 2014 by Institute of Fundamental Technological Research
Polish Academy of Sciences, Warsaw, Poland