Vibrations of double-string complex system under moving forces. Closed solutions |
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Authors: | Jaros?aw Rusin Piotr ?niady |
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Affiliation: | a Institute of Civil Engineering, Wroc?aw University of Technology, Poland 50-370 Wroc?aw, Wybrze?e Wyspiańskiego 27, Poland b Institute of Mathematics, Polish Academy of Sciences, ul. ?niadeckich 8, 00-956 Warszawa, Poland |
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Abstract: | In this paper the dynamic response of a double-string system traversed by a constant or a harmonically oscillating moving force is considered. The force is moving with a constant velocity on the top string. The strings are identical, parallel, one upon the other and continuously coupled by a linear Winkler elastic element. The classical solution of the response of a double-string system subjected to a force moving with a constant velocity has a form of an infinite series. The main goal of this paper is to show that in the considered case a part of the solution can be presented in a closed, analytical form instead of an infinite series. The presented method of finding the solution in a closed, analytical form is based on the observation that the solution of the system of partial differential equations in the form of an infinite series is also a solution of an appropriate system of ordinary differential equations. |
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