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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 44
Edited by: B.H.V. Topping
Paper V.3

Simulation of the Duffing Oscillator with Time-Varying Mass by a BEM in Time

H.J. Holl, A.K. Belyaev and H. Irschik

Division of Technical Mechanics, Johannes Kepler University of Linz, Linz, Austria

Full Bibliographic Reference for this paper
H.J. Holl, A.K. Belyaev, H. Irschik, "Simulation of the Duffing Oscillator with Time-Varying Mass by a BEM in Time", in B.H.V. Topping, (Editor), "Advances in Boundary Element Methods", Civil-Comp Press, Edinburgh, UK, pp 113-120, 1996. doi:10.4203/ccp.44.5.3
A semi-analytical time-integration procedure is presented in the following for the integration of discretized dynamic mechanical systems. This method utilizes the advantages of the boundary element method (BEM), well known from quasi-static field problems. Motivated by these spatial formulations, the present dynamic method is based on influence functions in time, and gives exact solutions in the linear time-invariant case. Similar to domain-type BEM's for non-linear field problems, the method is extended for nonlinear and lime-varying dynamic systems, where the Duffing oscillator with time-varying mass is used as a representative model problem. The numerical stability and accuracy of the semi-analytical method is discussed in separated steps for time-varying masses and for nonlinear Duffing type restoring forces. As an illustrative example, a Duffing oscillator with exponentially varying mass is studied in some detail. The case of a linear restoring force and an exponentially varying mass is compared to the closed form solution, derived in the present paper. A sinusoidal variation of the mass in time is studied, too.

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