Simulation of the Duffing-oscillator with time-varying mass by a BEM in time

✍ Scribed by H.J. Holl; A.K. Belyaev; H. Irschik

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 259 KB
• Volume: 73
• Category: Article
• ISSN: 0045-7949
• DOI: 10.1016/s0045-7949(98)00281-8

✦ Synopsis

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 ®eld problems. Motivated by these spatial formulations, the present dynamic method is based on in¯uence functions in time, and gives exact solutions in the linear time-invariant case. Similar to domaintype BEMs for nonlinear ®eld problems, the method is extended for nonlinear and time-varying dynamic systems, where the Dung oscillator with time-varying mass is used as a representative model problem. The numerical stability and accuracy of the semi-analytical method are discussed in separated steps for time-varying masses and for nonlinear Dung type restoring forces. As an illustrative example, a Dung 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.