A numerical algorithm for nonlinear dynamic problems based on BEM

• Published in: Engineering analysis with boundary elements Vol. 23; no. 5; pp. 503 - 513
• Main Authors: Holl, H.J., Belyaev, A.K., Irschik, H.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.05.1999
• Subjects: Nonlinear dynamic systems; Rotordynamic system; Time-integration; Time-varying mass; Time-varying mass; Nonlinear dynamic systems; Time-integration; Rotordynamic system
• ISSN: 0955-7997; 1873-197X
• DOI: 10.1016/S0955-7997(98)00105-2

A semi-analytical time-integration procedure for the integration of discretized dynamic mechanical systems is presented. 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 nonlinear field problems, the method is extended for different nonlinear dynamic systems having nonclassical damping and time-varying mass. The numerical stability and accuracy of the semi-analytical method is discussed in two steps for the nonclassical damping and for the nonlinear restoring forces, e.g. of the Duffing type. The damped Duffing oscillator and a linear oscillator with time-varying mass are used as representative model problems. For a nonlinear rotordynamic system, a comparison is given to other conventionally used time integration procedures, which shows the efficiency of the present method.