A time‐integration algorithm for non‐linear dynamic systems of first and second order. Issue 1 (12th November 2019)

• Record Type: Journal Article
• Authors: Holl, Helmut J.
• Other Names: Eberhardsteiner J. guestEditor.; Schöberl M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 19:Issue 1(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-11-12
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201900397
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: Non‐linear dynamic systems are defined by mechanical models involving differential equations of second order where also first order differential equations are present frequently. If some degrees of freedom have no corresponding mass, if the stiffness parameters vanish in a part of the equations or if a controller is implemented in the system, then differential equations of first order result. For linear systems of first and second order a variety of solutions is presented in [1] and various numerical procedures for solving the differential equations in [2]. A semi‐analytical method is presented which is exact for the linear dynamic and decoupled systems of first and second order. A modal transformation of the equations is necessary after a suitable partitioning of the system equations. After a discretisation in the time‐domain the relevant equations for a suitable and effective time‐integration algorithm are defined taking the non‐linearity into account. The resulting procedure is derived and the formulation is analogous to the BEM‐formulation in time, described in [3] for a system of second order. The method is extended to the coupled non‐linear differential equations of first order and is applied to a system with two degrees of freedom.