A generalized constraint reduction method for reduced order MBS models

Abstract

In this paper we deal with the problem of ill-conditioned reduced order models in the context of redundant formulated nonlinear multibody system dynamics. Proper Orthogonal Decomposition is applied to reduce the physical coordinates, resulting in an overdetermined system. As the original set of algebraic constraint equations becomes, at least partially, redundant, we propose a generalized constraint reduction method, based on the ideas of Principal Component Analysis, to identify a unique and well-conditioned set of reduced constraint equations. Finally, a combination of reduced physical coordinates and reduced constraint coordinates are applied to one purely rigid and one partly flexible largescale model, pointing out method strengths but also applicability limitations.

On the relevance of inertia related terms in the equations of motion of a flexible body in the floating frame of reference formulation

“…The third benefit is that negligence of the terms including W 1 , W 2 and W 3 leads to equations of motion where the mass matrix and the quadratic velocity vector are decoupled with respect to the translational, rotational and flexible degrees of freedom. This fact simplifies considerations with respect to separated time integration [19] or model reduction of multibody systems [22] tremendously.…”

Vibration Reduction in Ballasted Track Using Ballast Mat: Numerical and Experimental Evaluation by Wheelset Drop Test

“…This procedure is usually achieved through model reduction on the degrees of freedom (DOFs) of finite element model. Various reduction techniques can be applied to the finite element model, such as the Guyan method, dynamic condensation method, and component mode synthesis method [25][26][27][28][29]. According to the Guyan method, the undamped system vibration equation takes the following form:…”

A new approach to model reduction of nonlinear control systems using smooth orthogonal decomposition

“…The methodologies for obtaining low-dimensional subspaces are, though not limited to, linear normal modes [15,16], proper orthogonal decomposition (POD) (also known as singular value decomposition, principal component analysis, or Karhunen-Loève expansion) [8,[17][18][19][20][21][22][23], and SOD [5][6][7]24]. In addition, Krylov subspace projections [25], Hankel norm approximations [26][27][28][29], truncated balance realizations [30,31], and a recently developed Beysian approach [32] are to be mentioned.…”