Optimal modal reduction of dynamic subsystems: Extensions and improvements

Abstract

SUMMARYThe problem of optimal reduction of a linear dynamic subsystem is revisited. The subsystem may represent, for example, a complex but minor part of a large elastic structure. The goal is to drastically reduce the number of degrees of freedom of a subsystem attached through an interface to a main system in such a way as to affect the dynamic behavior of the main system in the least possible way. In a recent publication, the Optimal Modal Reduction (OMR) algorithm was developed to this end. This algorithm seeks a reduction of the subsystem that will have minimal effect, in the L 2 norm, on the Dirichlet-to-Neumann (DtN) map on the interface. Here this algorithm is extended and improved in a number of ways. First, a family of alternative formulations are derived for the DtN map, which lead to alternative OMR algorithms; one of them, called OMR j=2 , is shown to yield better results than the original formulation. Second, the OMR algorithm, which was originally developed for undamped subsystems, is extended to subsystems undergoing Rayleigh damping. In addition, an enhanced derivation of the original OMR algorithm is presented, and the good pointwise performance of OMR is explained by relating to minimization with respect to the H 1 norm. The extensions mentioned above are discussed theoretically as well as demonstrated via numerical examples. Experiments and discussion include comparison of the OMR algorithm to simple coarsening of the subsystem discretization. In all cases, central finite difference discretization in space and explicit time-stepping are employed to solve the scalar wave equation.

Multiphysics model reduction of symmetric vibro‐acoustic formulation with a priori error estimation criteria

“…In the ROM field, it is very difficult to construct a reduced model of appropriate size to satisfy both efficiency and accuracy, which is one of the most important issues. To handle this issue, a lot of researchers have developed various techniques for traditional model reduction of structural dynamics and vibration 7,8,17‐24,26‐29,32 . However, it is still an open question in the field of multiphysics including FSI.…”

“…Section 4 develops a new mode selection procedure for coupled FSI model reduction process. To this end, we adopt various salient features of existing structural mode selection criteria 17‐24 and adapt them to be applicable for coupled acoustic‐structure interaction problems. The mode selection issue becomes much more complicated in the multiphysics problems that should consider over two physics at once.…”

Position-Dependent Multibody Dynamic Modeling of Machine Tools Based on Improved Reduced Order Models

“…The reduced structural matrices by way of projection on the subspace T become A/«,., = T^MT, Kg^^ = T^KT, /^,^, = T^f (13) Since the reduction procedure involves eliminating a subset of DOFs from u, the system matrices are partitioned into exterior/ interface DOFs (E), and interior DOFs (I) as \ME M,,…”

“…Other methods [9,12,13] sort and retain the most significant modes based on the strength of interaction between the subsystem and the main system. Their main concern however, was not the dynamical substructural system, but its effect on the main system.…”

Reduction of Coupling Interface Degrees of Freedom in Mixed-Interface Component Mode Synthesis

“…In any type of the CMS methods, the most important and difficult task is choosing an appropriate reduced component modes involving modal reduction and mode synthesis, and this continues to be an area of research [15][16][17][18][19][20][21][22]. Lots of work have been done to make improvements on modal reduction of internal DOFs [23][24][25][26][27], but no order reduction is performed on the boundary.…”