Nonlinear Moment Matching for the Simulation-Free Reduction of Structural Systems

Abstract

This paper transfers the concept of moment matching to nonlinear structural systems and further provides a simulation-free reduction scheme for such nonlinear second-order models. After first presenting the steady-state interpretation of linear moment matching, we then extend this reduction concept to the nonlinear second-order case based on Astolfi [2010]. Then, similar simplifications as in Cruz Varona et al. [2019] are proposed to achieve a simulation-free nonlinear moment matching algorithm. A discussion on the simplifications and their limitations is presented, as well as a numerical example which illustrates the efficiency of the algorithm.

A Novel Derivation for Modal Derivatives Based on Volterra Series Representation and Its Use in Nonlinear Model Order Reduction

“…In many publications, e.g. [27,19,23,3], it has been shown that the reduction of a nonlinear structural system with a pure linear reduction basis V φ = φ 1,eq , . .…”

“…The symmetric tensors K (1) ∈ R n×n , K (2) ∈ R n×n×n and K (3) ∈ R n×n×n×n can be obtained from different strategies [11,19]: they can be calculated analytically within the finite element assembly procedure, numerically via finite differences, or identified via e.g. the Implicit Condensation and Expansion (ICE) method [6] or the Enforced Displacement (ED) method [12,17].…”

“…to reformulate the solution q 2 (t) in (40) a little differently and also for later purposes. Using the trigonometric product-to-sum identities 3 , the solution of the second subsystem can be rewritten as:…”