Shift Independent Model Reduction of Large Scale Second Order Mechanical Structures

Abstract

Nonmodal model order reduction (MOR) techniques present accurate and efficient ways to approximate input–output behavior of largescale mechanical structures. In this regard, Krylovbased model reduction techniques for secondorder mechanical structures are typically known to require a priori knowledge of the original system parameters, such as expansion points (or eigenfrequencies). The calculation of the eigenfrequencies of the original finiteelement (FE) model can be significantly timeconsuming for largescale structures. Existing iterative rational Krylov algorithm (IRKA) addresses this issue by iteratively updating the expansion points for firstorder formulations until convergence criteria are achieved. Motivated by preserving the model properties of secondorder systems, this paper extends the IRKA method to secondorder formulations, typically encountered in mechanical structures. The proposed secondorder IRKA method is implemented on a largescale system as an example and compared with the standard Krylov and CraigBampton reduction techniques. The results show that the secondorder IRKA method provides tangibly reduced error for a multiinputmultioutput (MIMO) mechanical structure compared to the CraigBampton. In addition, unlike the standard Krylov methods, the secondorder IRKA does not require the information on expansion points, which eliminates the need to perform a modal analysis on the original structure. This can be especially advantageous for largescale systems where calculations of the eigenfrequencies of the original structure can be computationally expensive. For such largescale systems, the proposed MOR technique can lead to significant reductions of the computational time.