System equivalent model mixing

Abstract

This paper introduces SEMM: a method based on Frequency Based Substructuring (FBS) techniques that enables the construction of hybrid dynamic models. With System Equivalent Model Mixing (SEMM) frequency based models, either of numerical or experimental nature, can be mixed to form a hybrid model. This model follows the dynamic behaviour of a predefined weighted master model. A large variety of applications can be thought of, such as the DoF-space expansion of relatively small experimental models using numerical models, or the blending of different models in the frequency spectrum. SEMM is outlined, both mathematically and conceptually, based on a notation commonly used in FBS. A critical physical interpretation of the theory is provided next, along with a comparison to similar techniques; namely DoF expansion techniques. SEMM's concept is further illustrated by means of a numerical example. It will become apparent that the basic method of SEMM has some shortcomings which warrant a few extensions to the method. One of the main applications is tested in a practical case, performed on a validated benchmark structure; it will emphasize the practicality of the method.

Experimental Joint Identification Using System Equivalent Model Mixing in a Bladed Disk

“…Therefore, expansion methods can be used to extrapolate the dynamic information to those DoF. One such method is SEMM [11] based on the LM-FBS whose inputs are a parent model Y par , an overlay model Y ov , and a removed model Y rem , and the output is a hybrid model Y SEMM (or expanded numerical model). In this subsection, all the quantities belong to a substructure and not to a coupled structure.…”

“…These FE models were then reduced by HCB transformation to retain only the physical master DoF together with 200 fixed-interface eigen modes, according to Eq. (11). The retained master DoF include all the internal DoF in Figs.…”

“…Generally, SEMM is affected when the mode shapes of the numerical model are no longer representative, which might be the case in this scenario [11]. In the future, the numerical models should be updated to include these effects, especially point two.…”

“…On the other hand, frequency-based substructuring (FBS) methods provide a great advantage due to the fact that the directly measured FRFs are utilized without any modal parameters estimation. A recently developed expansion method, system equivalent model mixing (SEMM) [11], based on the FBS formulation provides a direct and convenient way to expand the measured FRFs over the numerical FRFs. It is a method of coupling (and decoupling) different equivalent models of the same (sub)structure, namely, parent, overlay, and removed models.…”

Joint Identification through Hybrid Models Improved by Correlations

“…System Equivalent Model Mixing (SEMM) [20] allows expansion of the measured dynamics on the internal DoF to the interface DoF. The peculiarity of SEMM is that it uses different formulations of the same system, coupling the numerical model with experimental measurements performed on a limited number of locations.…”