Kriging Surrogate Models for Predicting the Complex Eigenvalues of Mechanical Systems Subjected to Friction-Induced Vibration

E Denimal,L Nechak,S Nacivet,J.-J Sinou

doi:10.1155/2016/3586230

Abstract

This study focuses on the kriging based metamodeling for the prediction of parameter-dependent mode coupling instabilities. The high cost of the currently used parameter-dependent Complex Eigenvalue Analysis (CEA) has induced a growing need for alternative methods. Hence, this study investigates capabilities of kriging metamodels to be a suitable alternative. For this aim, kriging metamodels are proposed to predict the stability behavior of a four-degree-of-freedom mechanical system submitted to friction-induced vibrations. This system is considered under two configurations defining two stability behaviors with coalescence patterns of different complexities. Efficiency of kriging is then assessed on both configurations. In this framework, the proposed kriging surrogate approach includes a mode tracking method based on the Modal Assurance Criterion (MAC) in order to follow the physical modes of the mechanical system. Based on the numerical simulations, it is demonstrated by a comparison with the reference parameter-dependent CEA that the proposed kriging surrogate model can provide efficient and reliable predictions of mode coupling instabilities with different complex patterns.

Highlights

Studies of mechanical systems subjected to friction-induced vibrations benefit from a growing interest due to the large amount of applications in the field of mechanical engineering
The different and complex mechanisms that can be responsible for undesirable dynamic characteristics and appearance of instabilities in many mechanical systems have been extensively studied in the last decades [1,2,3,4,5]
In order to investigate the efficiency of kriging surrogate models and to offer easy viewing of metamodels for both real and imaginary parts in comparison with the reference based on Complex Eigenvalue Analysis (CEA), we propose to draw envelopes for each real and imaginary part of eigenvalues while keeping the representation of variations according to the control parameter μ

Summary

Introduction

Studies of mechanical systems subjected to friction-induced vibrations benefit from a growing interest due to the large amount of applications in the field of mechanical engineering. While the variation of the friction coefficient is considered as one of the most important factors for the emergence of instability in the first category (i.e., in the case of a tribological approach), the origin of friction-induced vibrations is rather related to kinematic constraints or sprag-slip phenomenon [6] and modal coupling in the second case (i.e., in the case of a structural dynamics approach based on geometrical conditions). In this last case, the emergence of instability can be detected even with a constant friction coefficient. This last approach that is based on structural coupling mechanism will be discussed

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Conclusion