Abstract
The numerical prediction of the dynamic behaviour of mechanical systems subjected to friction-induced vibrations is still a tedious problem. Different methodologies exist nowadays to study it. The first one is the complex eigenvalue analysis, which is widely used by the scientists and the industrials to predict the appearance of instabilities despite its disadvantages. Other methodologies, namely temporal integration and frequential approaches, have been developed to determine the transient and/or the steady-state response to assess the history of the dynamic response, and so to identify the unstable modes involved in the nonlinear dynamic response as well as the vibration levels. However, because of their complex implementation, their high numerical cost and sometimes the strong assumptions made on the form of the solutions, these methods are not widely and currently used in industry. To cope with the limitations of the CEA, namely the over- or under-predictability and the lack of information about modal participations in the nonlinear dynamic response, developing complementary tools is necessary. Thus, this paper is devoted to the extension and generalization of a nonlinear approach, called the modal amplitude stability analysis, to the multi-instability case. The method, called the Generalized Modal Amplitude Stability Analysis (GMASA), allows to identify the evolutions and contributions of unstable modes involved in the nonlinear self-sustaining vibration response and to estimate the limit cycles. The method is applied on a phenomenological system for which it is easy to provide an understanding of the unstable mode(s) contribution to the nonlinear dynamic response of the system and for which the calculations can be performed with reasonable computational times. Thus, the efficiency and validity of the GMASA approach are investigated by comparing the GMASA results with those of the reference results based on temporal approach.
Highlights
Instabilities for mechanical systems subjected to frictioninduced vibrations are a complex phenomenon studied by both industrials and academics since several decades [1,2,3]
The Complex Eigenvalue Analysis (CEA) is the first step of the Generalized Modal Amplitude Stability Analysis (GMASA) method, and it identifies the unstable modes to be taken into consideration initially in the GMASA
The GMASA makes it possible to follow the contributions of the two unstable modes for different modal amplitudes and leads to decide on the participation of each unstable mode initially identified by the CEA in the final steady-state regime of the system
Summary
Instabilities for mechanical systems subjected to frictioninduced vibrations (squeal, for example) are a complex phenomenon studied by both industrials and academics since several decades [1,2,3]. The objective of the present paper is to extend the MASA method to the case where several instabilities are identified by the CEA and to cope with the coupling effects that may exist between unstable modes This extended approach is named generalized Modal Amplitude Stability Analysis (GMASA). One of the main objectives is to demonstrate the validity of this new extension of the MASA methodology by considering an application on a phenomenological model for which it is possible to perform temporal integration to obtain rapidly reference results The use of this simplified model allows to provide a deep understanding of the contribution of each unstable mode to the nonlinear dynamic response of the system and so to make extensive comparisons between the GMASA and the reference solutions. The prediction results of the GMASA method are compared to the reference results from the temporal integration and the validity of the method is demonstrated
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