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首页> 外文期刊>Nonlinear dynamics >Generalized Modal Amplitude Stability Analysis for the prediction of the nonlinear dynamic response of mechanical systems subjected to friction-induced vibrations
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Generalized Modal Amplitude Stability Analysis for the prediction of the nonlinear dynamic response of mechanical systems subjected to friction-induced vibrations

机译：预测摩擦振动的机械系统非线性动力响应预测的广义模态幅度稳定性分析

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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.
机译：经受摩擦诱导的振动的机械系统动态行为的数值预测仍然是一个繁琐的问题。现在存在不同的方法来研究它。第一个是复杂的特征值分析，这是科学家和工业的广泛应用，尽管有缺点，但是尽管有缺点。已经开发了其他方法，即时间集成和频繁方法，以确定评估动态响应历史的瞬态和/或稳态响应，以识别非线性动态响应中涉及的不稳定模式以及振动水平。然而，由于它们的复杂实施，它们的高值成本和有时对解决方案形式的强烈假设，这些方法并不广泛，目前在工业中使用。为了应对CEA的局限性，即有关非线性动态响应的模态参与的过度或不可预测性和缺乏信息，所以需要开发互补工具。因此，本文致力于非不稳定性情况的非线性方法的延伸和泛化，称为模态幅度稳定性分析。该方法称为广义模态幅度稳定性分析（GMASA），允许识别非线性自维持振动响应中涉及的不稳定模式的演变和贡献，并估计极限循环。该方法应用于现象学系统，其易于提供对系统的非线性动态响应的不稳定模式的理解，并且可以使用合理的计算时间来执行计算。因此，通过将GMASA结果与基于时间方法的参考结果的比较来研究GMASA方法的效率和有效性。

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