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Comparison of different harmonic balance based methodologies for computation of nonlinear modes of non-conservative mechanical systems

机译：基于不同谐波平衡的非保守机械系统非线性模式计算方法的比较

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摘要

For the determination of periodic solutions for forced or free vibrations of nonlinear systems, several proven methods exist. The motion of autonomous nonlinear non conservative mechanical systems is in general non-periodic which contradicts the computation of their nonlinear modes as natural periodic solutions. Utilizing the harmonic balance method (HBM) two approaches for nonlinear mode computation of non conservative systems exist - the so called concept of complex nonlinear modes (CNM) and the extension of the periodic motion concept (E-PMC). Each nonlinear mode computed using one of these methods is then described by its frequency, damping, the harmonics, and the corresponding phase angles of each degree of freedom as functions of the generalized amplitude. Applying averaging methods transient system responses of the system can be efficiently computed regarding one nonlinear mode. In this work differences between complex nonlinear modes and the extended periodic motion concept as well as corresponding results will be addressed. (C) 2019 Elsevier Ltd. All rights reserved.
机译：为了确定非线性系统的强迫振动或自由振动的周期解，存在几种可靠的方法。自治非线性非保守机械系统的运动通常是非周期性的，这与将其非线性模式作为自然周期解的计算相矛盾。利用谐波平衡法（HBM），可以使用两种方法对非保守系统进行非线性模式计算-所谓的复杂非线性模式（CNM）概念和周期性运动概念（E-PMC）的扩展。然后，使用这些方法之一计算出的每个非线性模式，将其频率，阻尼，谐波以及每个自由度的相应相角作为广义幅度的函数来描述。应用平均方法可以针对一种非线性模式有效地计算系统的瞬态系统响应。在这项工作中，将解决复杂的非线性模式与扩展的周期性运动概念之间的差异以及相应的结果。 （C）2019 Elsevier Ltd.保留所有权利。

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