Abstract Although the identification and analysis of structures with a localized nonlinearity, either weak or strong, is within reach, identification of multiple nonlinearities coexisting at different locations is still a challenge, especially if these nonlinearities are strong. In such cases, identifying each nonlinearity separately requires a tedious work or may not be possible at all in some cases. In this paper, an approach for experimental modal analysis of nonlinear systems by using Response-Controlled stepped-sine Testing (RCT) is proposed. The proposed approach is applicable to systems with several nonlinearities at various different locations, provided that modes are well separated and no internal resonances occur. Step-sine testing carried out by keeping the displacement amplitude of the driving point constant yields quasi-linear frequency response functions directly, from which the modal parameters can be identified as functions of modal amplitude of the mode of concern, by employing standard linear modal analysis tools. These identified modal parameters can then be used in calculating near-resonant frequency response curves, including the unstable branch if there is any, for various untested harmonic forcing cases. The proposed RCT approach makes it also possible to extract nonlinear normal modes experimentally without using sophisticated control algorithms, directly from the identified modal constants, and also to obtain near-resonant frequency response curves experimentally for untested constant-amplitude harmonic forcing cases by extracting isocurves of constant-amplitude forcing from the measured Harmonic Force Surface (HFS), a new concept proposed in this paper. The key feature of the HFS is its ability to extract unstable branches together with turning points of constant-force frequency response curves directly from experiment, accurately. The method is validated with numerical and experimental case studies. The numerical example consists of a 5 DOF lumped system with strong several conservative nonlinear elements. Experimental case studies consist of a cantilever beam supported at its free-end by two metal strips which create strong stiffening nonlinearity, and a real missile structure which exhibit moderate damping nonlinearity mostly due to several bolted joints on the structure.

中文翻译：

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使用响应控制的步进正弦测试对非线性系统进行实验模态分析

摘要 虽然识别和分析具有局部非线性的结构，无论是弱的还是强的，都是可以实现的，但识别在不同位置共存的多个非线性仍然是一个挑战，尤其是当这些非线性很强的时候。在这种情况下，单独识别每个非线性需要繁琐的工作，或者在某些情况下可能根本不可能。在本文中，提出了一种使用响应控制步进正弦测试 (RCT) 对非线性系统进行实验模态分析的方法。所提出的方法适用于在不同位置具有多种非线性的系统，前提是模式分离良好且不发生内部共振。通过保持驱动点的位移幅度恒定进行的步进正弦测试直接产生准线性频率响应函数，通过采用标准线性模态分析，模态参数可以识别为关注模式的模态幅度的函数工具。然后，这些确定的模态参数可用于计算近谐振频率响应曲线，包括针对各种未经测试的谐波强迫情况的不稳定分支（如果有的话）。所提出的 RCT 方法还可以在不使用复杂的控制算法的情况下，直接从识别的模态常数中通过实验提取非线性正态模态，并且还通过从测量的谐波力面（HFS）中提取恒幅强迫的等值曲线，以实验方式获得未经测试的恒幅谐波强迫情况下的近共振频率响应曲线，这是本文提出的一个新概念。HFS 的主要特点是能够直接从实验中准确地提取不稳定的分支以及恒力频率响应曲线的转折点。该方法通过数值和实验案例研究得到验证。数值示例由一个 5 DOF 集总系统组成，其中包含多个强大的保守非线性元素。实验案例研究包括悬臂梁在其自由端由两个金属条支撑，这些金属条产生很强的刚性非线性，