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Experimental modal analysis of nonlinear systems by using response-controlled stepped-sine testing

机译：使用响应控制的阶梯式测试的非线性系统的实验模态分析

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摘要

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.
机译：尽管识别和分析具有局部非线性的结构，无论是弱还是强，都在达到范围内，鉴定在不同位置共存的多个非线性仍然是一个挑战，特别是如果这些非线性强烈。在这种情况下，分别识别每个非线性需要繁琐的工作，或者在某些情况下可能是不可能的。本文提出了一种通过使用响应控制的阶梯式正弦测试（RCT）的非线性系统实验模态分析方法。所提出的方法适用于各种不同位置的具有多个非线性的系统，条件是模式分开很好，没有发生内部共振。通过保持驱动点恒定的位移幅度来执行步骤 - 正弦测试，通过采用标准线性模态分析，可以直接产生准线性频率响应函数的正线线性频率响应函数，从中识别出模态参数作为临界模式的模态幅度的功能工具。然后可以在计算近谐振频率响应曲线时使用这些识别的模态参数，如果存在任何未经测试的谐波强制案例，则包括不稳定分支。所提出的RCT方法使得可以通过直接来自所识别的模态常数，实验地实验提取非线性正常模式，并且还通过提取异沟，实验地获得近谐振频率响应曲线。从测量的谐波表面（HFS）中强制稳定，本文提出的新概念。 HFS的关键特征是其能够直接从实验中与恒力频率响应曲线的转动点提取不稳定分支。该方法具有数值和实验案例研究验证。数值例子由具有强大的几个保守非线性元件的5个DOF集成系统组成。实验情况研究包括由其自由端支撑的悬臂梁，其两个金属条带产生强烈的加强非线性，以及真正的导弹结构，其主要是由于该结构上的几个螺栓接头而具有适度阻尼非线性的真正导弹结构。

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