The development process of mechanical systems involves the evaluation of its modes of vibrations in the frequency range of interest. In general, a linear modal analysis is sufficient to determine whether the system can operate in dynamic conditions. However, in some cases the assembly is composed of many subsystems connected through nonlinear connections which make the response depend on the amplitude and frequency of the excitation. In those cases, Linear Normal Modes (LNMs) are not sufficient to fully describe the dynamics of the system and Nonlinear Normal Modes (NNMs) must be used. Using substructuring techniques it is possible to treat nonlinear joints as independent subsystems. However, a reliable nonlinear model is needed to use this approach. The experimental characterization is the only way to correctly estimate the nonlinear behavior of the connection. Thus, the aim of this work is to develop and validate the experimental characterization to build an experimental nonlinear modal model of a strongly nonlinear element that can be used to connect different linear subsystems and can be regarded as a localized source of nonlinearity. The NNMs identification is performed using the single-point single-harmonic phase resonance method, and the experimental nonlinear modal model of the NLCE is obtained by retaining only the first harmonic term of each NNM in order to get nearly uncoupled modal equations.

中文翻译：

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考虑到非线性模态耦合的一组连接元件的实验非线性模型

机械系统的开发过程涉及评估其在感兴趣的频率范围内的振动模式。一般来说，线性模态分析足以确定系统是否可以在动态条件下运行。然而，在某些情况下，组件由许多通过非线性连接连接的子系统组成，这使得响应取决于激励的幅度和频率。在这些情况下，线性简正模态 (LNM) 不足以完全描述系统的动态，必须使用非线性正则模态 (NNM)。使用子结构技术，可以将非线性关节视为独立的子系统。然而，使用这种方法需要可靠的非线性模型。实验表征是正确估计连接非线性行为的唯一方法。因此，这项工作的目的是开发和验证实验表征，以建立强非线性元件的实验非线性模态模型，该模型可用于连接不同的线性子系统，并可被视为局部非线性源。采用单点单谐波相位谐振法进行NNM辨识，仅保留各NNM的一次谐波项，得到近解耦模态方程，得到NLCE的实验非线性模态模型。