In this work, we address Nonlinear System Identification (NSI) of geometrically nonlinear structures using experimental response data. Specifically we consider nonlinear structures with large inertia effects. A laboratory scale cantilever-type beam structure is considered, which is chosen for its large inertial effects. Free decay data is gathered from the experimental cantilever-type beam system using an image-based measurement technique. A general mathematical model is derived for nonlinear systems with large inertia, by taking inspiration from model reduction methods. Specifically, a reduced-order modelling method, which accounts for the kinetic energy of the modes not included in the reduction basis, is utilised for experimental NSI. Experimental system identification using the ROM-inspired model shows superior accuracy compared to standard stiffness nonlinear models typically used for modelling such systems. We also identify the damping of the structure by projecting the effect of unmodelled modes onto non-conservative dissipative forces in the ROM-inspired model. We show that this addresses issues of poor fit associated with using a linear damping model. This results in a nonlinear damping force in the ROM-inspired model which accounts for the damping effect of the unmodelled modes. These nonconservative effects of unmodelled modes are often neglected, which results in an incorrect damping estimation. A crude Finite-Element (FE) model of the cantilever-type beam is used to generate the nonlinear mapping of nonlinear damping force. The free decay response of the identified nonconservative ROM-inspired model closely matches the measurement decay response. This further validates the accuracy of the ROM-inspired model in NSI.

中文翻译：

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减阶模型启发的阻尼非线性结构的实验识别


在这项工作中，我们使用实验响应数据来解决几何非线性结构的非线性系统识别（NSI）问题。具体来说，我们考虑具有大惯性效应的非线性结构。考虑了实验室规模的悬臂梁结构，因其大的惯性效应而被选择。使用基于图像的测量技术从实验悬臂梁系统收集自由衰变数据。受模型降维方法的启发，推导了大惯量非线性系统的通用数学模型。具体来说，实验 NSI 采用降阶建模方法，该方法考虑了未包含在降阶基础中的模式的动能。与通常用于建模此类系统的标准刚度非线性模型相比，使用 ROM 启发模型进行的实验系统识别显示出更高的准确性。我们还通过将未建模模式的影响投影到 ROM 启发模型中的非保守耗散力来确定结构的阻尼。我们证明这解决了与使用线性阻尼模型相关的拟合不良问题。这导致 ROM 启发模型中产生非线性阻尼力，该模型解释了未建模模式的阻尼效应。未建模模态的这些非保守效应常常被忽略，从而导致阻尼估计不正确。悬臂梁的原始有限元 (FE) 模型用于生成非线性阻尼力的非线性映射。所识别的非保守 ROM 启发模型的自由衰减响应与测量衰减响应密切匹配。这进一步验证了 NSI 中 ROM 启发模型的准确性。