Development of Experimental Nonlinear Modal Analysis methods under special consideration of exciter-structure interaction

目前的项目有雄心勃勃的目标，以扩展模态测试，这是一个典型的技术，在线性情况下，非线性情况。利用本项目开发的方法，人们将能够提取每个感兴趣的模态的固有频率，模态阻尼比和振动挠度形状（包括谐波），作为振动水平的函数。提取的模态属性将有助于复杂非线性行为的数据驱动建模，用于验证、更新和升级非线性物理驱动建模方法。正在进行的项目部分揭示了一个主要的挑战，即激励-结构的相互作用。这一挑战将是建议项目部分中方法开发的焦点。WP1的目标是扩展非线性模态理论以纳入激励器模型。发展将是足够普遍的，可以考虑线性附件的模型，它是由具有时不变系数的线性微分方程描述的。附件不需要是纯机械性质的，但可以包含，例如，电，磁或空气动力学模型，这将非线性模式的实用范围扩展到结构修改，智能结构或能量收集等多种应用中。在适当的激励器模型下，扩展的非线性模型有望准确预测众所周知的近共振力降和耦合激励-结构系统的响应。在WP2中，正在进行的项目部分开发的相位控制方案将扩展到更高的谐波。除了扩展非线性模态试验方法的范围和精度外，该控制方案还将有助于在频率响应试验中实现纯谐波激励，从而极大地促进结构动力模型的验证。在WP3中，将开发一种基于速度反馈的相位谐振测试的替代方法。预计这将大大简化控制任务，因此更健壮。最后，在WP4中，将为基础激励的常见情况开发一种非线性模态测试方法，而不是迄今为止所考虑的激振器-推力杆激励。假设具有重滑动台的大型激振器的动力学不受轻试件动力学的显著影响，基底激励具有减少激振器-结构相互作用的潜力。

The present project has the ambitious goal to extend modal testing, which is a quintessential technique in the linear case, to the nonlinear case. With the methods developed in this project, one will be able to extract the natural frequency, modal damping ratio and vibrational deflection shape (including harmonics), for each mode of interest, as a function of the vibration level. The extracted modal properties will be useful for data-driven modeling of complicated nonlinear behavior, for validating, updating and upgrading nonlinear physics-driven modeling approaches.The ongoing project part revealed a major challenge, the exciter-structure interaction. This challenge will be a focus of the method developments in the proposed project part. The goal of WP1 is to extend the Nonlinear Mode Theory to incorporate an exciter model. The development will be sufficiently general that models of linear attachments can be considered, which are described by linear differential equations with time-invariant coefficients. The attachments do not need to be of purely mechanical nature, but may contain, for instance, electric, magnetic or aerodynamic models, which extends the range of utility of nonlinear modes to applications as diverse as structural modification, smart structures or energy harvesting. With an appropriate exciter model, the extended nonlinear-mode model is expected to provide an accurate prediction of the well-known near-resonant force drop and the response of the coupled exciter-structure system. In WP2, the phase control scheme developed in the ongoing project part will be extended to higher harmonics. Besides extending the range and accuracy of the nonlinear modal testing method, the control scheme will also be useful to achieve a purely harmonic excitation during frequency response tests, and will thus greatly facilitate structural dynamic model validation in general. In WP3, an alternative to phase-resonant testing will be developed, based on velocity feedback. This is expected to considerably simplify the control task, and therefore to be more robust. Finally, in WP4, a nonlinear modal testing method will be developed for the common case of base excitation, as opposed to the shaker-stinger excitation considered so far. Assuming that the dynamics of a large shaker with heavy slip table is not significantly affected by the dynamics of a light specimen, base excitation has the potential to reduce exciter-structure interaction.