Nonlinear Modal Testing and Analysis of Multiple Degree of Freedom Engineering Structures using a Frequency Domain method

尽管计算能力和建模能力得到了共同的提高，但最优设计的一个主要障碍是目前无法通过实验来捕捉(识别)许多工程结构所特有的非线性动态行为。可以说，结构动力学预测能力的精度(即用于模拟的模型的精度)的阶跃变化只有在及时地捕获和建模非线性特性的情况下才会发生。目前，标准的工程实践是应用可以提供被测试系统是否是非线性的答案的技术，但无助于识别非线性的类型和大小。因此，在一个标准的动态实验中，有机会实施一种对非线性行为进行“检测和量化”的方法。实验模态分析，或称模态测试，每天都会在大学和行业的动力学实验室中进行。最终目标是将一组测量数据转换为一组模态参数，最终将允许(重新)构建(或验证)空间模型(最明显的是有限元模型)。然而，到目前为止，如果振动结构表现出非线性行为，那么用于进行模态分析的理论就不再有效。本项目提出的工作旨在为继续和扩展非线性结构动力学中的模态分析的理论和实践而做出更有条理的努力。这一建议响应了引入一种新的非线性结构模态分析技术的需要，该技术的目的是从测量的频率响应函数中提取结构非线性的类型和大小，至少达到一级近似。这是必要的，以便超越几十年前确立的良好线性技术的当前边界，这些边界不再足以响应诸如有限元等模拟方法的扩展能力。

Despite the combined improvements in computing power and modelling capabilities one major hindrance to optimal design is the present incapability to capture experimentally (identify) nonlinear dynamic behaviour which characterise many engineering structures. It can be argued that a step-change in the accuracy of structural dynamics prediction capability (i.e. the accuracy of the models used for simulations) can only occur if the nonlinear characteristics are opportunely captured and modelled. Currently, it is standard engineering practice to apply techniques that can provide an answer to whether or not the system being tested is nonlinear but do not help to identify the type and magnitude of nonlinearity. There is thus scope for implementing, within a standard dynamic experiment, a method for 'detection and quantification' of the nonlinear behaviour. Experimental Modal Analysis, or Modal Testing, is practiced on a daily basis in dynamics labs of universities and industries alike. The final goal is to transform a set of measured data into a set of modal parameters which eventually will allow the (re)construction (or validation) of a spatial model (most notably a Finite Element model). However, the theory developed to perform modal analysis so far ceases to be valid if the vibrating structure exhibits nonlinear behaviour. The work proposed in this project intends to initiate a more structured effort for the continuation and the expansion of theory and practice of modal analysis in nonlinear structural dynamics. This proposal responds to the need of introducing a novel modal analysis technique for nonlinear structures which aims, at least to a first degree of approximation, to extract type and magnitude of structural nonlinearity from measured frequency response functions. This is necessary in order to progress beyond the current boundaries of the well established linear techniques set decades ago and which no longer suffice to respond the expanding capabilities of simulation methods such as the finite elements.