Modal Identification by Decomposition Methods

这项工作是在结构振动领域。 为了理解结构振动特性，将开发解释试验数据的新方法，其潜在应用于航空航天、民用和机械系统。本提案的目标是开发进行实验模态分析的分解方法。 分解方法在没有测量输入信号的情况下进行，这扩大了它们对模态分析的吸引力。 本文的工作包括新的状态变量模态分解（SVMD）、本征正交分解（POD）和光滑正交分解（SOD）。 在建议的SVMD，基于数据的特征值问题的构造和相关的广义特征值问题与自由振动的状态变量制定的线性多自由度系统的解决方案。特征值导致频率和模态阻尼的估计。 特征向量导致的模式形状的估计。 该解释适用于具有多模态自由响应的线性系统，无论阻尼是大的还是小的，模态的还是非模态的，并且不需要输入数据。 将分解与状态变量微分方程联系起来，可以深入了解随机激励下的应用。这一观点也适用于SOD。 分解方法简单，不需要测量输入，使工程师能够使用基本的数值软件包（如Matlab）掌握过程，学习曲线很小。 由于不需要测量的输入，该过程将在柔性结构和不可访问的过程中启用，例如在交通或风的随机激励下的桥梁振动。 将这些工具扩展到随机激励进一步拓宽了应用范围，并适应例如风洞中或飞行期间飞机机翼上的湍流载荷。 SVMD的直接模态阻尼估计适用于比大多数当前方法更大阻尼的结构。 该项目将支持博士生学习状态变量建模，随机振动，信号处理和实验仪器，除了在博士课程所需的课程工作学习。代表性不足的少数民族，妇女和经济上处于不利地位的学生将通过MSU工程多样性办公室寻求。 一名本科生将协助建立，仪器和运行实验。 PI将参加MSU中学生暑期课程，数学科学与技术（MST），共同教授“机械工程”课程。

This work is in the area of structural vibrations. New methods will be developed for interpreting test data in order to understand structural vibration properties, with potential applications to aerospace, civil, and mechanical systems.The goal of this proposal is to develop decomposition methods for performing experimental modal analysis. The decomposition methods are performed without measured input signals, which broadens their appeal for modal analysis. The work involves the new state-variable modal decomposition (SVMD), the proper orthogonal decomposition (POD) and the smooth orthogonal decomposition (SOD). In the proposed SVMD, a data-based eigenvalue problem is constructed and related to the generalized eigenvalue problem associated with free-vibration solutions of the state-variable formulation of linear multi-degree-of-freedom systems. The eigenvalues lead to estimates of frequencies and modal damping. The eigenvectors lead to estimates of the mode shapes. The interpretation holds for linear systems with multi-modal freeresponses, whether damping is large or small, modal or nonmodal, and without the need of input data. The connection of the decomposition to the state-variable differential equations provides insight into the application under random excitation. This insight carries over to SOD. Also, the POD is developed to accommodate general mass distributions.Decomposition methods are easy, and need no measured inputs, enabling engineers to master the process with very little learning curve, using basic packages of numerical software, such as Matlab. Since measured inputs are not needed, the process will be enabled on flexible structures and also inaccessible processes, for example the vibrations of a bridge under random excitation of traffic or wind. The extension of these tools to random excitation further broadens the applicability, and accommodates, for example, the turbulence loading on an airplane wing in the wind tunnel or during flight. The direct modal damping estimations of the SVMD are applicable to structures with larger damping than most current approaches. The project will support a doctoral student to learn state-variable modeling, random vibration, signal processing, and experimental instrumentation, in addition to course-work learning required in the doctoral program. Under-represented minorities, women, and economically disadvantaged students will be sought through the MSU Engineering Diversity Office. An undergraduate student will assist in setting up, instrumenting and running experiments. The PI will take part in an MSU summer program for middle schoolers, Mathematics Science and Technology (MST), by co-teaching a 'Mechanical Engineering' class.