Modal Identification by Decomposition Methods

通过分解方法进行模态识别

• 批准号: 0727838
• 负责人: Brian Feeny
• 金额: $ 17万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-09-01 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0727838&HistoricalAwards=false
• 关键词: Modal; Identification; Decomposition; Methods

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.

这项工作是在结构振动领域进行的。为了理解结构的振动特性，将开发新的方法来解释试验数据，潜在地应用于航空航天、民用和机械系统。该提案的目标是开发用于执行实验模态分析的分解方法。分解方法不需要测量输入信号，这扩大了它们对模态分析的吸引力。工作包括新的状态变量模式分解(SVMD)、真正交分解(POD)和光滑正交分解(SOD)。在所提出的SVMD中，构造了一个基于数据的特征值问题，并将其与线性多自由度系统状态变量形式的自由振动解相关的广义特征值问题联系起来。这些特征值导致了频率和模态阻尼的估计。这些特征向量导致了对振型的估计。这种解释适用于具有多模态自由响应的线性系统，无论阻尼值是大是小，是模态还是非模态，并且不需要输入数据。这种分解与状态变量微分方程组之间的联系提供了在随机激励下的应用。这种洞察力延续到了超氧化物歧化酶。另外，POD是为适应一般质量分布而开发的。分解方法简单，不需要测量输入，使工程师能够使用数值软件的基本软件包，如MatLab，以很少的学习曲线掌握这一过程。由于不需要测量输入，因此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桥梁的振动。将这些工具扩展到随机激励，进一步扩大了适用范围，并考虑了例如飞机机翼在风洞中或飞行过程中的湍流载荷。SVMD的直接模态阻尼法适用于具有比大多数现有方法更大阻尼值的结构。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，以及博士课程所要求的课程学习。代表不足的少数民族、妇女和经济困难的学生将通过密歇根州立大学工程多样性办公室进行寻找。本科生将帮助建立，仪器和运行实验。PI将参加密歇根州立大学为中学生举办的数学科学与技术(MST)暑期项目，方法是共同教授一节机械工程课。