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.

这项工作属于结构振动领域。 将开发新的方法来解释测试数据，以了解结构振动特性，并在航空航天、民用和机械系统中具有潜在的应用。该提案的目标是开发用于执行实验模态分析的分解方法。 分解方法无需测量输入信号即可执行，这扩大了它们对模态分析的吸引力。 该工作涉及新的状态变量模态分解（SVMD）、适当正交分解（POD）和平滑正交分解（SOD）。 在所提出的 SVMD 中，构建了基于数据的特征值问题，并将其与与线性多自由度系统状态变量公式的自由振动解相关的广义特征值问题相关联。特征值导致频率和模态阻尼的估计。 特征向量导致模态振型的估计。 该解释适用于具有多模态自由响应的线性系统，无论阻尼是大还是小、模态还是非模态，并且不需要输入数据。 分解与状态变量微分方程的联系提供了对随机激励下应用的深入了解。这种见解也适用于 SOD。 此外，POD 的开发是为了适应一般的质量分布。分解方法很简单，不需要测量输入，使工程师能够使用基本的数值软件包（例如 Matlab）以很少的学习曲线掌握该过程。 由于不需要测量输入，因此该过程将在柔性结构和难以访问的过程上启用，例如交通或风的随机激励下桥梁的振动。 这些工具扩展到随机激励进一步拓宽了适用性，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阻尼比大多数当前方法更大的结构。 除了博士课程所需的课程学习外，该项目还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。密歇根州立大学工程多样性办公室将寻找代表性不足的少数族裔、女性和经济弱势学生。 本科生将协助设置、安装和运行实验。 该 PI 将参加密歇根州立大学针对中学生的暑期课程——数学科学与技术 (MST)，并共同教授“机械工程”课程。