A New Approach to Accelerate Frequency-Domain Studies of Complex Structures

主要研究者姓名：J. Gregory McDanielInstitution: Boston university提案号：9978747提案标题：一种加速复杂结构频域研究的新方法项目摘要：目前，复杂结构振动建模的努力受到计算成本的严重限制，无论是寻找结构的模态特性还是强迫响应。通过开发一种压缩运动动力学方程的新方法，所提出的研究可以大大减少这些费用，从而使更完整和准确的振动研究成为可能。初步估计表明，对于当前工业感兴趣的结构，计算时间的减少将是几个数量级。该方法基于一个前提，即人们通常对某一频段内结构的动态响应感兴趣。通过近似在带外共振的模式的影响，矩阵运动方程被降阶。在提出的方法中，这种减少将通过一种创新的转换来实现，该转换使用在频带中几个采样频率下评估结构的强迫响应。由于带中的强迫响应主要由带中共振的模态组成，因此这种转换自然保留了位于带中的模态。该方法将在精心挑选的行业相关结构模型测试平台的背景下开发，范围从1000到100万自由度。通过创建一个名为虚拟振动实验室的独特交互式软件包，该研究将用于加强结构振动的本科和研究生教育，该软件包将允许学生探索真实工业相关结构模型的基本振动现象和振动控制技术。探索将向学生介绍诸如主动振动控制、模态定位和高级阻尼处理等主题。预计该软件包将为工业参与工程教育创造新的途径。

Principal Investigator's Name: J. Gregory McDanielInstitution: Boston UniversityProposal Number: 9978747Proposal Title: A New Approach to Accelerate Frequency-Domain Studies of Complex StructuresProject AbstractCurrently, efforts to model the vibrations of complex structures are severely limited by the computational expenses incurred in finding either the modal properties or the forced responses of the structures. The proposed research could dramatically reduce these expenses, and hence enable more complete and accurate vibration studies, by developing a novel means of condensing the dynamic equations of motion. Preliminary estimates indicate that, for structures of current interest to industry, the reductions in computational times will be several orders of magnitude. The approach is based on the premise that one is typically interested in a structure's dynamic response inside a frequency band. By approximating the effects of modes that resonate outside the band, the matrix equation of motion is reduced in rank. In the proposed approach, this reduction will be achieved by an innovative transformation that uses the forced responses of the structure evaluated at a few sampled frequencies in the band. As the forced responses in the band are mostlycomprised of the modes that resonate in the band, this transformation naturally retains modes lying in the band. The method will be developed in the context of a carefully selected testbed of industry-relevant structural models, ranging from one thousand to one million degrees-of-freedom. The research will be used to enhance undergraduate and graduate education in structural vibrations through the creation of a unique interactive software package entitled the Virtual Vibrations Laboratory, which will allow students to explore fundamental vibration phenomena and vibration control techniques for models of real industry-relevant structures. The explorations will introduce students to topics such as active vibration control, mode localization, and advanced damping treatments. It is expected that this software package will create a new avenue for the involvement of industry in engineering education.