Modeling the Vibrations and Energy Flows in Complex Dynamic Systems

摘要本研究旨在为复杂动态系统的建模提供一种通用的方法，尤其是在临界中频范围内。这项研究建立在PI最近关于弹性约束梁和板的振动和能量流分析的工作基础上。研究的一般方法是将复杂动力系统分解为若干个子系统或部件，基于两个创新思想：1)每个部件上的位移表示为广义快速收敛的傅立叶级数展开；2)各部件在连接处的相互作用以力平衡或位移连续方程的形式精确地描述。这项研究将有可能导致复杂系统在较宽频率范围内动态分析的数值方法方面的重大进展。这些进展将允许创建一个统一的工具，用于确定各种结构或结合点的动态特性，例如波传输系数和模态参数，而不考虑边界条件、耦合条件、结合点配置或涉及的组件数量。目前的模型将忠实地表示在实际系统条件下各个组件的相互作用，并将克服必须先验计算或指定联接或组件特性的问题。这项研究还将通过关注与制造和建模过程相关的重要不确定性和敏感性问题，促进对复杂动态系统的基本理解和设计。这项研究将集中在关键的中频，并将导致噪音和振动问题的解决方案，这些问题影响到从消费产品到飞机的广泛动态系统的设计。该研究将开发建模工具，将设计者从创建模型、提取组件的模态属性和其他模型变量、或定制公式和求解程序以适应边界条件、耦合配置或其他系统或组件条件的微小变化或变化的工作中解放出来。研究生将直接参与这个项目。本科生，特别是少数民族学生，将通过高级设计项目、与产业合作伙伴的实习和本科生研究项目参与进来。通过这个项目，未来的专业人员将被培养具有广泛的背景和强大的技能，以解决实际工程问题和进行高级研究。

AbstractThis proposed research aims to develop a general method for the modeling of complex dynamic systems, especially in the critical mid-frequency range. The research builds on the PI's recent work on the vibration and energy flow analyses of elastically restrained beams and plates. The general approach of the research is to divide a complex dynamic system into a number of subsystems or components, based on two innovative ideas: 1) the displacements on each component are expressed as a generalized fast-converging Fourier series expansion; 2) the interactions of various components at junctions are accurately described in the form of force balance or displacement continuity equations. The research will potentially lead to major advances in numerical methods for the dynamic analysis of complex systems in a broad frequency range. These advances will allow the creation of a unified tool for determining the dynamic properties such as the wave transmission coefficients and modal parameters for various structures or junctions, regardless of boundary conditions, coupling conditions, joint configurations, or the number of components involved. The current model will represent the interactions of the individual components faithfully as under the actual system condition and will overcome the problem of having to calculate or specify, a priori, the joint or component properties. The research will also advance the fundamental understanding and design of complex dynamic systems by focusing on the important uncertainty and sensitivity issues related to the manufacturing and modeling processes. The research will be focused on the critical mid-frequencies and will lead to solutions of the noise and vibration problems that impact the design of a wide range of dynamic systems from consumer products to aircrafts. The research will develop modeling tools that will free the designers from the often enormous effort in creating models, extracting component modal properties and other model variables, or customizing the formulations and solution procedures to accommodate minor changes or variations in boundary conditions, coupling configurations, or other system or component conditions. Graduate students will be directly involved with this project. Undergraduate students, especially minority students, will be involved via senior design projects, internship with the industrial partner, and through undergraduate research projects. Through this project, future professionals will be trained with broad backgrounds and strong skills to solve practical engineering problems and to perform advanced researches.