Modeling the Vibrations and Energy Flows in Complex Dynamic Systems

摘要本研究旨在发展复杂动态系统的通用建模方法，特别是在中频临界范围内。该研究建立在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一个复杂的动态系统划分为多个子系统或组件，基于两个创新思想：1)将每个组件上的位移表示为广义的快速收敛傅立叶级数展开；2)以力平衡或位移连续方程的形式精确描述结点处各构件的相互作用。这项研究将有可能导致在广泛频率范围内复杂系统动态分析的数值方法取得重大进展。这些进步将允许创建一个统一的工具，用于确定各种结构或结的动态特性，如波传输系数和模态参数，而不考虑边界条件、耦合条件、关节配置或所涉及的组件数量。当前的模型将忠实地表示单个组件的相互作用，就像在实际系统条件下一样，并且将克服必须计算或先验地指定关节或组件属性的问题。该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，推进复杂动态系统的基本理解和设计。研究将集中在关键的中频，并将导致噪声和振动问题的解决方案，影响从消费产品到飞机的各种动态系统的设计。该研究将开发建模工具，将设计师从创建模型，提取组件模态属性和其他模型变量，或定制公式和解决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通常巨大的努力中解放出来。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，与工业合作伙伴实习，以及通过本科生研究项目参与。通过该项目，将培养具有广泛背景和强大技能的未来专业人员，以解决实际工程问题并进行高级研究。

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.