CAREER: Vibration and Stability of Distributed Structures with Industrial Applications

摘要本课题的研究目标是：1）针对具有时变长度、速度和/或横截面的一类系统的新的动态稳定性理论，2）设计能够稳定分布式结构的最大数目的模式的振动阻尼器或控制器的新方法，（3）用半解析方法分析具有强非线性和复杂非线性的分布结构高维模型的振动和稳定性。 本文提出了一种新的波动法来分析具有周期变化参数的多个分布系统的动态稳定性。 值得注意的是，参数共振的条件与经典共振的条件相似。 将从理论和实验上研究这种不稳定条件。 将分析电梯系统的动态响应和稳定性，并开发消除其纵向振动的方法。 最佳的阻尼位置和常数张拉梁将确定相结合的渐近分析的所有高模式和数值分析的低模式和实验验证。 该方法将应用于电力行业分裂导线间隔阻尼器的设计，以消散高频模式。 增量谐波平衡法将扩展到分布式陀螺系统和一个强大的算法将开发自动化的解决方案的过程。 该方法被证明在摩擦引导平移梁具有小的弯曲刚度。 其智力价值在于发展了几种新的方法来分析分布式结构的振动和稳定性及其在重要工业问题中的应用。 这项研究的成功将推进动力系统一般领域的知识基础，并导致电梯，皮带和磁带驱动器和输电线路的新设计。 该教育计划包括：1）一个独特的未来工程师在动态系统（FEDS）学院的发展，沉浸在两个星期的课堂为基础的，理论驱动的学习，基于实验室的理论内容的应用，并动手探究为基础的实验，以发展团队建设和沟通技巧，2）为各级学生和实践工程师提供创新的多媒体教学材料。 FEDS学院的成立将提高高中生对工程教育的理解，促进动态系统的研究和教育计划。 多媒体教材的使用将使所有学生积极参与教育过程，并促进技术向工作场所的转移。

AbstractThe research objectives are to develop: 1) a new dynamic stability theory for a class of systems with time-varying length, speed, and/or cross-section, 2) a novel method to design a vibration damper or controller that can stabilize the largest number of modes of a distributed structure, and 3) a semi-analytical method to analyze the vibration and stability of high-dimensional models of distributed structures with strong and/or complex nonlinearities. A new wave method is developed to analyze the dynamic stability of several distributed systems with periodically varying parameters. It is remarkable to find that the condition for parametric resonance is similar to that for classical resonance. This instability condition will be investigated theoretically and experimentally. The dynamic response and stability of elevator systems will be analyzed and methods to dissipate their longitudinal vibration will be developed. The optimal damping location and constant for a tensioned beam will be identified by combining an asymptotic analysis for all the higher modes and a numerical analysis for the lower modes and validated experimentally. The methodology will be applied to the design of spacer dampers of bundled conductors in the electric power industry to dissipate high-frequency modes. The Incremental Harmonic Balance method will be extended for distributed gyroscopic systems and a robust algorithm will be developed to automate the solution procedure. The methodology is demonstrated on a friction-guided translating beam with small bending stiffness. The intellectual merit lies in the development of several new methodologies to analyze the vibration and stability of distributed structures and their applications to important industrial problems. The success of this research will advance the knowledge base in the general field of dynamic systems and lead to new designs of elevators, belt and tape drives, and power transmission lines. The educational plan includes the development of 1) a unique Future Engineers in Dynamic Systems (FEDS) Academy to immerse the underrepresented high school youth in two weeks of classroom-based, theory-driven learning, laboratory-based application of theoretical content, and hands-on inquiry-based experimentation to develop team-building and communication skills, and 2) innovative multimedia educational materials for students at all levels and practicing engineers. The establishment of the FEDS Academy will enhance the high school students' understanding of engineering education and promote the research and educational programs in dynamic systems. The use of multimedia educational materials will actively involve all students in the educational process and facilitate the technology transfer to the workplace.