CAREER: Vibration and Stability of Distributed Structures with Industrial Applications

摘要本文的研究目标是：1)为一类具有时变长度、速度和/或截面的系统建立一种新的动态稳定性理论；2)设计一种新的方法来稳定分布结构的最大模态数的减振器或控制器；3)一种半解析方法来分析具有强非线性和/或复杂非线性的分布结构的高维模型的振动和稳定性。提出了一种新的波法来分析参数周期性变化的分布式系统的动态稳定性。值得注意的是，参数共振的条件与经典共振的条件相似。本文将对这种不稳定条件进行理论和实验研究。本文将对电梯系统的动力响应和稳定性进行分析，并提出消除电梯纵向振动的方法。张力梁的最佳阻尼位置和常数将通过结合对所有高模态的渐近分析和对低模态的数值分析来确定，并通过实验验证。该方法将应用于电力工业中捆扎导体的间隔阻尼器的设计，以消散高频模式。将增量谐波平衡法扩展到分布式陀螺仪系统，并开发一种鲁棒算法来实现求解过程的自动化。该方法在小弯曲刚度的摩擦导向平动梁上得到了验证。智力上的优点在于开发了几种新的方法来分析分布结构的振动和稳定性，并将其应用于重要的工业问题。这项研究的成功将促进动态系统一般领域的知识基础，并导致电梯，皮带和磁带驱动器以及输电线路的新设计。该教育计划包括：1)建立一个独特的动态系统未来工程师学院（federal Academy），让未被充分代表的高中青年沉浸在两周的课堂学习、理论驱动学习、实验室应用理论内容和实践探究性实验中，以培养团队建设和沟通技能；2)为各级学生和实践工程师提供创新的多媒体教育材料。联邦工程学院的成立将提高高中学生对工程教育的理解，促进动态系统的研究和教育项目。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.