CAREER: Vibration and Stability of Distributed Structures with Industrial Applications

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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.