Modeling vibrational behaviour of non-smooth large scale dynamical systems

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Large-scale dynamical systems (LSDS) exist in every industry and in virtually every aspect of science and engineering. An LSDS consists of inter-connected sub-systems or components, transferring loads, energy and heat through interfaces, and more importantly interacting with each other through surface-to-surface frictional contact in a non-smooth manner. A mechanical system, used in manufacturing and other industries, has many components connected together by joints to complete various sophisticated tasks. During operations, each topologically complex component experiences elasto-rigid motion. As a result, a large number of degrees of freedom (DOF's) are required to describe time-varying configurations of all components with sufficient accuracy. Non-smooth LSDS can respond violently to disturbances and excitations in a deterministic or even chaotic manner, and can cause poor machine precision, excessive noise, accelerated component wear, etc. As examples of non-smooth large scale LSDS, vibration of a CANDU nuclear fuel string, excited by pulsating coolant flow, has caused severe wear damage to the pressure tube and fuel bundle component failure in the Canadian nuclear industry; a high-speed machine having flexible links and joints can lose its stability when operated near a critical speed; motion of a vibrating machine with gap-activated springs can become chaotic at certain operating points, which result in poor system performance. Study of vibration of non-smooth LSDS is of ultimate importance to both system design and maintenance engineers. ***In the proposed research, computational models will be developed to simulate vibrational behaviour of non-smooth LSDS with a focus on generic and efficient modelling of joints/interfaces with imperfections. This is a most challenging problem in the world dynamics community, which cannot be solved by a commercially available software. While the computer models are generic, the following two projects are pursued as applications and training of graduate students for employment in the Canadian industries: (i) vibration of a fuel bundle string in a CANDU reactor core, (ii) vibration of machine centre structure including drive, spindle and fixtures. Successful completion of the proposed research represents an important milestone achievement. The algorithms and computer models (1) allow researchers and engineers to model and understand vibrational behaviour of non-smooth LSDS under various excitations, and (2) provide manufacturers and operators with a tool for simulating the performance of a real mechanical system with imperfect interfaces/joints, and wear damage through frictional contact. These will result in reduction in product development time, and help reduce unnecessary and costly system shut-downs in the case of nuclear reactor. This will no doubt bring about economic and environmental benefits to Canada and the world. **