Modeling vibrational behaviour of non-smooth large scale dynamical systems

大规模动力系统（LSDS）存在于每一个工业和科学与工程的几乎每一个方面。LSDS由相互连接的子系统或部件组成，通过界面传递载荷、能量和热量，更重要的是通过表面与表面的摩擦接触以非光滑的方式相互作用。用于制造业和其他工业的机械系统由许多部件通过接头连接在一起以完成各种复杂的任务。在操作过程中，每个拓扑结构复杂的部件都经历了弹刚性运动。因此，需要大量的自由度（DOF）来以足够的精度描述所有部件的时变结构。非光滑LSDS对扰动和激励的响应会以确定性甚至混沌的方式剧烈响应，并可能导致机器精度差、噪声过大、部件磨损加速等问题。在加拿大核工业中，CANDU核燃料管柱在脉动冷却剂的激励下产生振动，导致压力管严重磨损，燃料束组件失效，这是大型非光滑LSDS的一个例子。具有柔性连杆和关节的高速机器在接近临界速度时可能失去稳定性；采用间隙激活弹簧的振动机在某些工作点会产生运动混沌，从而导致系统性能不佳。研究非光滑lds的振动对系统设计和维护工程师都具有重要意义。

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.