Modeling vibrational behaviour of non-smooth large scale dynamical systems

大规模动力系统（LSDS）存在于每一个行业，几乎在科学和工程的每一个方面。LSDS由相互连接的子系统或组件组成，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。用于制造业和其他行业的机械系统具有通过接头连接在一起的许多部件，以完成各种复杂的任务。在操作过程中，每个拓扑复杂的组件经历弹性-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配置。非光滑LSDS可以以确定性甚至混沌的方式对扰动和激励做出剧烈响应，并且可以导致差的机器精度、过大的噪声、加速的部件磨损等。作为非光滑大尺度LSDS的示例，CANDU核燃料串的振动由脉动冷却剂流激励，已经对加拿大核工业中的压力管和燃料束部件故障造成严重的磨损损坏;具有柔性连杆和接头的高速机器在接近临界速度操作时可能失去其稳定性;具有间隙致动弹簧的振动机器的运动在某些操作点可能变得混乱，这导致系统性能差。非光滑减振系统的振动特性研究对减振系统的设计和维护具有重要意义。 * 在拟议的研究中，将开发计算模型来模拟非光滑LSDS的振动行为，重点是对有缺陷的接头/界面进行通用和有效的建模。这是世界动力学界最具挑战性的问题，商业软件无法解决。虽然计算机模型是通用的，但以下两个项目是作为应用和培训研究生在加拿大工业中就业而进行的：（一）CANDU反应堆堆芯中燃料束串的振动，（二）包括驱动器、主轴和固定装置在内的机器中心结构的振动。成功完成拟议的研究是一个重要的里程碑式的成就。算法和计算机模型（1）允许研究人员和工程师对非光滑LSDS在各种激励下的振动行为进行建模和理解，并且（2）为制造商和操作者提供用于模拟具有不完美界面/接头的真实的机械系统的性能以及通过摩擦接触的磨损损伤的工具。这将减少产品开发时间，并有助于减少核反应堆不必要和昂贵的系统关闭。这无疑将为加拿大和世界带来经济和环境效益。**

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. **