Modeling vibrational behaviour of non-smooth large scale dynamical systems

大型动力系统(LSD)存在于每个行业，几乎存在于科学和工程的各个方面。LSD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，它们之间通过面对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有许多部件通过关节连接在一起，以完成各种复杂的任务。在运行过程中，每个拓扑复杂的部件都经历了弹性刚体运动。因此，需要大量的自由度(DOF)来准确地描述所有构件的时变构形。非光滑LSD会以确定性甚至混沌的方式对扰动和激励做出剧烈响应，会导致机器精度差、噪声过大、部件加速磨损等。以非光滑大型LSD为例，在脉动冷却剂流动的激励下，CANDU核燃料串的振动已经对加拿大核工业的压力管和燃料束部件造成严重的磨损破坏；具有柔性连杆和关节的高速机器在接近临界速度时可能会失去稳定性；带有间隙激活弹簧的振动机器在某些工作点会变得混乱，导致系统性能不佳。研究非光滑LSD的振动对系统设计和维护工程师都具有极其重要的意义。

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.