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最近,对非线性动力学中复杂运动的特性,有一些新的发现。这些新的概念,正在改变着物理学特别是流体力学与固体力学中有关动力学系统的许多观念。一个新的现象是,没有随机输入的确定性系统,它的输出表面上象是随机的或浑沌的。另一个新现象是,甚至当运动并非浑沌时,许多系统的长期动态历史对初始条 件也是敏感的。描述这种现象的新的数学思想,正在进入非线性振动的领域,它们包括来自拓扑学和数学分析的思想,象Poincaré映射、非整维、Cantor集和奇怪吸引子(简称怪引子)等。这些新思想已在工程振动试验室中逐步得到成功。这个领域的进一步研究,是必须把这些新的思想扩展到多自由度和连续介质振动问题中去。还应该研究在某些非线性问题中丧失可测性的问题,因为它影响非线性材料和结构的力学中数值模拟的范围。
Recently, some new discoveries have been made on the characteristics of complex motions in nonlinear dynamics. These new concepts are changing many of the notions of dynamics in physics, especially in fluid mechanics and solid mechanics. A new phenomenon is that there is no deterministic system without random input, and its output appears to be random or chaotic on the surface. Another new phenomenon is that the long-term dynamic history of many systems is sensitive to initial conditions, even when the movement is not chaotic. The new mathematical ideas that describe this phenomenon are entering the realm of nonlinear vibrations. They include ideas from topological and mathematical analysis, such as Poincaré mapping, non-integral dimensions, Cantor sets, and strange attractors. These new ideas have gradually gained success in vibration engineering laboratories. Further research in this area requires that these new ideas must be extended to problems of multiple degrees of freedom and continuous medium vibrations. The problem of loss of testability in some nonlinear problems should also be studied as it affects the range of numerical simulations in mechanics of nonlinear materials and structures.