【作者】 郑兆昌；

【Author】 Zheng Zhaochang (Department of Engineering Mechanics,School of Aerospace,Tsinghua University,Beijing 100084)

【机构】 清华大学,航天航空学院工程力学系；

【摘要】 十九世纪欧洲有关于一件驻波和两件行波的故事:一是沙盘呈现模态到正确建立弹性薄板振动方程、边界条件的过程,经具有学术民主和哥廷根精神的诸多力学大师努力下得到本征值解;二是麦克斯韦尔借鉴于力学学科已形成的弹性理论,经过抽象思维、数学演绎推理,发展成电磁学新理论麦克斯韦尔方程组,并为实验所证实。三是由罗苏从观察到孤立波的现象,建立描述这一现象的KdV方程并寻求解,而后又发展成非线性KdV波理论并逐步找到解。理性思维和实验研究形成古代和近代科学的发展史。抽象化形成各种概念和理论,而后经试验验证用于实践;反之亦然。自牛顿定律用微分方程表述,始于力学的直观性经精确表达成为各类科学发展史的领头羊。线性振动理论是力学和数学中最高度发展的典范,丰富多彩并广为应用。欧拉发现模态叠加理论,简单印记描绘自然规律,非线性振动由于失去线性系统四性而成为世界性难题,成为本世纪研究的主要对象,线性系统小修改但可能产生的大效应,危险的突发性灾难事故,事实上是由少数甚之单模态所控制,利用模态减缩将大型工程中非线性问题化为少数模态甚至单个。于是可进行局部试验获取参数,渐近定性分析预测,防止分岔发生。惊呼模态运动真奇妙。更多还原

【Abstract】 19 century in Europe about the story of a standing wave and the two traveling waves:（1） From the normal modes are presented on sad table, around half century the model analysis of thin elastic plate is established under the effect of various mechanical of academic with the democracy of science as will as the Goetingen sprits.The applied elastic theory without satisfied all the equation and boundary conditions is developed for bar,beam,plate and shell and widely used in engineering practice.（2）Based on the theory of fluid and elastics, Maxwell introduced the concept of velocity field to study the fluid flow,found physical meaning of flow velocity is a vector.Comparison of different science is an important method of scientific researches.Maxwell’s equation is a paradigm of interdisciplinary development.（3）Russell observed solitary wave phenomenon, KdV equation is established to describe the phenomenon and to find solutions. The nonlinear wave of KdV equation is developed and solutions are found gradually.Rational thinking and experimental research promote scientific development either in case of old or modern.From the observed phenomena through abstractional thinking formed various concepts and theory,then go to the real world by test to verification;vice versa.Since Newton’s 2^nd law describes with calculus,the intuiting of mechanics with accuracy expression become a leader in history of scientific development.The theory of linear vibration is the most highly developed nonesuch of mechanics and mathematics,the wide applications play rich and colorful.The model superposition invented by Euler. simple sigil describes the nature.The nonlinear vibration is a world difficulty problem due to lose of the linear four characteristics.The small changes of linear system may be produced a big effect.The dangerous accident may be happened suddenly.In fact only few modes even single-mode control the event.The normal mode seems as a bridge communicated the linear and non linear vibration.The nonlinear problem of large scale engineering can be reduced to few modes even one by model reduction mothod,then the approximate quantity analysis can be prediction the bifurcation of the system.What I more than once called"the fantastic moving of modes".更多还原