高度非线性孤立波与Euler梁的耦合作用研究  

The coupling mechanism between highly nonlinear solitary waves with Euler beam

作　　者：董珊珊 王砚[1] 

机构地区：[1]西安理工大学土木建筑工程学院工程力学系,西安710048

出　　处：《应用力学学报》2018年第4期803-809,共7页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11202159)

摘　　要：无预压缩一维颗粒链中的机械撞击以高度非线性孤立波的形式传播,该孤立波是一种能量包,在较长距离内保持稳定波幅。本文研究高度非线性孤立波与Euler梁的耦合作用,对颗粒链采用离散元模型,基于Hertz定律和Euler梁振动方程并考虑Euler梁的横向振动,建立颗粒链与Euler梁耦合的微分方程组。采用Runge-Kutta法进行求解,得到晶体链中各颗粒的位移、速度解。分析回弹波出现的时间、波幅以及Euler梁的材料特性和几何特性参数等对反射孤立波的影响,结果表明,反射孤立波对Euler梁的弹性模量和几何尺寸在一定范围内是敏感的。本文的研究成果丰富和完善了孤立波探伤理论,为一维颗粒链的实际应用提供了广阔的应用前景。The mechanical impact in one-dimensional granular chains without pre-compression propagates in the form of highly nonlinear solitary waves, which are energy packets that maintains stable amplitude over a long period of time. The coupling mechanism between highly nonlinear solitary waves and Euler beam is investigated. Based on the Hertz's law and the Euler beam vibration equation and considering the lateral vibration of the Euler beam, the complete coupling differential equation system between solitary wave and Euler beam can be obtainedby building a discrete element model. By solving the equations with Runge-Kutta method, the curves of the displacement and velocity of the particles in the crystal chain are attained. By analyzing the time of reflected wave, the energy carried by the reflected wave and the effect of the material properties parameters and geometric characteristic parameters of the Euler beam on solitary wave, it is found that reflected solitary waves are sensitive especially to the Young's module and geometry of the beam. The research results presented in this paper may enrich and perfect the theory of solitary wave flaw detection and provide a broad application prospect for the practical application of one-dimensional particle chains.

关 键 词：一维颗粒链 孤立波 Hertz定律 振动方程 无损检测 

分 类 号：O326[理学—一般力学与力学基础]