高度非线性孤立波与弹性大板的耦合作用研究

发布时间：2018-03-05 10:43

本文选题：孤立波　切入点：赫兹定律　出处：《固体力学学报》2017年01期 　论文类型：期刊论文

【摘要】：一维颗粒链的一端受到一个有初速度颗粒的撞击,导致颗粒连中产生稳定传播的应力波——高度非线性孤立波,该应力波的波长、波速以及幅值都能保持很好的稳定性,且遇到边界才会反射.孤立波是一种良好的信息载体,广泛应用于无损检测技术中.基于孤立波的特性,研究高度非线性孤立波与弹性大板耦合作用,基于赫兹定律和板的内在非弹性理论,推导出晶体链与大板的耦合微分方程组.用龙格库塔法求解该微分方程组,得到颗粒链中各颗粒的位移、速度曲线.通过分析回弹波出现的时间、回弹波所携带的能量以及模量、厚度、重力等对孤立波的影响,发现反射孤立波对大板的弹性模量和厚度尤为敏感,此外,颗粒链的摆放对整个耦合过程也有影响.研究的结果为孤立波对结构体的无损探伤提供了理论依据,该技术可实现对结构体的快速检查和可控性研究.
[Abstract]:One end of the one-dimensional particle chain is impacted by a particle with initial velocity, which leads to the stable propagation of a highly nonlinear solitary wave in the particle connection. The wave length, wave velocity and amplitude of the stress wave can all maintain good stability. The solitary wave is a good information carrier and widely used in nondestructive testing. Based on the characteristics of the solitary wave, the coupling effect between the highly nonlinear solitary wave and the elastic plate is studied. Based on Hertz's law and the inner inelastic theory of plates, the coupled differential equations of crystal chains and large plates are derived. The Runge-Kutta method is used to solve the differential equations, and the displacement of each particle in the particle chain is obtained. Velocity curve. By analyzing the time when the springback wave appears, the influence of the energy and modulus, thickness and gravity of the springback wave on the solitary wave, it is found that the reflected solitary wave is particularly sensitive to the elastic modulus and thickness of the large plate. The results of the study provide a theoretical basis for the nondestructive inspection of the structure by solitary waves, and the technique can be used for the rapid inspection and controllability study of the structure.
【作者单位】：西安理工大学土木建筑工程学院工程力学系;
【基金】：国家自然科学基金项目(11202159)资助
【分类号】：O302

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