高度非线性孤立波与功能梯度材料的耦合作用研究

发布时间：2018-07-12 17:13

本文选题：颗粒链 + 高度非线性孤立波　；参考：《西安理工大学》2017年硕士论文

【摘要】：一维颗粒链是一种特殊的介质,一维颗粒链中包含着线性、弱非线性以及强非线性动态响应,其中,强非线性动态响应使得颗粒链受碰撞后产生一种应力波——高度非线性孤立波,孤立波的稳定性强,可控性好,是一种非常好的信息载体。功能梯度材料(Functionally graded materials, FGM)是一种新型材料,功能梯度材料的材料要素(组成、结构)沿某一方向呈现连续梯度变化,其材料属性在该方向上也呈现连续变化的状态,功能梯度材料广泛应用在航空航天领域中,研究人员致力于研究其力学特性以及结构优化设计。一维颗粒链受到撞击后会产生稳定的孤立波,基于高度非线性孤立波对弹性大板的健康诊断和无损检测理论,研究一维颗粒链和功能梯度材料的耦合作用,全面探究反射孤立波对与之直接接触的功能梯度材料的材料属性、几何构型的敏感程度。本文以一维颗粒链中的高度非线性孤立波为信息载体,将功能梯度材料作为与之直接接触的结构体,研究一维颗粒链与功能梯度材料的耦合作用,并进行建模和仿真分析,主要研究内容如下:1、介绍颗粒以及颗粒链的性质:基于牛顿摆引出特殊的介质——颗粒链,通过颗粒以及颗粒链的性质,引出本文所要研究的主要内容;基于赫兹接触定律推导颗粒与不同几何构型的结构体作用时,压缩量与接触力的关系。确定颗粒的数量和颗粒的材料属性,基于经典牛顿定律推导一维颗粒链和功能梯度材料耦合作用的待定方程组。2、研究一维颗粒链与半无限功能梯度结构体的耦合作用:基于Hertz接触定律和梯度半空间接触问题下荷载与压入深度的关系,通过牛顿第二定律,建立一维颗粒链与半无限功能梯度结构体耦合作用的微分方程组,并采用四阶Runge-Kutta法求解。得到不同弹性模量和梯度参数下中间颗粒的速度曲线和各个颗粒的位移曲线,分析结构体的弹性模量和梯度参数对回弹孤立波的影响。3、研究一维颗粒链与功能梯度薄板的耦合作用:基于Hertz定律、梯度半空间接触问题下荷载与压入深度的关系,通过牛顿第二定律以及板的内在非弹性理论,建立一维颗粒链与功能梯度薄板耦合作用的微分方程组,并采用四阶Runge-Kutta法求解。分别得到五个不同物性参数下中间颗粒的速度曲线和各个颗粒的位移曲线,分析功能梯度薄板的物性参数在其变化范围内对回弹孤立波的影响。4、对接触和碰撞过程进行建模与仿真分析:对单个颗粒和半无限均质材料的接触过程进行有限元仿真分析;对一维颗粒链和半无限均质材料碰撞过程进行有限元仿真分析。
[Abstract]:One-dimensional particle chain is a special medium, which contains linear, weakly nonlinear and strongly nonlinear dynamic responses. Because of the strong nonlinear dynamic response, a kind of stress wave-high nonlinear solitary wave is produced after the particle chain is collided. The solitary wave has strong stability and good controllability. It is a very good information carrier. Functional graded materials (FGM) is a new type of material. The material elements (composition, structure) of functionally graded materials (FGM) show continuous gradient changes along a certain direction, and the material properties of FGM also show continuous changes in that direction. Functionally graded materials (FGM) are widely used in aeronautics and astronautics. Researchers focus on their mechanical properties and structural optimization design. One dimensional particle chain will produce stable solitary waves after impact. Based on the health diagnosis and nondestructive testing theory of high nonlinear solitary waves, the coupling effect between one-dimensional particle chains and functionally graded materials is studied. The sensitivity of reflective solitary waves to the material properties and geometric configurations of functionally graded materials in direct contact with them is investigated. In this paper, the highly nonlinear solitary wave in one-dimensional particle chain is used as the information carrier, and the functionally graded material is taken as the structure directly in contact with it. The coupling effect between the one-dimensional particle chain and the functionally graded material is studied, and the modeling and simulation are carried out. The main research contents are as follows: 1. The properties of particles and their chains are introduced. Based on Newtonian pendulum, the special media-particle chain is introduced, and the main contents of this paper are introduced by the properties of particles and particle chains. Based on Hertz's contact law, the relation between the amount of compression and the contact force is derived for the interaction between particles and structures with different geometric configurations. Determine the number of particles and the material properties of the particles, Based on the classical Newton's law, the undetermined equations of one-dimensional particle chain and functionally graded material coupling are derived. The coupling between one-dimensional particle chain and semi-infinite functionally gradient structure is studied: based on Hertz's contact law and gradient half-space. The relationship between load and indentation depth under contact problem, By means of Newton's second law, the differential equations for the coupling of one-dimensional particle chains with semi-infinite functionally gradient structures are established and solved by the fourth-order Runge-Kutta method. The velocity curves of the intermediate particles and the displacement curves of each particle are obtained under different elastic modulus and gradient parameters. The influence of elastic modulus and gradient parameters on springback solitary wave is analyzed. The coupling effect of one-dimensional particle chain and functionally graded thin plate is studied. Based on Hertz's law, the relationship between load and indentation depth under gradient half-space contact problem is studied. By means of Newton's second law and the inner inelastic theory of plates, the differential equations of one-dimensional particle chain coupled with functionally graded thin plates are established and solved by the fourth-order Runge-Kutta method. The velocity curves of the intermediate particles and the displacement curves of each particle were obtained under five different physical parameters. The influence of physical parameters of functionally gradient thin plate on springback solitary wave is analyzed. The contact and collision processes are modeled and simulated. The contact process of single particle and semi-infinite homogeneous material is simulated by finite element method. The collision process of one-dimensional particle chain and semi-infinite homogeneous material is simulated by finite element method.
【学位授予单位】：西安理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TB34;O34

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