非均匀球壳结构弹性波理论分析及数值计算

发布时间：2018-01-10 10:19

本文关键词：非均匀球壳结构弹性波理论分析及数值计算　出处：《北京科技大学》2016年博士论文　论文类型：学位论文

【摘要】：大型球壳结构广泛使用于各个工业领域内,针对该类结构的安全保障技术也一直是学术和工程研究的热点。弹性导波检测技术是在传统超声波检测基础上发展而来的,能够沿较长的距离传播,因此利用很少的传感器就能实现一个较大范围的损伤检测和材料性能测试。同时,当结构受到动载冲击时,结构内的夹杂(空洞)将导致弹性波的散射以及动应力集中,这将极大影响结构的强度和使用寿命。针对大型球壳结构的检测、安全评价与材料性能测试问题,本文主要研究内容如下：(1)研究了带粘弹性涂层球壳中的弹性波传播特性,以及粘弹性层厚度和阻尼因子对传播特性的影响。粘弹性层的材料性能用标准线性固体描述,带涂层球壳结构中的弹性波频散方程采用传递矩阵法推导出,最后分别计算出弹性波的频散曲线和衰减曲线,以及涂层厚度和阻尼因子对频散曲线和衰减曲线的影响。(2)针对球壳结构的材料参数沿半径方向呈指数型变化的情况,提出了一种直接针对位移的分离变量方法,成功的实现了位移函数的变量分离,简化了分析过程,得到了各位移分量的解析解,并建立的频散方程。文章对频散方程进行无量纲化后,对一系列的材料梯度因子进行了参数化研究,分别求解了该系列结构的频散曲线。(3)针对球壳结构中存在的空洞、夹杂问题引起的弹性波散射和动应力集中问题,以双球坐标描述球形厚板中心和夹杂中心的空间位置,根据不同弹性波场的物理性质,将球形板中的入射波、散射波和夹杂中的驻波分别采用不同的球坐标表示。文章采用了一种球波函数加法,实现了不同球坐标下球波函数的变换,并推导了位移、应力分量的解析解。最后结合球形厚板的边界条件和夹杂界面的连续条件,求解了不同材料属性夹杂,以及空洞情况下,弹性波的散射和动应力集中因子三维分布情况。
[Abstract]:Large spherical shell structures are widely used in various industrial fields. The safety and security technology for this kind of structures has been a hot topic in academic and engineering research. Elastic guided wave detection technology is developed on the basis of traditional ultrasonic detection and can spread over a long distance. Therefore, a large range of damage detection and material performance testing can be achieved by using a few sensors. At the same time, when the structure is subjected to dynamic impact. The inclusion (cavity) in the structure will lead to elastic wave scattering and dynamic stress concentration, which will greatly affect the strength and service life of the structure. The main contents of this paper are as follows: (1) the propagation characteristics of elastic wave in a spherical shell with viscoelastic coating are studied. The material properties of viscoelastic layer are described by standard linear solid, and the dispersion equation of elastic wave in spherical shell with coating is derived by transfer matrix method. Finally, the dispersion curve and attenuation curve of elastic wave are calculated respectively. The influence of coating thickness and damping factor on dispersion curve and attenuation curve. In this paper, a method of separating displacement variables directly is proposed, which successfully realizes the separation of displacement function variables, simplifies the analysis process, and obtains the analytical solutions of each displacement component. After dimensionless dispersion equation, a series of material gradient factors were parameterized. The dispersion curves of this series of structures are solved respectively. The elastic wave scattering and dynamic stress concentration problems caused by the inclusion problem and the cavity in the spherical shell structure are solved respectively. The space position of the center of thick spherical plate and the center of inclusion is described by double spherical coordinates. According to the physical properties of different elastic wave fields, the incident wave in spherical plate is described. The scattering wave and the standing wave in the inclusion are represented by different spherical coordinates. In this paper, a spherical wave function addition method is used to realize the transformation of the spherical wave function under different spherical coordinates, and the displacement is derived. Finally, the boundary conditions of spherical thick plate and the continuity condition of inclusion interface are combined to solve the inclusions with different material properties, as well as in the case of voids. Three dimensional distribution of scattering and dynamic stress concentration factors of elastic waves.
【学位授予单位】：北京科技大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O347.41

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