浅水波越过周期排列的系列人工沙坝的能带分析

发布时间：2018-05-30 06:20

本文选题：水波能带理论 + 能带间隙　；参考：《广西民族大学》2017年硕士论文

【摘要】：众所周知,在晶体结构中,周期排列的原子和光子能够对电子波以及声波产生调制作用,从而产生能带结构.同样的,如果海洋波越过海底的周期性结构地势,同样也会使海洋表面波产生能带结构.若能带结构中出现频带间隙,那么频率落在频带间隙中的水波将会被禁阻,即形成了全反射.早在九十年代,科学家们已经开始关注并研究布洛赫态,这些有关越过周期性海洋地势时产生的布洛赫波相关研究已经取得了非常重要的结果.人们在近海海岸常常能够发现与海岸平行且等间距周期性变化的规则性沙坝.这些天然的沙坝可以反射外海的波浪,减少入射波产生波能侵蚀海岸和破坏近岸建筑物.由于天然沙坝在海洋工程中具有重大意义和研究的价值,人们开始着眼于建立人工沙坝来保护海岸.为了结合人工沙坝结构的稳定性,本学位论文主要研究半余弦形,弓形以及抛物形人工沙坝阵列的能带情况.在前二十多年中,对于水波越过周期性地势的研究,多数都是针对常数水深,其中包括分段常数和分片常数.而本文所研究的半余弦形沙坝,弓形沙坝和抛物形沙坝均是变水深结构.研究内容为浅水波越过系列周期性人工沙坝阵列时产生的能带分析.在问题的求解上,本文采用浅水波方程作为控制方程.求解变水深区域的自由水面高程函数时,应用变量替换、Taylor级数展开或Frobenius级数展开方法,求得浅水波方程的级数解析解.再利用布洛赫原理,计算相应地形下的能带表达式.通过将透射系数趋于0的频率所在区域与能带频率的区域进行对比,可以验证能带表达式的准确性.最后,本文讨论了人工沙坝阵列的参数(如宽度等)对能带结构产生的影响,从而给出建造人工沙坝的理论建议,为在实际近海工程中对这三类人工沙坝的建造和优化提供颇具价值的理论指导.
[Abstract]:It is well known that in crystal structure periodically arranged atoms and photons can modulate electron waves and acoustic waves thus producing band structures. Similarly, if ocean waves cross the periodic structure of the sea floor, they will also cause the energy band structure of the ocean surface waves. If the band gap occurs in the energy band structure, then the water wave which falls in the frequency band gap will be blocked, that is, the total reflection will be formed. As early as the 1990s, scientists began to pay attention to and study the Bloch state, and these studies on the Bloch waves generated over the periodic ocean topography have obtained very important results. Regular sandbars parallel to coasts and periodically varying at equal intervals are often found on offshore coasts. These natural sandbars can reflect waves off the sea, reducing the incidence of waves that can erode the coast and destroy coastal buildings. Due to the great significance and research value of natural sand dams in marine engineering, people begin to focus on the establishment of artificial sand dams to protect the coast. In order to combine the stability of artificial sand dam structure, the energy band of semi-cosine, arched and parabolic artificial sand dam arrays is studied in this dissertation. In the past twenty years, most of the researches on the periodic topography of water waves have focused on the constant water depth, including piecewise constants and piecewise constants. The semi-cosine sand dam, the arch sand dam and the parabolic sand dam studied in this paper are all variable water depth structures. The study focuses on the energy band analysis of shallow water waves over a series of periodic artificial sand dam arrays. In order to solve the problem, the shallow water wave equation is used as the governing equation in this paper. In order to solve the free water surface elevation function in the region of varying water depth, the series analytic solution of shallow water wave equation is obtained by using the method of replacing the Taylor series expansion or Frobenius series expansion with variables. The energy band expression under the corresponding terrain is calculated by using Bloch principle. The accuracy of the energy band expression can be verified by comparing the region where the transmission coefficient tends to 0 with the region of the band frequency. Finally, the influence of the parameters of artificial sand dam array (such as width etc.) on the energy band structure is discussed, and the theoretical suggestions for the construction of artificial sand dam are given. It provides valuable theoretical guidance for the construction and optimization of these three types of artificial sand dams in the actual offshore engineering.
【学位授予单位】：广西民族大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P753

【参考文献】