發(fā)布時間：2018-05-30 06:20

  本文選題：水波能帶理論 + 能帶間隙　； 參考：《廣西民族大學(xué)》2017年碩士論文

【摘要】：眾所周知,在晶體結(jié)構(gòu)中,周期排列的原子和光子能夠?qū)﹄娮硬ㄒ约奥暡óa(chǎn)生調(diào)制作用,從而產(chǎn)生能帶結(jié)構(gòu).同樣的,如果海洋波越過海底的周期性結(jié)構(gòu)地勢,同樣也會使海洋表面波產(chǎn)生能帶結(jié)構(gòu).若能帶結(jié)構(gòu)中出現(xiàn)頻帶間隙,那么頻率落在頻帶間隙中的水波將會被禁阻,即形成了全反射.早在九十年代,科學(xué)家們已經(jīng)開始關(guān)注并研究布洛赫態(tài),這些有關(guān)越過周期性海洋地勢時產(chǎn)生的布洛赫波相關(guān)研究已經(jīng)取得了非常重要的結(jié)果.人們在近海海岸常常能夠發(fā)現(xiàn)與海岸平行且等間距周期性變化的規(guī)則性沙壩.這些天然的沙壩可以反射外海的波浪,減少入射波產(chǎn)生波能侵蝕海岸和破壞近岸建筑物.由于天然沙壩在海洋工程中具有重大意義和研究的價值,人們開始著眼于建立人工沙壩來保護(hù)海岸.為了結(jié)合人工沙壩結(jié)構(gòu)的穩(wěn)定性,本學(xué)位論文主要研究半余弦形,弓形以及拋物形人工沙壩陣列的能帶情況.在前二十多年中,對于水波越過周期性地勢的研究,多數(shù)都是針對常數(shù)水深,其中包括分段常數(shù)和分片常數(shù).而本文所研究的半余弦形沙壩,弓形沙壩和拋物形沙壩均是變水深結(jié)構(gòu).研究內(nèi)容為淺水波越過系列周期性人工沙壩陣列時產(chǎn)生的能帶分析.在問題的求解上,本文采用淺水波方程作為控制方程.求解變水深區(qū)域的自由水面高程函數(shù)時,應(yīng)用變量替換、Taylor級數(shù)展開或Frobenius級數(shù)展開方法,求得淺水波方程的級數(shù)解析解.再利用布洛赫原理,計算相應(yīng)地形下的能帶表達(dá)式.通過將透射系數(shù)趨于0的頻率所在區(qū)域與能帶頻率的區(qū)域進(jìn)行對比,可以驗證能帶表達(dá)式的準(zhǔn)確性.最后,本文討論了人工沙壩陣列的參數(shù)(如寬度等)對能帶結(jié)構(gòu)產(chǎn)生的影響,從而給出建造人工沙壩的理論建議,為在實際近海工程中對這三類人工沙壩的建造和優(yōu)化提供頗具價值的理論指導(dǎo).
[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.
【學(xué)位授予單位】：廣西民族大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：P753

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本文編號：1954256