沈沒式平板之消波效應

Abstract

本文應用線性元素之邊界元素法，結合有限元素法解析，線性波浪與沈沒 式平板間之交互作用的問題，主要是探討在不同的入射波條件，及不同的 平板長度下，放置不同材質的板子，改變不同的厚度，及轉成不同的角度 ，其結構物對波浪之影響程度。首先，將整個區域畫分成純流體區及彈性 平板區，在純流體區須滿足勢能流理論，在彈性平板區須符合尤拉－白努 利樑方程式(Euler-Bernoulli Beam Equation)，依線性波理論，並配合 線性化的動量方程式與邊界條件及交界面之關係條件，再應用邊界元素法 及有限元素法來解析問題，求得反射係數、透過係數，用來衡量波浪影響 程度。發現當入射波之頻率，於其平板材料之自然頻率接近時，平板會產 生共振，使得反射係數幾乎達到1.0；而且，轉動角度時，平板離自由水 面越近，則反射係數越大；其厚度取太薄時，也使得板子勁度不夠抵擋波 浪而震動，產生彈性行為，加大反射效果，所以，以適當的板長、厚度及 材料強度，可得到幾乎全反射的效果。 Based on a two dimensional potential flow theory,the boundary element method(BEM) is developed and applied tostudy the interaction of linear water wave with a submerged elastic plate. The computational domainis divied into two regions, i.e., a water region and a elastic plate region.The elastic plate is considered as a fleble beam and its defomation is inpure bending. In this thesis, Boundary element method and Finite elementmethod(FEM) are developed and combined to study this interaction problem.The water region is modelling by BEM with linear element, and the flexiblebeam is modelling by one- dimension FEM.Numerical result show that the reflection and transmission coefficients dependon the characteristics of the elastic plate (such as its material, thick, and length)and the location of the elastic plate.The optimum conditions of the submerged plate to archieve minimumtransmission of the waves, can be deduced from the numerical results.Optimun plate length was found to be 0.5-0.7 of the wavelength above the rigid plate. A dramatic results, complete reflection, appeared when wave length almost equalto the nature frequence of the elastic plate.