本文以彈簧與質量塊組成的週期系統為基礎，提出一個由兩種質量塊交錯擺放組合的結構，並且計算此結構的色散關係與等頻圖，得到其可以造成負折射之現象的結果。並且藉由有限差分的模擬方式模擬波實際上在結構中傳遞的行為是否與從等頻圖中預測的結果相符，可見其結果為吻合。為了增加此結構的應用性，藉由參數分析如何得到較大的頻寬，發現在兩質量塊質量接近時能得到較大的頻寬並且等頻圖不會呈現直線以至於折射波趨於準直現象，若使兩質量塊質量相差很大或是增加彈簧常數k_2的大小，雖然都能得到相當大的頻寬，但是有較大的比例等頻圖呈現直線以至於折射波趨於準直現象。
為了使前述離散的彈簧質量系統得到的結果格能有效地應用，本文將彈簧質量塊系統類比成平板中的結構，在色散曲線中可以在同頻率帶處找到一條曲線具負斜率，經過等頻圖的折射角判斷並且以有限元素的全波模擬證實其負折射的效果。

In this paper, basing on the periodic system consisting of spring and mass, presents a structure composed of two mass masses arranged in a staggered pattern. Then can calculating the dispersion relation and the equifrequency contour of the structure to obtain the result that it can cause negative refraction. By simulating with the finite difference method, the result showed that the wave actually transmitted in the structure behaves negative refraction. In order to increase the applicability of this structure, how to get a larger bandwidth that can get negative refraction is an issue. By parameter analysis, we can find that when the masses of two masses are close, a larger bandwidth can be obtained and the contour do not appear straight so that the refracted waves tend to be collimation.
In order to apply the results obtained by the discrete spring mass system described above effectively, the spring mass system is applied in the structure as phononic crystal in a plate. In the dispersion curve, a curve with a negative slope can be found at the same frequency that can find negative refraction in spring mass system. With finite element analysis, the negative refraction can be found in the phononic crystal plate.

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