本文選題：周期性復(fù)合結(jié)構(gòu) + 禁帶　； 參考：《湖南大學(xué)》2014年碩士論文

【摘要】：本文在討論了周期性復(fù)合材料現(xiàn)有基本理論和研究方法的基礎(chǔ)上，提出了一種新的周期性材料，并研究了這種周期性高斯結(jié)構(gòu)薄板的禁帶特性和隔聲降噪性能，對其禁帶進行了優(yōu)化，尋求最低頻帶隙最寬時薄板的結(jié)構(gòu)參數(shù)，，探究其用于工程結(jié)構(gòu)中振動噪聲控制的可行性。主要研究內(nèi)容包括： 利用本征模式匹配法計算了周期性高斯結(jié)構(gòu)薄板的能帶結(jié)構(gòu)，并且采用有限元法對能帶結(jié)構(gòu)進行了驗證，發(fā)現(xiàn)兩種不同方法計算得出的結(jié)果吻合得較好，而用有限元法計算的傳輸譜進一步驗證了本征模式匹配法的合理性與準確性。當把薄板中的高斯結(jié)構(gòu)替換成同面積同高度的長方形時，本文提出的結(jié)構(gòu)能產(chǎn)生更寬的低頻帶隙。從另一種理論的角度，采用“彈簧—質(zhì)量”方法估算了兩種結(jié)構(gòu)的低頻帶隙，比較得出，周期性高斯機構(gòu)薄板產(chǎn)生的低頻帶隙更寬，從而驗證了以上發(fā)現(xiàn)。此外，本文發(fā)現(xiàn)當結(jié)構(gòu)中高斯區(qū)域的高度、薄板厚度以及填充率三個幾何參數(shù)變化時，能帶結(jié)構(gòu)將會發(fā)生顯著的變化。由此，探究了當三個參數(shù)在一定范圍內(nèi)漸變時，能帶結(jié)構(gòu)中最低的三條帶隙的變化情況，旨在尋找能夠發(fā)揮更好的隔聲降噪功能的結(jié)構(gòu)，它應(yīng)當具有較寬的低頻帶隙并且該低頻帶隙有恰當?shù)钠鹗碱l率與截止頻率。 此外，優(yōu)化了周期性高斯結(jié)構(gòu)薄板的最低頻帶隙，以及周期性長方結(jié)構(gòu)薄板的最低頻帶隙，目標為帶隙最寬。采用的方法為RBF徑向基函數(shù)、拉丁超立方采樣和遺傳算法。最終，本文提出結(jié)構(gòu)的最寬低頻帶隙優(yōu)化值為0.1523MHz，真實值為0.1501MHz，而周期性長方結(jié)構(gòu)薄板的最寬低頻帶隙優(yōu)化值為0.1604MHz，真實值為0.1553MHz。兩種結(jié)構(gòu)的優(yōu)化值與真實值之間的誤差均不大于5%，這證明優(yōu)化結(jié)果是正確可靠的，并且，利用RBF徑向基函數(shù)及遺傳算法對低頻帶隙進行優(yōu)化也是比較準確的。
[Abstract]:On the basis of discussing the basic theories and research methods of periodic composite materials, this paper presents a new periodic material, and studies the forbidden band characteristics and noise reduction and noise reduction performance of this periodic Gauss structure sheet, optimizes the band gap and seeks the structural parameters of the thin plate with the widest band gap, and explores its application. The feasibility of vibration and noise control in engineering structures is discussed.
The energy band structure of the periodic Gauss structural plate is calculated by the eigenmode matching method, and the finite element method is used to verify the energy band structure. It is found that the results calculated by the two different methods are in good agreement, and the transmission spectra calculated by the finite element method further verify the rationality and accuracy of the eigenmode matching method. When the Gauss structure in a thin plate is replaced with a same area of same height, the structure proposed in this paper can produce a wider low frequency band gap. From the point of view of another theory, the "spring mass" method is used to estimate the low frequency band gap of the two structures. It is found that the low frequency band gap produced by the periodic Gauss mechanism thin plate is more wide, thus the testing of the low frequency band gap is obtained. In addition, it is found that when the height of the Gauss region, the thickness of the plate and the three geometric parameters of the filling rate are changed in the structure, the band structure will be changed significantly. Thus, the change of the lowest three band gaps in the energy band structure when the three parameters are gradually changed in a certain range is explored in order to find the possible hair. The structure of better sound insulation and noise reduction function should have a wider low frequency band gap and the low frequency band gap has the appropriate starting frequency and cut-off frequency.
In addition, the most low frequency band gap of periodic Gauss structure plate and the lowest band gap of periodic rectangular thin plate are optimized. The aim is the band gap is the most wide. The method is RBF radial basis function, Latin hypercube sampling and genetic algorithm. Finally, the optimum value of low frequency band gap is 0.1523MHz, and the true value is 0.1501MHz The optimum value of the maximum low frequency band gap of the periodic rectangular plate is 0.1604MHz, and the error between the real value and the real value of the two structures of 0.1553MHz. is not more than 5%, which proves that the optimization results are correct and reliable, and it is also more accurate to optimize the low frequency band gap by using the RBF radial basis function and genetic algorithm.
【學(xué)位授予單位】：湖南大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：TB535

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