本文關(guān)鍵詞：具有自相似結(jié)構(gòu)的聲學(xué)超材料板的帶隙特性研究　出處：《哈爾濱工業(yè)大學(xué)》2016年碩士論文　論文類型：學(xué)位論文

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【摘要】：聲學(xué)超材料是具有頻率帶隙的人工復(fù)合結(jié)構(gòu),它對(duì)一定頻率的彈性波具有阻隔的作用,這使其在隔聲降噪領(lǐng)域得到了廣泛的研究。本文對(duì)聲學(xué)超材料的帶隙行為及聲載荷響應(yīng)進(jìn)行了研究。在振動(dòng)吸收器原理的基礎(chǔ)上,通過(guò)理論分析和仿真計(jì)算,研究了局部共振聲學(xué)超材料板胞元帶隙的變化規(guī)律,建立了聲學(xué)超材料板的質(zhì)量彈簧分析模型,根據(jù)薄板彎曲振動(dòng)理論給出了聲學(xué)超材料板的振動(dòng)控制方程,通過(guò)MATLAB編程計(jì)算得到了結(jié)構(gòu)的色散關(guān)系,模態(tài)分析表明,反相位共振模態(tài)出現(xiàn)在帶隙范圍內(nèi),從而驗(yàn)證了結(jié)果的正確性。質(zhì)量塊和薄膜的初始變形量是結(jié)構(gòu)的振動(dòng)特性的主要影響因素,通過(guò)計(jì)算不同質(zhì)量塊質(zhì)量和薄膜預(yù)載荷條件下結(jié)構(gòu)的色散關(guān)系,發(fā)現(xiàn)質(zhì)量塊質(zhì)量和初始變形量必須控制在合理的范圍內(nèi)才能在低頻獲得寬頻帶的帶隙結(jié)構(gòu)。進(jìn)一步分析了無(wú)質(zhì)量塊聲學(xué)超材料板中Bragg散射和局部共振兩種帶隙產(chǎn)生機(jī)理的轉(zhuǎn)化條件,給出了相應(yīng)的材料參數(shù)變化范圍。考慮到質(zhì)量塊的存在有利于實(shí)現(xiàn)聲學(xué)超材料板低頻寬帶帶隙特性,基于自相似結(jié)構(gòu)形狀,提出了多質(zhì)量環(huán)構(gòu)成的自相似聲學(xué)超材料板的設(shè)計(jì)方案,并驗(yàn)證了結(jié)構(gòu)的帶隙特征。結(jié)果表明,質(zhì)量環(huán)的增加使得聲學(xué)超材料板的帶隙頻帶變寬,帶隙的中心頻率降低,帶隙的個(gè)數(shù)增加,窄質(zhì)量環(huán)比寬質(zhì)量環(huán)更能獲得寬頻帶隙。對(duì)自相似結(jié)構(gòu)聲振響應(yīng)分析發(fā)現(xiàn),第一次共振時(shí)質(zhì)量塊的位移遠(yuǎn)大于其它部位,此時(shí)的質(zhì)量塊在振動(dòng)過(guò)程吸收大部分的能量;第二次共振時(shí),質(zhì)量塊和邊框的共振位移很小,內(nèi)部環(huán)和膜振動(dòng)消耗的能量增加;質(zhì)量環(huán)的增加有利于結(jié)構(gòu)能量的均勻分布。通過(guò)比較超材料板的透射聲壓和入射聲壓,給出了多組合板結(jié)構(gòu)的傳遞函數(shù)。研究表明,組合數(shù)越多,傳遞函數(shù)絕對(duì)值越大;聲學(xué)超材料板之間的距離對(duì)傳遞函數(shù)的影響類似于正弦函數(shù)變化規(guī)律;組合數(shù)和兩板之間的距離只有在合適范圍內(nèi)傳遞函數(shù)才能取得較為理想的值,這為聲學(xué)超材料板的隔聲檢測(cè)提供參考依據(jù)。
[Abstract]:Acoustic metamaterial is an artificial composite structure with frequency band gap. It has the function of blocking the elastic waves at a certain frequency, making it widely studied in the field of sound insulation and noise reduction. The band gap behavior and acoustic load response of acoustic supermaterials are studied in this paper. Based on the principle of vibration absorber, through theoretical analysis and simulation, changes of cell bandgap metamaterials in the local resonance acoustic research, established a quality spring acoustic metamaterial plate model, vibration control equation of acoustic metamaterial plate based on thin plate bending vibration theory is given, the dispersion relation of structure through the MATLAB programming calculation, modal analysis shows that the anti phase resonance modes in the band gap range, so as to verify the correctness of the results. The initial mass and the deformation of the film is the main influence factors of the vibration characteristics of the structure, through the dispersion relation calculation of different mass and film pre loading conditions, found that the mass and initial deformation must be controlled in a reasonable range can be obtained with wide band gap structure in low frequency. The transformation conditions of the two kinds of bandgap generation mechanism of Bragg scattering and local resonance in mass free bulk acoustic metamaterials are further analyzed, and the corresponding range of material parameters is given. Considering the existence of mass blocks, the low-frequency broadband bandgap characteristics of acoustic metamaterials are realized. Based on the shape of self similar structures, the design scheme of self similar acoustic metamaterials with multiple mass rings is proposed, and the band gap characteristics of the structures are verified. The results show that the increase of mass ring makes the band gap of acoustic metamaterials wider, the central frequency of band gap decreased, the number of band gaps increased, and the wide band gap of narrow mass ring wider mass ring can be obtained. The self similar structure of sound and vibration response analysis, the first resonance mass displacement is far greater than the other parts, the mass in the process of vibration absorb most of the energy; the second resonance, resonance mass displacement and border is very small, the internal energy ring and membrane vibration increased consumption; increase the quality of the ring beneficial to uniform distribution of energy structure. By comparing the transmission sound pressure and the incident sound pressure of the supermaterial plate, the transfer function of the multi composite plate structure is given. Research shows that the combination of the number, the greater the absolute value of the transfer function between the acoustic material board; ultra distance is similar to the sine function variation of the transfer function; between the number and the two in the distance is only in the appropriate range of transfer function can achieve the ideal value, to provide reference for the detection of ultra acoustic insulation a sheet of material.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類號(hào)】：TB34
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本文編號(hào)：1347195