本文選題：聲固耦合系統(tǒng) + 有限元法��； 參考：《湖南大學(xué)》2015年博士論文

【摘要】：聲固耦合系統(tǒng)廣泛存在于汽車、輪船、飛機(jī)、潛艇和航天器等運(yùn)載工具之中。聲固耦合系統(tǒng)的結(jié)構(gòu)振動所產(chǎn)生的中低頻噪聲是上述運(yùn)載工具的主要噪聲來源之一。基于聲固耦合系統(tǒng)聲學(xué)性能分析的優(yōu)化設(shè)計(jì)技術(shù)是控制結(jié)構(gòu)中低頻噪聲最直接和最有效的方法。傳統(tǒng)的聲固耦合系統(tǒng)的分析與優(yōu)化一般是基于確定系統(tǒng)參數(shù)，并借助經(jīng)典CAE技術(shù)和優(yōu)化方法進(jìn)行求解。然而，在許多實(shí)際工程問題中，制造、裝配和測量的誤差，環(huán)境的變化莫測和外部激勵的不可預(yù)測等因素引起的不確定性廣泛存在于聲固耦合系統(tǒng)。大多數(shù)情況下，這些不確定性因素的影響較小，但當(dāng)它們耦合在一起時(shí)，則可能導(dǎo)致實(shí)際聲固耦合系統(tǒng)的響應(yīng)產(chǎn)生較大偏差，甚至導(dǎo)致反相現(xiàn)象的出現(xiàn)。以不準(zhǔn)確的聲固耦合系統(tǒng)響應(yīng)為基礎(chǔ)，對聲固耦合系統(tǒng)進(jìn)行優(yōu)化，可能導(dǎo)致優(yōu)化后的聲固耦合系統(tǒng)無法滿足給定設(shè)計(jì)要求。 要實(shí)現(xiàn)不確定聲固耦合系統(tǒng)的有效分析與優(yōu)化，首先須借助不確定性理論構(gòu)建不確定聲固耦合系統(tǒng)的數(shù)值分析模型，并提出相應(yīng)的不確定數(shù)值分析算法，以研究不確定性因素對聲固耦合系統(tǒng)響應(yīng)的影響；再依據(jù)不確定性因素對聲固耦合系統(tǒng)響應(yīng)的影響，建立不確定聲固耦合系統(tǒng)的優(yōu)化模型，并提出相應(yīng)的高效優(yōu)化算法，以實(shí)現(xiàn)不確定聲固耦合系統(tǒng)的高效優(yōu)化設(shè)計(jì)。為此，本文擬從單一不確定模型（隨機(jī)模型和區(qū)間模型）入手，逐步深入到混合不確定模型（隨機(jī)與區(qū)間混合不確定模型和區(qū)間隨機(jī)模型），并在此基礎(chǔ)上對不確定聲固耦合系統(tǒng)的數(shù)值分析與優(yōu)化算法進(jìn)行系統(tǒng)性研究。 論文完成的主要研究工作包括： （1）建立了變量變換隨機(jī)攝動有限元法，可用于隨機(jī)聲固耦合系統(tǒng)響應(yīng)分析。變量變換隨機(jī)攝動有限元法采用一階攝動技術(shù)將聲固耦合系統(tǒng)的響應(yīng)近似為隨機(jī)變量的線性函數(shù)；接著，采用變量變換技術(shù)計(jì)算響應(yīng)的概率密度函數(shù)；最后，在響應(yīng)概率密度函數(shù)的基礎(chǔ)上，根據(jù)置信區(qū)間的定義計(jì)算響應(yīng)的置信區(qū)間。某隨機(jī)殼結(jié)構(gòu)聲固耦合系統(tǒng)的數(shù)值分析結(jié)果表明：變量變換隨機(jī)攝動有限元法能有效地分析隨機(jī)聲固耦合系統(tǒng)響應(yīng)的概率密度函數(shù)和置信區(qū)間。 （2）提出了修正區(qū)間攝動有限元法，，可用于區(qū)間聲固耦合系統(tǒng)的響應(yīng)分析。區(qū)間攝動有限元法以一階Taylor級數(shù)展開和一階Neumann級數(shù)展開為基礎(chǔ)；子區(qū)間攝動有限元法將區(qū)間變量劃分為若干個子區(qū)間，再采用區(qū)間攝動有限元法和區(qū)間并集運(yùn)算求解區(qū)間聲固耦合系統(tǒng)的響應(yīng)變化范圍；修正區(qū)間攝動有限元法以一階Taylor級數(shù)展開和修正Neumann級數(shù)展開為基礎(chǔ)。某殼結(jié)構(gòu)聲固耦合系統(tǒng)的數(shù)值分析結(jié)果表明：區(qū)間攝動有限元法僅適用于不確定區(qū)間較小的聲固耦合系統(tǒng)響應(yīng)分析；子區(qū)間攝動有限元法通過將區(qū)間變量劃分為若干個子區(qū)間，可有效提高區(qū)間聲固耦合系統(tǒng)的分析精度，但其計(jì)算成本隨著子區(qū)間數(shù)的增加呈指數(shù)形式增加；修正區(qū)間攝動有限元法通過考慮高階Neumann級數(shù)項(xiàng)，能在小幅增加計(jì)算成本的條件下，大幅提高區(qū)間聲固耦合系統(tǒng)的分析精度。 （3）建立了混合攝動頂點(diǎn)法，可有效且高效地分析隨機(jī)與區(qū)間混合不確定聲固耦合系統(tǒng)響應(yīng)的期望和方差變化范圍�；旌蠑z動頂點(diǎn)法將隨機(jī)與區(qū)間混合不確定聲固耦合系統(tǒng)的響應(yīng)近似為隨機(jī)變量和區(qū)間變量的線性函數(shù)，接著，根據(jù)響應(yīng)與區(qū)間變量的線性關(guān)系，采用頂點(diǎn)法計(jì)算響應(yīng)的上下界；然后，采用隨機(jī)矩技術(shù)計(jì)算響應(yīng)上下界的期望和方差，并以上下界的期望為期望的上下界，以上下界的方差為方差的上下界。某殼結(jié)構(gòu)聲固耦合系統(tǒng)的數(shù)值分析結(jié)果表明，混合攝動頂點(diǎn)法與大樣本下混合攝動Monte-Carlo法的計(jì)算精度相同，但混合攝動頂點(diǎn)法的計(jì)算效率遠(yuǎn)高于大樣本下混合攝動Monte-Carlo法。 （4）提出了區(qū)間隨機(jī)攝動頂點(diǎn)法，可用于區(qū)間隨機(jī)聲固耦合系統(tǒng)響應(yīng)分析。區(qū)間隨機(jī)攝動頂點(diǎn)法在區(qū)間攝動技術(shù)和隨機(jī)攝動技術(shù)的基礎(chǔ)上提出區(qū)間隨機(jī)攝動技術(shù)，將區(qū)間隨機(jī)聲固耦合系統(tǒng)的響應(yīng)近似為區(qū)間隨機(jī)變量和區(qū)間變量的線性函數(shù)；再根據(jù)響應(yīng)與區(qū)間變量的線性關(guān)系，采用頂點(diǎn)法計(jì)算響應(yīng)的上下界；最后采用隨機(jī)矩技術(shù)計(jì)算響應(yīng)上下界的期望和標(biāo)準(zhǔn)差，并以上下界的期望為期望的上下界，以上下界的方差為方差的上下界。某殼結(jié)構(gòu)聲固耦合系統(tǒng)和某汽車內(nèi)聲場的數(shù)值分析結(jié)果表明：區(qū)間隨機(jī)攝動頂點(diǎn)法能有效且高效地預(yù)測區(qū)間隨機(jī)聲固耦合系統(tǒng)響應(yīng)期望和方差的變化范圍。 （5）構(gòu)建了混合不確定模型（隨機(jī)與區(qū)間混合不確定模型和區(qū)間隨機(jī)模型）下聲固耦合系統(tǒng)的嵌套優(yōu)化模型；提出了優(yōu)化模型目標(biāo)函數(shù)和約束條件的混合攝動-隨機(jī)矩法和混合攝動-變量變換法，實(shí)現(xiàn)了嵌套優(yōu)化模型向單層優(yōu)化模型的轉(zhuǎn)換。板結(jié)構(gòu)聲固耦合系統(tǒng)優(yōu)化設(shè)計(jì)結(jié)果表明：混合攝動-隨機(jī)矩法和混合攝動-變量變換法能有效且高效地計(jì)算混合不確定優(yōu)化模型的目標(biāo)函數(shù)與約束條件；采用混合不確定優(yōu)化方法對混合不確定聲固耦合系統(tǒng)進(jìn)行優(yōu)化，能有效降低聲固耦合系統(tǒng)的聲壓響應(yīng)，改善混合不確定聲固耦合系統(tǒng)的聲學(xué)性能。 （6）提出了區(qū)間攝動波函數(shù)法，可用于區(qū)間聲場低頻和中頻響應(yīng)分析；提出了混合攝動波函數(shù)法，可用于隨機(jī)與區(qū)間混合不確定聲場低頻和中頻響應(yīng)分析。三維聲腔模型的數(shù)值分析結(jié)果表明，與區(qū)間攝動有限元法相比，區(qū)間攝動波函數(shù)法能更有效地預(yù)測區(qū)間聲場低頻和中頻響應(yīng)的上界；與混合攝動有限元法相比，混合攝動波函數(shù)法能更有效地在低頻和中頻段預(yù)測隨機(jī)與區(qū)間混合不確定聲場響應(yīng)期望與標(biāo)準(zhǔn)差的上界。 本文對不確定聲固耦合系統(tǒng)的數(shù)值分析與優(yōu)化方法進(jìn)行了深入系統(tǒng)地研究，針對不確定聲固耦合系統(tǒng)的低頻響應(yīng)數(shù)值分析問題，提出了變量變換隨機(jī)攝動有限元法、修正區(qū)間攝動有限元法、混合攝動頂點(diǎn)法和區(qū)間隨機(jī)攝動頂點(diǎn)法；針對混合不確定聲固耦合系統(tǒng)低頻響應(yīng)的優(yōu)化設(shè)計(jì)問題，提出了基于混合攝動-隨機(jī)矩法和混合攝動-變量變換法的混合不確定聲固耦合系統(tǒng)低頻響應(yīng)優(yōu)化方法；針對不確定聲場中頻響應(yīng)的數(shù)值分析問題，提出了不確定聲場中頻響應(yīng)數(shù)值分析的區(qū)間攝動波函數(shù)法和混合攝動波函數(shù)法。用本文方法分別對板殼結(jié)構(gòu)聲固耦合系統(tǒng)、汽車內(nèi)聲場和三維聲腔模型進(jìn)行了數(shù)值分析，結(jié)果驗(yàn)證了本文方法的有效性和高效性。
[Abstract]:Sound solid coupling systems are widely used in vehicles, ships, aircraft, submarines and spacecraft. The low and low frequency noise produced by the structural vibration of the sound solid coupling system is one of the main sources of noise. The optimal design technique based on the acoustic performance analysis of the sound solid coupling system is the most low frequency noise in the control structure. The analysis and optimization of the traditional sound solid coupling system is generally based on determining the parameters of the system and using the classical CAE technology and the optimization method. However, in many practical engineering problems, the error of manufacturing, assembly and measurement, the unpredictable changes of the environment and the unpredictability of external excitation are caused by many practical engineering problems. Uncertainty exists widely in sound solid coupling systems. In most cases, these uncertainties are less affected, but when they are coupled together, they may lead to a larger deviation in the response of the actual sound solid coupling system and even the emergence of a reverse phase phenomenon. The optimization of the combined system may lead to the optimization of the acoustic structure coupling system which can not meet the specified design requirements.
In order to realize the effective analysis and optimization of the uncertain sound solid coupling system, the numerical analysis model of the uncertain sound solid coupling system must be constructed with the help of the uncertainty theory, and the corresponding uncertain numerical analysis algorithm is put forward to study the influence of the uncertain factors on the response of the sound solid coupling system, and then the acoustic solid is based on the uncertain factors. With the influence of the coupling system response, the optimization model of the uncertain sound solid coupling system is set up, and the corresponding efficient optimization algorithm is proposed to achieve the efficient optimization design of the uncertain sound solid coupling system. This paper, starting with a single uncertain model (random model and interval model), is gradually going deep into the mixed uncertainty model (random and area). Based on the mixed uncertainty model and interval stochastic model, the numerical analysis and optimization algorithm of uncertain acoustic structure coupling system are systematically studied.
The main research work completed in this paper includes:
(1) a variable transformation stochastic perturbation finite element method is established for the response analysis of the stochastic acoustic coupling system. The variable transformation random perturbation finite element method is used to approximate the response of the sound solid coupling system to the linear function of the random variable by the first order perturbation technique; then, the variable transformation technique is used to calculate the probability density function of the response; finally, the variable transformation technique is used to calculate the probability density function of the response. On the basis of the response probability density function, the confidence interval of the response is calculated according to the definition of confidence interval. The numerical analysis results of a random shell structure sound solid coupling system show that the probability density function and confidence interval of the response of the random sound solid coupling system can be effectively analyzed by the variable transformation random perturbation finite element method.
(2) the modified interval perturbation finite element method is proposed for the response analysis of the interval acoustic solid coupling system. The interval perturbation finite element method is based on the first order Taylor series expansion and the first order Neumann series expansion. The interval perturbation finite element method is used to divide the interval variables into several subregions, and then the interval perturbation finite element method and the interval method are used. The interval perturbation finite element method is based on the first order Taylor series expansion and the modified Neumann series expansion. The numerical analysis results of the acoustic solid coupling system of a shell structure show that the interval perturbation finite element method is only applicable to the sound solid coupling system with small uncertain interval. The subinterval perturbation finite element method can effectively improve the analysis precision of the interval sound solid coupling system, but the calculation cost increases exponentially with the increase of the number of subinterval, and the modified interval perturbation finite element method can be added to a small amplitude by considering the higher order Neumann series term. The accuracy of interval acoustic structure coupling system is greatly improved under the condition of cost.
(3) a mixed perturbation vertex method is established, which can effectively and efficiently analyze the expectation and variance range of the response of the stochastic and interval mixed uncertainty sound solid coupling system. The mixed perturbation vertex method approximated the response of the random and interval uncertain acoustic solid coupling system to a linear function of the random variable and the interval variable, followed by the response. With the linear relation of the interval variables, the upper and lower bounds of the response are calculated by the vertex method. Then, the expectation and variance of the upper and lower bounds of the response are calculated by the random moment technique, and the expectation of the above lower bounds is the upper and lower bounds of the expectation, and the variance of the above lower bounds is the upper and lower bounds of the variance. The computational accuracy of the dynamic vertex method and the mixed perturbation Monte-Carlo method under the large sample is the same, but the calculation efficiency of the mixed perturbation vertex method is much higher than the mixed perturbation Monte-Carlo method under the large sample.
(4) an interval random perturbation vertex method is proposed, which can be used for the response analysis of an interval random sound coupled system. Interval random perturbation vertex method is applied to the interval perturbation technique and random perturbation technique. The interval random perturbation technique is proposed to approximate the response of the interval random sound solid coupling system to the interval random variable and the interval variable. According to the linear relationship between the response and the interval variable, the upper and lower bounds of the response are calculated by the vertex method. Finally, the expectation and standard deviation of the upper and lower bounds of the response are calculated by the random moment technique, and the expectation of the above lower bounds is the upper and lower bounds of the expected. The variance of the above lower bounds is the upper and lower bounds of the variance. The numerical analysis of the internal sound field shows that the interval random perturbation vertex method can effectively and efficiently predict the variation range of the response expectation and variance of the interval random sound solid coupling system.
(5) the nested optimization model of the acoustic solid coupling system under the mixed uncertainty model (random and interval mixed uncertainty model and interval random model) is constructed, and the mixed perturbation random moment method and mixed perturbation variable transformation method are proposed to optimize the target function and constraint conditions of the model, and the transformation of the nested optimization model to the single layer optimization model is realized. The optimal design results of the sound solid coupling system of the plate structure show that the mixed perturbation random moment method and the mixed perturbation variable transformation method can effectively and efficiently calculate the objective function and constraint conditions of the mixed uncertain optimization model, and the hybrid uncertain optimization method is used to optimize the mixed uncertain sound solid coupling system effectively. The sound pressure response of the acoustic structure coupling system improves the acoustic performance of the mixed uncertain acoustic solid coupling system.
(6) the interval perturbation wave function method is proposed, which can be used for the analysis of the low frequency and intermediate frequency response of the interval sound field. A mixed perturbation wave function method is proposed, which can be used to analyze the low frequency and intermediate frequency response of the random and interval uncertain sound fields. The numerical analysis results of the three-dimensional sound cavity model show that the interval perturbation finite element method is compared with the interval perturbation finite element method. Compared with the mixed perturbation finite element method, the mixed perturbation wave function method can more effectively predict the upper bound of the expectation and the standard deviation of the random and interval uncertainty of the acoustic field response.
In this paper, the numerical analysis and optimization method of the uncertain acoustic solid coupling system are systematically studied. In order to solve the problem of the low frequency response of the sound solid coupling system, the variable transformation random perturbation finite element method, the modified interval perturbation finite element method, the mixed perturbation vertex method and the interval random perturbation vertex method are proposed. For the optimal design of low frequency response of mixed uncertain sound solid coupling system, a low frequency response optimization method based on mixed perturbation random moment method and mixed perturbation variable transformation method for mixed uncertain sound solid coupling system is proposed. In view of the numerical analysis problem of the medium frequency response of the uncertain sound field, the uncertainty of the medium frequency response number of the sound field is proposed. The interval perturbation wave function method and the mixed perturbation wave function method are used to analyze the acoustic solid coupling system of the plate and shell structure, the internal sound field and the three-dimensional sound cavity model of the car respectively. The results verify the effectiveness and efficiency of the proposed method.
【學(xué)位授予單位】：湖南大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2015
【分類號】：TB535

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