本文選題：聲固耦合系統(tǒng)　切入點(diǎn)：有限元法　出處：《湖南大學(xué)》2016年碩士論文　論文類型：學(xué)位論文

【摘要】：一直以來,國內(nèi)外學(xué)者對聲固耦合系統(tǒng)問題進(jìn)行研究時(shí),一般都是基于確定性分析方法。然而,實(shí)際工程中的聲固耦合系統(tǒng)往往在部件材料屬性、外部載荷和邊界條件等方面都存在一定的不確定性。一般情況下,單一的不確定因素在數(shù)值上可能比較小,但是當(dāng)多個(gè)不確定因素相互耦合時(shí),就有可能導(dǎo)致聲固耦合系統(tǒng)響應(yīng)產(chǎn)生很大的偏差。為了研究各類不確定因素對聲固耦合系統(tǒng)響應(yīng)的影響,本文開展隨機(jī)不確定、證據(jù)不確定和隨機(jī)與證據(jù)混合不確定三類不確定聲固耦合系統(tǒng)的分析研究。在隨機(jī)、證據(jù)及其混合模型的基礎(chǔ)上構(gòu)建聲固耦合系統(tǒng)的不確定數(shù)值分析模型,并研究相應(yīng)的不確定數(shù)值分析算法,以更加深入地研究不確定性聲固耦合系統(tǒng)問題。本文開展并完成的主要研究工作包括:(1)研究了隨機(jī)攝動(dòng)有限元法,以預(yù)測隨機(jī)聲固耦合系統(tǒng)響應(yīng)結(jié)果的期望和方差。該方法首先構(gòu)造隨機(jī)聲固耦合系統(tǒng)的隨機(jī)FEM/FEM模型;然后進(jìn)行隨機(jī)聲固耦合系統(tǒng)響應(yīng)的隨機(jī)攝動(dòng)分析;最后求解得到隨機(jī)聲固耦合系統(tǒng)響應(yīng)結(jié)果的期望和方差。用隨機(jī)攝動(dòng)有限元法對某殼結(jié)構(gòu)聲固耦合系統(tǒng)進(jìn)行了數(shù)值分析,結(jié)果表明:隨機(jī)攝動(dòng)有限元法能有效預(yù)測隨機(jī)聲固耦合系統(tǒng)響應(yīng)結(jié)果的期望和方差。(2)研究了證據(jù)理論有限元法,以預(yù)測證據(jù)不確定聲固耦合系統(tǒng)響應(yīng)期望和方差范圍。該方法首先運(yùn)用區(qū)間攝動(dòng)分析法構(gòu)造證據(jù)子區(qū)間不確定聲固耦合模型,進(jìn)而求得子區(qū)間對應(yīng)系統(tǒng)響應(yīng)的變化范圍;然后,采用證據(jù)理論期望和方差求解方法得到證據(jù)不確定聲固耦合系統(tǒng)響應(yīng)期望和方差的變化范圍。用證據(jù)理論有限元法對某殼結(jié)構(gòu)聲固耦合系統(tǒng)進(jìn)行了數(shù)值分析,結(jié)果表明:證據(jù)理論有限元法能有效預(yù)測證據(jù)不確定聲固耦合系統(tǒng)響應(yīng)期望和方差范圍。(3)研究了混合證據(jù)和隨機(jī)有限元分析方法,以預(yù)測證據(jù)和隨機(jī)混合不確定聲固耦合系統(tǒng)響應(yīng)期望和方差范圍。該方法首先將混合攝動(dòng)分析法應(yīng)用到構(gòu)造證據(jù)子區(qū)間與隨機(jī)混合不確定聲固耦合模型;然后,采用隨機(jī)矩法計(jì)算子區(qū)間與隨機(jī)混合系統(tǒng)近似響應(yīng)的期望和方差;再根據(jù)系統(tǒng)響應(yīng)期望和方差與子區(qū)間變量間的線性關(guān)系,采用頂點(diǎn)法計(jì)算系統(tǒng)響應(yīng)期望和方差變化范圍的上下界;最后,對每個(gè)由隨機(jī)向量和聯(lián)合焦元構(gòu)成的子區(qū)間組成的混合不確定組合重復(fù)計(jì)算上述過程即得到證據(jù)與隨機(jī)混合系統(tǒng)響應(yīng)期望和方差的變化范圍。用混合證據(jù)和隨機(jī)有限元法對某殼結(jié)構(gòu)聲固耦合系統(tǒng)進(jìn)行了數(shù)值分析,結(jié)果表明:混合證據(jù)和隨機(jī)有限元法能有效預(yù)測證據(jù)不確定聲固耦合系統(tǒng)響應(yīng)期望和方差范圍。
[Abstract]:For a long time, scholars at home and abroad have been studying the problem of acousto-solid coupling system, which is usually based on deterministic analysis method. However, in practical engineering, the acousto-solid coupling system is usually based on the material properties of components. There are some uncertainties in external loads and boundary conditions. In general, a single uncertainty may be relatively small numerically, but when multiple uncertainties are coupled with each other, In order to study the influence of all kinds of uncertain factors on the response of acousto-solid coupling system, random uncertainty is carried out in this paper. Analysis and Research on three kinds of uncertain Acousto-Structure Coupling Systems of evidence uncertainty and Stochastic and mixed uncertainty. On the basis of stochastic, evidential and mixed models, the uncertain numerical analysis model of acousto-solid coupling system is constructed. The corresponding uncertain numerical analysis algorithm is studied to study the problem of acousto-solid coupling system with uncertainty more deeply. The main research work done in this paper includes: 1) the stochastic perturbed finite element method is studied. In order to predict the expectation and variance of the response results of the stochastic acousto-solid coupling system, the stochastic FEM/FEM model of the stochastic acousto-solid coupling system is constructed firstly, and then the random perturbation analysis of the response of the stochastic acousto-solid coupling system is carried out. Finally, the expectation and variance of the response results of the stochastic acousto-solid coupling system are obtained. The numerical analysis of the acousto-solid coupling system of a shell structure is carried out by using the stochastic perturbation finite element method. The results show that the stochastic perturbation finite element method can effectively predict the expected and variance of the response results of stochastic acousto-solid coupling systems. In order to predict the expected and variance range of acousto-solid coupling system response with uncertain evidence, the method first constructs the acousto-solid coupling model with interval perturbation analysis method, and then obtains the variation range of the system response corresponding to the subinterval. The variation range of response expectation and variance of acousto-solid coupling system with uncertain evidence is obtained by using the method of expectation and variance of evidence theory. The finite element method of evidence theory is used to analyze the acousto-solid coupling system of a shell structure. The results show that the evidence theory finite element method can effectively predict the response expectation and variance range of acousto-solid coupling systems with uncertain evidence. Based on predictive evidence and random mixed uncertain acousto-solid coupling system response expectation and variance range, the mixed perturbation analysis method is first applied to construct the acousto-solid coupling model with evidence subinterval and random mixing uncertainty. The stochastic moment method is used to calculate the expectation and variance of approximate response of subinterval and stochastic mixed system, and then according to the linear relation between system expectation and variance and subinterval variable, The vertex method is used to calculate the upper and lower bounds of the variation range of system response expectation and variance. For each mixed uncertain combination consisting of a random vector and a joint focal element, the above process is calculated repeatedly to obtain the range of variation of the expected and variance of the evidence and the response of the stochastic mixed system. The mixed evidence and the random are used to calculate the variation range of the expected and variance of the response of the stochastic mixed system. The finite element method is used to analyze the acousto-solid coupling system of a shell structure. The results show that the mixed evidence and stochastic finite element method can effectively predict the expected response and variance range of the acousto-solid coupling system.
【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】：2016
【分類號】：TB115

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