本文選題：三維聲場　切入點：快速多極基本解法　出處：《沈陽工業(yè)大學》2016年博士論文　論文類型：學位論文

【摘要】：機械工程中噪聲預測常用的數值方法主要有限元法和邊界元法,對于一般的聲學問題,有限元尚可解決,但求解外場聲輻射問題,有限元法便無法自動識別邊界,且對于大規(guī)模問題,僅僅劃分網格就需要昂貴的計算資源和時間成本。邊界元法因其能自動滿足遠場輻射條件,僅需對邊界進行網格劃分,極大提高了網格劃分的效率,因而非常適于求解聲輻射的外場問題。但邊界元法的缺點是特征頻率處解不唯一和核函數的奇異積分問題。與邊界元法相比,傳統(tǒng)基本解法除了具有邊界元法的優(yōu)點外,傳統(tǒng)基本解法因其將源點布置于求解域外,從而避免了奇異積分的問題。傳統(tǒng)基本解法用于聲場預測時,所形成的系統(tǒng)矩陣是稠密、非對稱矩陣,所需存儲量大,求解速度慢。為提高傳統(tǒng)基本解法的計算效率,將快速多極方法引入到傳統(tǒng)基本解法中,形成了快速多極基本解法,并將之用于機械噪聲的預測。通過引入快速多極算法,結合傳統(tǒng)基本解法形成二維快速多極基本解法,給出了快速多極基本解法的具體實現步驟和計算的復雜性分析。以二維脈動圓環(huán)聲輻射為例,研究了快速多極基本解法的計算精度和計算效率。討論了源點分布對二維快速多極基本解法計算精度的影響規(guī)律。結果表明,對于二維問題,傳統(tǒng)基本解法采用共形源點布置的計算精度要優(yōu)于環(huán)形源點布置。為解決三維噪聲預測問題,將快速多極基本解法由二維拓展為三維,推導了三維快速多極基本解法的理論公式,并用于消聲器的聲學性能預測,計算結果與邊界元法的計算值吻合較好,從而驗證了三維快速多極基本解法的正確性。快速多極基本解法的求解效率隨著求解問題的規(guī)模越來越大,它在求解效率方面的優(yōu)勢越明顯。鑒于工程中的噪聲預測主要為半空間問題,將三維全空間的快速多極基本解法拓展到三維半空間的快速多極基本解法,推導了多極系數展開和多極系數轉移的相關公式。因快速多極基本解法的計算精度主要由源點數和源點分布決定,源點和配置點之間的距離d過小時,計算誤差變大;d增大時,計算誤差變小,但會導致源點分布越來越密集,使矩陣呈現病態(tài)。針對源點的布置具有一定盲目性的問題,本文利用遺傳算法優(yōu)化源點分布,結合三維半空間快速多極基本解法,提出了基于遺傳算法的快速多極基本解法。以表面復雜的發(fā)動機為研究對象,利用遺傳算法優(yōu)化發(fā)動機計算模型的源點分布,進而利用快速多極基本解法預測發(fā)動機表面輻射聲場。結果表明,利用遺傳算法求得源點與配置點的最優(yōu)距離為34.5mm;截斷項數取值15時,避免了截斷項數過小引起的低頻不穩(wěn)定,同時保障了計算效率;利用遺傳算法優(yōu)化后的源點分布,在保證計算精度的基礎上,可實現減少源點數和配置點數的目的,進而提高了基于遺傳算法的快速多極基本解法的計算效率�；谶z傳算法的快速多極基本解法用于發(fā)動機表面輻射聲場的預測,提高了發(fā)動機輻射聲場預報精度,計算結果與試驗值吻合較好,驗證了本文方法的可行性和正確性,同時也為該方法在機械噪聲預測中的進一步應用提供了借鑒。
[Abstract]:The noise in the mechanical engineering prediction numerical method commonly used finite element method and boundary element method for acoustic problems in general, finite element method can solve, but for solving external acoustic radiation problem, finite element method is unable to automatically recognize the boundary, and for the large scale problems, only to divide grid requires computing resources and time cost is expensive. The boundary element method because it can automatically satisfy the radiation condition in the far field, only to mesh boundary, which greatly improves the efficiency of the grid, and is suitable for solving the problem of external acoustic radiation. But the boundary element method is singularity integral characteristic frequency solutions and kernel function compared with boundary element. The traditional method, the basic solution in addition to the advantages of the boundary element method, the traditional basic solution because of its source arrangement to solve abroad, so as to avoid the singular integral problem. The traditional method for basic sound Field prediction, system matrix formed is dense, non symmetric matrix, the required storage capacity, slow convergence speed. In order to improve the calculation efficiency of the traditional basic solution method, the fast multipole method is introduced into the traditional basic solution, forming a fast multipole method of fundamental solutions, and the prediction of mechanical noise. Through to the fast multipole algorithm, combined with the traditional basic solution to form 2D fast multipole fast multipole method for the basic solution, the specific implementation steps and the computational complexity analysis are given. By dimensional acoustic radiation ring as an example, the calculation accuracy and efficiency of the fast multipole method. The influence of the basic source of two-dimensional calculation precision the distribution of the fast multipole method of fundamental solutions. The results show that for the two-dimensional problem, the traditional method using basic precision conformal source arrangement is superior to the ring source to solve the layout. The 3-D noise prediction problem, the fast multipole method by 2D to 3D basic, this paper deduces theoretical formulas of 3-D fast multipole method of fundamental solutions, and used to predict the acoustic performance of the muffler, the calculation results and boundary element method are in good agreement, which proves the correctness of the basic solution of 3-D fast multipole. Fast multipole basic solving efficiency with the method for solving the problem of increasingly large scale, it in solving efficiency advantages more obvious. In view of the noise prediction in engineering for the half space problem, the fast multipole based three-dimensional space this method is extended to the fast multipole method for three dimensional basic half space, related formulas of coefficient and coefficient of multipole multipole transfer. Because of the fast multipole method for the calculation accuracy is mainly composed of source points and source distribution decision between the source point and configuration point distance of D is too small. The error is bigger; when D increases, the calculation error is smaller, but will lead to the source distribution is more and more intensive, the matrix of morbid state. According to the source point arrangement has certain blindness problem, this paper uses the genetic algorithm to optimize the source distribution, combined with the fast multipole method for 3D half space, put forward the basic fast multipole method based on genetic algorithm. The complex surface of the engine as the research object, using genetic algorithm to optimize the computational model of engine source distribution, and then use the basic solution of the fast multipole prediction of engine surface acoustic radiation. The results show that the optimal distance of source and configuration by using genetic algorithm for 34.5mm; the truncation value of 15, avoid the truncation too low caused by instability, while ensuring the computational efficiency; using genetic algorithm to optimize the source distribution, in order to ensure the accuracy of the calculation basis, can be realized To reduce the number and configuration of source points, and improves the computational efficiency of fast multipole method for genetic algorithm based on genetic algorithm. The fast multipole method of fundamental solutions for prediction of engine surface acoustic radiation based on improved radiation prediction accuracy of engine, the calculation results agree well with the experimental data, the proposed method is feasible and correct at the same time, but also for the further application of this method in mechanical noise prediction to provide reference.

【學位授予單位】：沈陽工業(yè)大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：TH113;TB53

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本文編號：1621934