三维声学快速多极基本解法在机械噪声预测中的应用研究

发布时间：2018-03-16 22:34

本文选题：三维声场　切入点：快速多极基本解法　出处：《沈阳工业大学》2016年博士论文　论文类型：学位论文

【摘要】：机械工程中噪声预测常用的数值方法主要有限元法和边界元法,对于一般的声学问题,有限元尚可解决,但求解外场声辐射问题,有限元法便无法自动识别边界,且对于大规模问题,仅仅划分网格就需要昂贵的计算资源和时间成本。边界元法因其能自动满足远场辐射条件,仅需对边界进行网格划分,极大提高了网格划分的效率,因而非常适于求解声辐射的外场问题。但边界元法的缺点是特征频率处解不唯一和核函数的奇异积分问题。与边界元法相比,传统基本解法除了具有边界元法的优点外,传统基本解法因其将源点布置于求解域外,从而避免了奇异积分的问题。传统基本解法用于声场预测时,所形成的系统矩阵是稠密、非对称矩阵,所需存储量大,求解速度慢。为提高传统基本解法的计算效率,将快速多极方法引入到传统基本解法中,形成了快速多极基本解法,并将之用于机械噪声的预测。通过引入快速多极算法,结合传统基本解法形成二维快速多极基本解法,给出了快速多极基本解法的具体实现步骤和计算的复杂性分析。以二维脉动圆环声辐射为例,研究了快速多极基本解法的计算精度和计算效率。讨论了源点分布对二维快速多极基本解法计算精度的影响规律。结果表明,对于二维问题,传统基本解法采用共形源点布置的计算精度要优于环形源点布置。为解决三维噪声预测问题,将快速多极基本解法由二维拓展为三维,推导了三维快速多极基本解法的理论公式,并用于消声器的声学性能预测,计算结果与边界元法的计算值吻合较好,从而验证了三维快速多极基本解法的正确性。快速多极基本解法的求解效率随着求解问题的规模越来越大,它在求解效率方面的优势越明显。鉴于工程中的噪声预测主要为半空间问题,将三维全空间的快速多极基本解法拓展到三维半空间的快速多极基本解法,推导了多极系数展开和多极系数转移的相关公式。因快速多极基本解法的计算精度主要由源点数和源点分布决定,源点和配置点之间的距离d过小时,计算误差变大;d增大时,计算误差变小,但会导致源点分布越来越密集,使矩阵呈现病态。针对源点的布置具有一定盲目性的问题,本文利用遗传算法优化源点分布,结合三维半空间快速多极基本解法,提出了基于遗传算法的快速多极基本解法。以表面复杂的发动机为研究对象,利用遗传算法优化发动机计算模型的源点分布,进而利用快速多极基本解法预测发动机表面辐射声场。结果表明,利用遗传算法求得源点与配置点的最优距离为34.5mm;截断项数取值15时,避免了截断项数过小引起的低频不稳定,同时保障了计算效率;利用遗传算法优化后的源点分布,在保证计算精度的基础上,可实现减少源点数和配置点数的目的,进而提高了基于遗传算法的快速多极基本解法的计算效率。基于遗传算法的快速多极基本解法用于发动机表面辐射声场的预测,提高了发动机辐射声场预报精度,计算结果与试验值吻合较好,验证了本文方法的可行性和正确性,同时也为该方法在机械噪声预测中的进一步应用提供了借鉴。
[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.

【学位授予单位】：沈阳工业大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TH113;TB53

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