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1.
传统基本解法在二维大规模模型的声场求解过程中,系统方程形成和求解的计算量正比于自由度N的二次方O(N~2)和三次方D(N~3),求解效率低;为此,引入快速多极子算法并采用广义极小残差法迭代求解,提出一种用于二维声场预测的快速多极基本解法。对无限长圆柱体及二维类车体辐射模型的仿真结果表明,当N为3000时,分别采用快速多极基本解法与传统基本解法求解所需的时间比值约为百分之四,且N越大比值越小;最终实现系统方程的形成和求解的计算量降低到正比于自由度O(N),提高了对二维大规模模型声场预测计算效率。  相似文献   

2.
李善德  黄其柏  李天匀 《物理学报》2012,61(6):64301-064301
传统外部声学Helmholtz边界积分方程无法在个人计算机上求解大规模工程问题. 为了有效解决这个问题, 将快速多极方法引入到边界积分方程中, 加速系统矩阵方程组的迭代求解. 由于在边界积分方程中引入基本解的对角形式多极扩展, 新的快速多极边界元法的计算效率与传统边界元相比显著提高, 计算量和存储量减少到O(N)量级(N为问题的自由度数). 包括含有420000个自由度的大型潜艇模型数值算例验证了快速多极边界元法的准确性和高效性, 清楚表明新算法在求解大规模声学问题中的优势, 具有良好的工程应用前景.  相似文献   

3.
传统外部声学Helmholtz边界积分方程无法在个人计算机上求解大规模工程问题. 为了有效解决这个问题, 将快速多极方法引入到边界积分方程中, 加速系统矩阵方程组的迭代求解. 由于在边界积分方程中引入基本解的对角形式多极扩展, 新的快速多极边界元法的计算效率与传统边界元相比显著提高, 计算量和存储量减少到O(N)量级(N为问题的自由度数). 包括含有420000个自由度的大型潜艇模型数值算例验证了快速多极边界元法的准确性和高效性, 清楚表明新算法在求解大规模声学问题中的优势,  相似文献   

4.
一种简捷求解定态薛定谔方程的方法:科尔-霍普夫变换法   总被引:1,自引:0,他引:1  
佘守宪  唐莹 《大学物理》2004,23(12):3-11
介绍一种求解各个能级及定态波函数的简捷方法,即借助于科尔-霍普夫(Cole-Hopf)变换法,将给定势函数的定态薛定谔方程变换成黎卡提(Riccati)方程,以求出各个能级及定态波函数.并以谐振子、球谐振子、氢原子、P schl-Teller势、Morse势、Hulth啨n势、双原子分子的三参量势函数、同调谐振子为实例,给出求解方法及结果.  相似文献   

5.
中心势近似下径向Dirac方程的求解是相对论性原子(离子)结构计算的基础.本文通过相对论性方程中径向波函数大分量与非相对论方程径向波函数的类比,提出了径向Dirac方程的一种数值解法.为了验证数值解法的精度和可靠性,首先将数值结果与类氢势作用下的解析解进行比较.然后,将这种算法扩展到基于解析势的相对论性原子结构计算中,并将计算出的总能量与实验结果和其他方法得到的结果进行对比.  相似文献   

6.
特解边界元法数值解三维Pennes方程及其应用   总被引:2,自引:0,他引:2  
应用特解边界元法对非稳态的三维Pennes方程求解,将解分为一满足泊松方程的通解与一特解之和,通解按照边界元法求解,特解用分离变量法给出,与位置有关的部分采用截断多项式,逐时间段计算边界元的温度及热流值,然后计算域内点的值,并将该方法用于热疗温度场的数值实例计算。  相似文献   

7.
戴保东  程玉民 《物理学报》2007,56(2):597-603
将基于径向基函数构造的具有插值特性的近似函数和局部边界积分方程方法相结合,建立了求解势问题的径向基函数——局部边界积分方程方法,推导了相应离散方程.与其他边界积分方程的无网格方法相比,本文方法具有数值实现过程简单、计算量小、精度高的优点,并可直接施加边界条件.最后通过算例说明了该方法的有效性. 关键词: 径向基函数 无网格方法 局部边界积分方程 势问题  相似文献   

8.
从理论上应用辛算法数值求解-维含时GP方程,研究存在陷浮势和陷浮势为零时三个玻色-爱因斯坦凝聚体间的干涉.当陷浮势存在时,玻色一爱因斯坦凝聚体间发生弹性碰撞;如果在t=0时陷浮势为零,三个凝聚体间发生干涉现象,并且发现几率密度随着时间的演化是振荡的.  相似文献   

9.
三维声学多层快速多极子边界元及其应用   总被引:1,自引:0,他引:1       下载免费PDF全文
吴海军  蒋伟康  鲁文波 《物理学报》2012,61(5):54301-054301
快速多极子边界元算法可以加速矩阵和向量乘法运算, 将传统边界元算法的计算量和内存占用量分别降为O(N log2N)和O(N), 适用于大型声学模型模拟计算. 本文发展了一种基于Burton-Miller方程的三维多层声学快速多极子边界元算法. 将新的自适应树状算法应用到对角形式的快速多极子边界元算法, 并使用最新提出的解析式源点矩计算公式, 进一步提高了快速多极子边界元的计算效率. 绝对软球体在内部共振频率处的散射声场计算, 验证了所发展算法在共振频率处求解的正确性. 与Bapat所提供的程序在多脉动球体辐射声场计算精度的比较, 验证了算法及程序在大型模型声学计算中的准确性, 同时显示了其求解的高效性. 最后, 将该算法用于车内声场及水下声学探测的分析计算.  相似文献   

10.
张爱萍  强稳朝 《中国物理 C》2007,31(11):1027-1031
在标量势和矢量势相等的情形, 研究了Rosen-MorseⅡ势的相对论效应, 应用超对称和形状不变势方法通过求解Klein-Gordon方程和Dirac方程得到了束缚态能量本征值, 最后, 讨论了Rosen-MorseⅡ势的一种特殊情况.  相似文献   

11.
A method of allowing for the spatial sound field structure in designing the sound-absorbing structures for turbojet aircraft engine ducts is proposed. The acoustic impedance of a duct should be chosen so as to prevent the reflection of the primary sound field, which is generated by the sound source in the absence of the duct, from the duct walls.  相似文献   

12.
孙中政  雷坤  王宇飞  韩旭 《应用声学》2021,40(1):156-162
针对汽车进气系统三通管路的特点,提出了多通管路的管壁传递损失测试方法。并以某车型的双涡轮增压发动机进气三通管道为例,采用该方法评价其用塑料代替铝后的声学性能,主要以声传递损失来评价涡轮增压器噪声通过三通连接管路管壁的辐射和透射特性。测试过程中,三通管道的两个连接涡轮增压器端口分别用声源两次发声,靠近进气歧管端口采用两种不同反射末端,然后在每段管路布置两个压力场扬声器进行测试,并基于平面波分离入射波和反射波,同时在三通管道外用声功率半球面十点分布法自由场扬声器测试,经过3次测量来计算管道管壁的声传递损失。由于声传递损失是管道本身特性决定,所以该测试方法能够准确找出塑料件和金属件在不同频率的声学特性差异。而后,在声传递损失测试结果的基础上,结合近场声全息方法和波束形成原理进行声源识别,可知该三通管路材质改为塑料后主要噪声来自焊缝薄弱处的中高频透射声和管壁结构的低频辐射声。  相似文献   

13.
This article describes a one-dimensional, linearized, analysis of fundamental mode sound generation and propagation in rigid-walled flow ducts with axial temperature variation. An acoustic wave equation, including damping effects and volume sources, is derived and its solution (in the absence of sources) by a numerical technique and an approximate analytical method is discussed. The “forced” wave equation is then solved (the existence of an oscillating solution to the “unforced” equation being assumed) for sound generation by a side-branch volume source in an infinite duct, and the results are applied to a duct of finite length. Reasonably good agreement is obtained between measurements and predictions of the sound pressure field in a flow duct, away from the source region.  相似文献   

14.
15.
An analysis has been carried out to investigate sound transmission in an unflanged circular duct of finite length. A new formulation for calculating the generalized radiation impedance of the opening of a finite length duct with a spinning source inside is presented. The effect of interference between the duct apertures at its two ends is identified in the calculations of radiation impedance, reflection coefficient, and the far field radiation pattern. The results show that the degree of interference between the two ends reduces for high frequency waves and/or for long ducts. Further, the interference effects on the far field for spinning sound are more serious than those for non-spinning sound.  相似文献   

16.
Most established techniques for analyzing sound transmission in ducts containing orifices plates are only applicable for plane wave propagation. Once the wavelength of the sound approaches the cross section of the duct, higher order mode propagation in the system must be considered in the analysis. This is a numerically intensive activity if fully coupled calculations of the higher order modes are undertaken. This investigation estimates the acoustic fields in a duct with a simple orifice plate installed using an uncoupled model to estimate the higher order mode contribution. The uncoupled model is then used as the basis for a hybrid decomposition approach to estimate the sound field in the regions before and after the orifice plate installed in a circular duct. This approach is applied to a duct, excited by a point source over a wide frequency range, containing a single orifice plate installed a distance inside the duct. Different orifice plates with one, two and multiple openings are investigated. Of particular interest is the location of the point source relative to the duct axis. If the source is located concentric to the duct axis then, without any orifice plate present, only axially symmetric higher order modes may be excited in the duct. Thus, the investigation considers the point source located in the concentric position and in eccentric positions to vary the contribution from the different types of higher order mode. Estimates of the acoustic fields in the duct obtained using the hybrid decomposition approach are compared with measured data and the applicability of using an uncoupled estimate for the acoustic fields is commented on.  相似文献   

17.
The general equation for the velocity potential of quasi-one-dimensional acoustic wave motion in a variable area, finite duct with one-dimensional flow is derived by using a perturbation technique. The non-linear second-order partial differential equation is linearized and then solved, by either a power series expansion method or the Runge-Kutta fourth-order method, for harmonic time dependence. The boundary condition taken at the duct mouth is that of matching the impedance of the duct sound field to that of the radiation field at the duct opening. Three axial Mach number variations along the duct axis are considered and the results obtained are compared with those for the case of constant Mach number, to determine the influence of the axial velocity gradient on sound propagation. The effect of flow on the radiation impedance is also considered.  相似文献   

18.
The near-ground behavior of the low-frequency (100 Hz to 500 Hz) sound field in the nocturnal sound duct is studied theoretically and experimentally. In the first few meters of the atmosphere, narrow-band sound fields are found to have a characteristic vertical structure. The sound field is the superposition of a "surface mode," whose magnitude decreases monotonically with altitude, with a sum of "higher modes," each of whose magnitudes has a pronounced minimum a few meters from the ground at approximately the same height. The surface mode attenuates to negligible levels after a few hundred meters from the source. Consequently, more than a few hundred meters from a narrow-band source, there is a "quiet height" at which the sound level is reduced by 10 to 15 dB relative to its value on the ground. The narrow-band quiet height is shown to be a robust feature of nocturnal sound propagation.  相似文献   

19.
The aim of this work is to show the energetic behavior when an active noise controller is applied in a one-dimensional waveguide, namely an ideal duct under the first critical frequency. In order to model the duct, a spectral element method, which is shown to be more practical for analyzing pipe networks than other commonly used analytical models, was used. The model used here consists of a duct with two sources, the primary source at one end of the duct, and the secondary source at the middle section. The error sensor was placed downstream from secondary source, and the other end of the duct was open with no flange. Three optimal control methods were applied: minimization of the potential energy density, minimization of the active intensity, and minimization of the total acoustic power radiated by the sources. It was observed that the three control methods achieved the same final result, and when the volume velocity of the secondary source was driven to the optimal volume velocity, neither the primary source nor the secondary source radiated any acoustic power. Furthermore, the controlled duct was equivalent to a duct opened-ended at the secondary source position with radiation impedance equal to zero.  相似文献   

20.
Knowledge of the modal content of the sound field radiated from a turbofan inlet is important for source characterization and for helping to determine noise generation mechanisms in the engine. An inverse technique for determining the mode amplitudes at the duct outlet is proposed using pressure measurements made in the near field. The radiated sound pressure from a duct is modeled by directivity patterns of cut-on modes in the near field using a model based on the Kirchhoff approximation for flanged ducts with no flow. The resulting system of equations is ill posed and it is shown that the presence of modes with eigenvalues close to a cutoff frequency results in a poorly conditioned directivity matrix. An analysis of the conditioning of this directivity matrix is carried out to assess the inversion robustness and accuracy. A physical interpretation of the singular value decomposition is given and allows us to understand the issues of ill conditioning as well as the detection performance of the radiated sound field by a given sensor array.  相似文献   

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