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More Than Six Elements Per Wavelength: The Practical Use of Structural Finite Element Models and Their Accuracy in Comparison with Experimental Results 每波长超过六个元素:结构有限元模型的实际应用及其与实验结果的精度比较
Q1 Mathematics Pub Date : 2017-03-28 DOI: 10.1142/S0218396X17500254
P. Langer, M. Maeder, C. Guist, M. Krause, S. Marburg
Choosing the right number and type of elements in modern commercial finite element tools is a challenging task. It requires a broad knowledge about the theory behind or much experience by the user. Benchmark tests are a common method to prove the element performance against analytical solutions. However, these tests often analyze the performance only for single elements. When investigating the complete mesh of an arbitrary structure, the comparison of the element’s performance is quite challenging due to the lack of closed or fully converged solutions. The purpose of this paper is to show a high-precision comparison of eigenfrequencies of a real structure between experimental and numerical results in the context of an element performance check with respect to a converged solution. Additionally, the authors identify the practically relevant accuracy of simulation and experiment. Finally, the influence of accuracy with respect to the number of elements per standing structural bending wave is shown.
在现代商业有限元工具中选择正确数量和类型的单元是一项具有挑战性的任务。它需要用户对背后的理论有广泛的了解或有丰富的经验。基准测试是根据分析解决方案证明元件性能的常用方法。然而,这些测试通常只分析单个元素的性能。当研究任意结构的完整网格时,由于缺乏闭合或完全收敛的解,单元性能的比较非常具有挑战性。本文的目的是在对收敛解进行单元性能检查的情况下,显示实际结构的本征频率在实验结果和数值结果之间的高精度比较。此外,作者还确定了模拟和实验的实际相关准确性。最后,显示了精度对每个直立结构弯曲波的单元数量的影响。
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引用次数: 50
Review: The Use of Equivalent Source Method in Computational Acoustics 综述:等效声源法在计算声学中的应用
Q1 Mathematics Pub Date : 2017-03-28 DOI: 10.1142/S0218396X16300012
Seongkyu Lee
This paper reviews the equivalent source method (ESM), an attractive alternative to the standard boundary element method (BEM). The ESM has been developed under different names: method of fundamental solutions, wave superposition method, equivalent source method, etc. However, regardless of the method name, the basic concept is very similar; that is to use auxiliary points called equivalent sources to reconstruct the acoustic pressure for radiation or scattering problems. The strength of the equivalent sources are then determined via various approaches such that the boundary conditions on the boundary surface are satisfied. This paper reviews several frequency-domain and time-domain ESMs. There are several distinct advantages in these types of methods: (1) the method is a meshless approach so that it is easy and simple to implement; (2) it does not have a numerical singularity problem that occurs in the BEM; (3) the number of equivalent sources can be fewer than the number of surface collocation points so that the matrix size is reduced and a fast computation is achieved for large problems. The main issue of the ESM is that there is no rule to find out the optimal number and position of equivalent sources. In addition, the ESM suffers from the numerical instability that is associated with the ill-conditioned matrix. Some guidelines have been suggested in terms of finding the number and position of the sources, and several numerical techniques have been developed to resolve the numerical instability. This paper reviews the common theories, numerical issues and challenges of the ESM, and it summarizes recent developments and applications of the ESM to aircraft noise.
本文综述了等效源法(ESM),它是标准边界元法(BEM)的一种有吸引力的替代方法。ESM有不同的名称:基本解法、波叠加法、等效源法等。然而,无论方法名称如何,基本概念都非常相似;即使用称为等效源的辅助点来重建辐射或散射问题的声压。然后通过各种方法确定等效源的强度,从而满足边界表面上的边界条件。本文综述了几种频域和时域ESM。这些类型的方法有几个明显的优点:(1)该方法是一种无网格方法,因此易于实现;(2) 它不存在BEM中出现的数值奇异性问题;(3) 等效源的数量可以少于表面配置点的数量,从而减小了矩阵的大小,并且对于大问题实现了快速计算。ESM的主要问题是没有找到等效源的最佳数量和位置的规则。此外,ESM还存在与病态矩阵相关的数值不稳定性。在寻找源的数量和位置方面,已经提出了一些指导方针,并且已经开发了几种数值技术来解决数值不稳定性。本文综述了ESM的一般理论、数值问题和挑战,并总结了ESM在飞机噪声中的最新发展和应用。
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引用次数: 41
Improved Integral Formulation for Acoustic Radiation Using Integral Equation of Frequency Averaged Quadratic Pressure 利用频率平均二次压力积分方程改进声辐射积分公式
Q1 Mathematics Pub Date : 2017-03-28 DOI: 10.1142/S0218396X17500047
Hong-sheng Gao, Sheng Li
This paper is concerned with the problem of obtaining a unique solution for radiation at irregular frequencies when an integral equation of frequency averaged quadratic pressure (FAQP) is used to get robust predictions at medium and high frequencies. It is proved that there is no unique solution of the integral equation of FAQP at irregular frequencies, and existence and uniqueness of solutions under four types of boundary conditions are discussed. A combined energy boundary integral equation formulation (CEBIEF) is presented and proves to be efficient to overcome the nonuniqueness of the integral equation of FAQP. The numerical examples are given to demonstrate the versatility of the CEBIEF method with a proposed function correctly indicating a solution.
本文研究了当使用频率平均二次压力积分方程(FAQP)在中高频下获得稳健预测时,获得不规则频率下辐射的唯一解的问题。证明了FAQP积分方程在不规则频率下不存在唯一解,并讨论了在四种边界条件下解的存在性和唯一性。提出了一种组合能量边界积分方程公式(CEBIEF),并证明了它能有效地克服FAQP积分方程的非唯一性。给出了数值例子来证明CEBIEF方法的通用性,所提出的函数正确地指示了解。
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引用次数: 1
Numerical Analysis of One-Dimensional Sound Propagation Through a Duct Containing Water Droplets 含水滴管道中一维声传播的数值分析
Q1 Mathematics Pub Date : 2017-03-28 DOI: 10.1142/S0218396X1650017X
Ersen Arslan, Yusuf Özyörük, M. Çaliskan
In this paper sound propagation through an air-filled circular duct containing water droplets has been studied by solving numerically one-dimensional linearized Euler equations in frequency domain. Interactions between the liquid and gas phases were accounted for by proper source terms. Waves were introduced into the domain via Perfectly Matched Layers (PML) equations applied in finite regions adjacent to the truncated ends of the duct. Absorption and dispersion results due to energy transfer from air to the water droplets were obtained as a function of average droplet diameter and droplet concentration as well as finite mass loading. Results agree well with those available in the literature.
本文通过在频域数值求解一维线性化欧拉方程,研究了声音在含水滴的充气圆形管道中的传播。液相和气相之间的相互作用用适当的源项来解释。通过在管道截断端附近的有限区域应用完美匹配层(PML)方程,将波引入该域。从空气到水滴的能量传递引起的吸收和分散结果是液滴平均直径和液滴浓度以及有限质量载荷的函数。结果与文献中的结果一致。
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引用次数: 2
This Submission is for Special Issue on Underwater Acoustics: Perfectly Matched Layer Technique for Parabolic Equation Models in Ocean Acoustics 这篇文章是为《水下声学:海洋声学中抛物方程模型的完美匹配层技术》的特刊而提交的
Q1 Mathematics Pub Date : 2017-03-28 DOI: 10.1142/S0218396X16500211
Chuanxiu Xu, S. Piao, Shie Yang, Haigang Zhang, Li Li
In ocean waveguides, the ocean bottom is usually approximated as a half-space. Thus, there exist no reflection waves at the half-space bottom and condition of radiation at infinity should be satisfied. In numerical solutions like parabolic equation methods, the depth domain has to be truncated, which can generate reflection waves from the truncated ocean bottom. To reduce the effect of reflection waves and to simulate an unbounded ocean bottom accurately, an artificial absorbing layer (ABL) was used. As was demonstrated, an ABL meets well the demand of accuracy in sound field calculation. However, both the sea-bottom layer and the artificial absorbing layer are needed to be set quite thick by using an ABL technique. Fortunately, a PML with several wavelengths can keep similar calculation accuracy with an ABL with dozens of wavelengths. In this paper, perfectly matched layer (PML) techniques for three parabolic equation (PE) models RAM, RAMS and a three-dimensional PE model in underwater acoustics are presented. A key technique of PML “complex coordinate stretching” is used to truncate unbounded domains and to simulate infinity radiation conditions instead of the ABL in those models. The numerical results illustrate that the PML technique is of higher efficiency than the ABL technique at truncating the infinity domain with minimal spurious reflections in PE models.
在海洋波导中,海底通常近似为半个空间。因此,在半空间底部不存在反射波,并且应满足无限远处的辐射条件。在像抛物方程方法这样的数值解中,深度域必须被截断,这可能会从截断的海底产生反射波。为了减少反射波的影响并准确模拟无界海底,使用了人工吸收层(ABL)。结果表明,ABL能很好地满足声场计算的精度要求。然而,海底层和人工吸收层都需要通过ABL技术设置得相当厚。幸运的是,具有几个波长的PML可以与具有几十个波长的ABL保持类似的计算精度。本文提出了水下声学中三个抛物方程(PE)模型RAM、RAMS和三维PE模型的完全匹配层(PML)技术。PML的一项关键技术“复坐标拉伸”用于截断无界域,并模拟无限辐射条件,而不是这些模型中的ABL。数值结果表明,在PE模型中,PML技术在以最小杂散反射截断无限域方面比ABL技术具有更高的效率。
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引用次数: 5
An Adjoint Operator Approach for Sensitivity Analysis of Radiated Sound Power in Fully Coupled Structural-Acoustic Systems 全耦合结构声系统辐射声功率灵敏度分析的伴随算子法
Q1 Mathematics Pub Date : 2017-03-28 DOI: 10.1142/S0218396X17500035
Leilei Chen, S. Marburg, Haibo Chen, Hao Zhang, H. Gao
Full interaction between structural and fluid domains must be considered for light structures immersed in heavy fluid (e.g. thin steel shells in water). The structural-acoustic design sensitivity analysis provides information on the effect of the design variable on acoustic performance, which makes it a key step for noise control and structural-acoustic optimization. This study uses the finite element method (FEM) to model the structure domain, while the fast multipole boundary element method (BEM) is applied to the exterior acoustic domain. An adjoint operator approach is developed to calculate the sensitivity of the radiated sound power with respect to the design variables, which can be any structural or fluid parameter (e.g. fluid or structural density, Poisson’s ratio, Young’s modulus, and geometric measures). Numerical examples are presented to demonstrate the validity and efficiency of the proposed algorithm.
对于浸入重流体中的轻结构(例如浸入水中的薄钢壳),必须考虑结构域和流体域之间的充分相互作用。结构声设计灵敏度分析提供了设计变量对声学性能影响的信息,是噪声控制和结构声优化的关键步骤。本文采用有限元法(FEM)对结构域进行建模,采用快速多极边界元法(BEM)对外声域进行建模。设计变量可以是任何结构或流体参数(如流体或结构密度、泊松比、杨氏模量和几何度量),本文提出了伴随算子方法来计算辐射声功率对设计变量的灵敏度。数值算例验证了该算法的有效性和高效性。
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引用次数: 33
Modeling of Propagation of Antiplane Acoustic Waves in Multiscale Media with Lognormal Distribution of Parameters 反平面声波在多尺度介质中传播的参数对数正态分布建模
Q1 Mathematics Pub Date : 2017-03-28 DOI: 10.1142/S0218396X17500072
O. Soboleva
The effective coefficients for the problem of propagation of acoustic waves in multifractal elastic media using the subgrid modeling approach are obtained. The maximum scale of heterogeneities of the medium in question is assumed to be small as compared with the wavelength. If a isotropic medium is assumed to satisfy the improved Kolmogorov similarity hypothesis, the term for the effective coefficient of the elastic stiffness coincides with the Landau–Lifshitz–Matheron formula. Both isotropic and anisotropic media are considered. The numerical testing for the wave propagating at a distance, which is of the same order as a typical wavelength of a source, illustrates the efficiency of the approach proposed.
利用子网格建模方法得到了声波在多重分形弹性介质中传播问题的有效系数。与波长相比,所讨论的介质的不均匀性的最大尺度被假设为较小。如果假设各向同性介质满足改进的Kolmogorov相似性假设,则弹性刚度的有效系数项与Landau–Lifshitz–Matheron公式一致。同时考虑各向同性和各向异性介质。对在一定距离上传播的波的数值测试表明了所提出方法的有效性,该距离与源的典型波长具有相同的阶数。
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引用次数: 1
Influence of Sound Speed Profile on Source Localization at Different Depths 声速剖面对不同深度震源定位的影响
Q1 Mathematics Pub Date : 2017-03-27 DOI: 10.1142/S0218396X17500266
Lin Su, Li Ma, Shengming Guo
The effect of sound speed profile (SSP) mismatch on source localization in shallow-water waveguides with a typical negative gradient (or thermocline) is studied numerically and experimentally. The results are interpreted using a normal mode model and a ray model. It is found that a matched-field processor is insensitive to SSP mismatch for sources above the thermocline. In addition, the sensitivity of the processor to SSP mismatch increases with the depth of sources above the thermocline.
本文对典型负梯度(或温跃层)浅水波导中声速分布失配对声源定位的影响进行了数值和实验研究。结果用法模模型和射线模型解释。发现匹配场处理器对温跃层以上源的SSP失配不敏感。此外,处理器对SSP失配的敏感性随温跃层以上源深度的增加而增加。
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引用次数: 4
Enhanced Sound Beam from a Sonic Crystal Waveguide via a Self-Collimating Sonic Crystal 自准直声波晶体增强声波晶体波导的声束
Q1 Mathematics Pub Date : 2017-03-16 DOI: 10.1142/S0218396X17500242
Jinfu Liang, Lun-Xun Gong
Two novel composite structures that couple a sonic crystal waveguide (SCW) to a self-collimating sonic crystal (SCSC) are proposed to control beam divergence and transmission. Finite element simulations indicate that an SCSC attached to the output of an SCW can reduce the half-power angular width by 48.81% and enhance the normal radiation intensity by 104.17%. This is due to both the high self-collimation properties and low interference of SCSCs. A composite consisting of four SCWs coupled via an SCSC exhibits high transmission with low cross talk when multiple signals are introduced. The proposed composites could be important in the SCW directional emission and SCW-based integrated circuit development.
提出了两种新型的复合结构,将声波晶体波导(SCW)耦合到自准直声波晶体(SCSC)上,以控制光束的发散和传输。有限元模拟表明,连接到SCW输出端的SCSC可以将半功率角宽度减小48.81%,并将正常辐射强度提高104.17%。这是由于SCSC具有高自准直特性和低干扰。当引入多个信号时,由经由SCSC耦合的四个SCW组成的复合物表现出具有低串扰的高传输。所提出的复合材料可能在SCW定向发射和基于SCW的集成电路开发中具有重要意义。
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引用次数: 0
Investigation of Sea Surface Effect on Shallow Water Reverberation by Coupled Mode Method 耦合模式法研究海面对浅水混响的影响
Q1 Mathematics Pub Date : 2017-03-16 DOI: 10.1142/S0218396X17500175
Bo Gao, Ning Wang, H. Wang
The effects of rough sea surface on the long-range bottom reverberation in shallow seas are studied by the coupled mode reverberation theory. The scattering effect caused by irregular rough sea surface is described by couple coefficients. The decaying rules of long-range bottom reverberation level are simulated at different sea states, and the rough sea surface effect on the coherence of distant bottom reverberation is also discussed. It is indicated that irregular upper boundary has changed the propagation effect of the shallow water waveguide, and bottom reverberation, which is dominated among other kinds of reverberation in shallow water, is affected by the sea surface scattering as the increasing sea state. Compared with other literatures, the emphasis of this paper is to present the mechanism of rough sea surface scattering by describing the transfer of energy between different modes, and the details of energy transitions between different modes which are caused by sea surface scattering are presente...
利用耦合模式混响理论研究了波涛汹涌的海面对浅海长程海底混响的影响。用耦合系数描述了不规则粗糙海面引起的散射效应。模拟了不同海况下长程海底混响水平的衰减规律,讨论了粗糙海面对远程海底混响相干性的影响。结果表明,不规则的上边界改变了浅水波导的传播效果,而在浅水中其他类型的混响中占主导地位的底部混响随着海况的增加而受到海面散射的影响。与其他文献相比,本文的重点是通过描述不同模式之间的能量传递来揭示粗糙海面散射的机制,并详细介绍了海面散射引起的不同模式之间能量跃迁。。。
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引用次数: 3
期刊
Journal of Computational Acoustics
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