Transfer matrix methods for sound attenuation in resonators with perforated intruding inlets

A resonator with perforated intruding inlet (PII) is a superior silencer element, since the use of perforated inlet extensions can dramatically improve the acoustic performance. In this work, both a one-dimensional (1D) and a two-dimensional (2D) transfer matrix methods are developed to predict the transmission loss of the resonator without considering the mean flow. Based on the two groups of comparisons with tests, it is found out that the applicability of 1D method is limited by the resonator geometry even when the frequency is below the cut-off value of plane wave. Whereas the 2D approach is much more accurate while predicting the transmission losses within entire frequency range. Subsequently, five groups of resonators are chosen to determine the effects of structure parameters to transmission loss based on the 2D approach. The resonant frequency decreases and more resonant peaks appear when the length of inlet extension increases. A higher perforation rate leads to a shift of resonant peak towards higher frequencies. Besides, better acoustic performance could be obtained with the perforation being properly designed. Reducing the inlet/outlet radius can obviously improve the transmission loss without changing the frequency of resonant peak. The theories and conclusions in this study can be used for the design and optimization of resonators in various engineering applications.     

Transfer matrix modeling of the vibroacoustic response of multi-materials structures under mechanical excitation

In several automotive and aircraft applications there is a need for simple tools to assess quickly and accurately the performance of sound packages. Statistical energy analysis (SEA) and the transfer matrix method (TMM) are examples of such methods. The used methodology (for modeling sound packages) is well validated for acoustic excitations (airborne). However, a simple and reliable methodology is still lacking for mechanical excitations (structure-borne). This work concentrates on the latter. It presents and compares three different simple approaches to model the vibration and acoustic response of a mechanically excited structure with an added noise control treatment. Various examples are presented to confirm their relevance and accuracy in comparison to more exact and costly methods, such as the finite element method. In particular, it is shown that the TMM with a size correction (FTMM) is accurate enough to eliminate the classical assumption of low coupling classically assumed in SEA modeling of sound packages and/or compute efficiently the structure-borne insertion loss of sound packages used in SEA and FEM models.     

Finite element acoustic simulation based shape optimization of a muffler

This paper describes a methodology which combines finite element analysis and Zoutendijk’s feasible directions method for mufflers shape design. The main goal is to obtain the dimensions of the acoustic muffler with the transmission loss (TL), being maximized in the frequency range of interest. The improved four parameters method is used for TL evaluations and the Helmholtz’s equation is solved numerically with the finite element method (FEM). The quadratic triangular finite element meshes are adequately constructed to control the pollution error and the optimization problem is solved using the Zoutendijk’s feasible directions method due to robustness and efficiency for problems with nonlinear constraints. Numeric experiments performed with circular expansion chambers with extended inlet and outlet show results for constrained and unconstrained shape optimization.     

声表面波器件变频快速模拟方法

声表面波器件的级联有限元模拟方法是从整体结构中分离出若干独立的基本单元,通过基本单元边界矩阵的级联实现有限长器件结构的模拟.在实际设计中,通过优化叉指换能器的指条周期,激发出不同波长的声表面波,调整声表面波器件的谐振频率,这导致级联有限元模拟方法存在频繁的单元建模与数据传输过程.为提高模拟效率,该文提出了一种波长(频率...     

Propagation of acoustic waves in a fluid-filled pipe with periodic elastic Helmholtz resonators

Helmholtz resonators are widely used to reduce noise in a fluid-filled pipe system. It is a challenge to obtain lowfrequency and broadband attenuation with a small sized cavity. In this paper, the propagation of acoustic waves in a fluid-filled pipe system with periodic elastic Helmholtz resonators is studied theoretically. The resonance frequency and sound transmission loss of one unit are analyzed to validate the correctness of simplified acoustic impedance. The band structure of infinite periodic cells and sound transmission loss of finite periodic cells are calculated by the transfer matrix method and finite element software. The effects of several parameters on band gap and sound transmission loss are probed.Further, the negative bulk modulus of periodic cells with elastic Helmholtz resonators is analyzed. Numerical results show that the acoustic propagation properties in the periodic pipe, such as low frequency, broadband sound transmission, can be improved.     

A novel hybrid ES-FE-SEA for mid-frequency prediction of Transmission losses in complex acoustic systems

The widely-used numerical modeling approaches such as the finite element method (FEM) and statistical energy analysis (SEA) often have limited applicability to the transmission loss prediction in mid-frequency range. In this paper, a novel hybrid edge-based smoothed FEM coupled with statistical energy analysis (ES-FE-SEA) method is proposed to further improve the accuracy of “mid-frequency” transmission loss predictions. The application of ES-FEM will “soften” the well-known ‘‘overly-stiff’’ behavior in the standard FEM solution and reduce the inherent numerical dispersion error. While the SEA approach deals with the physical uncertainty in the relatively higher frequency range. The plate of interest is appropriately described by an ES-FEM model, due to its relative robustness to perturbations. Its adjacent reverberation cavities are modeled by employing the SEA approach, because of their high model density. The coupling and interaction between SEA subsystems and the FE subsystem is governed by the “reciprocity relationship” theorem. A standard numerical example for benchmarking is examined and excellent agreement was achieved between the prediction and reference results. The proposed ES-FE-SEA is also verified by various numerical examples. The method is finally applied to the modeling a complicated engineering problem–acoustic fields on both sides of the front windshield in a passenger car.     

Coupled FEM/BEM for control of noise radiation and sound transmission using piezoelectric shunt damping

In this paper, we present a coupled finite element/boundary element method (FEM/BEM) for control of noise radiation and sound transmission of vibrating structure by passive piezoelectric techniques. The system consists of an elastic structure (with surface mounted piezoelectric patches) coupled to external/internal acoustic domains. The passive shunt damping strategy is employed for vibration attenuation in the low frequency range. The originality of the present paper lies in evaluating the classically used FEM/BEM methods for structural–acoustics problems when taking account smart systems at the fluid–structure interfaces.     

Numerical simulation of electromagnetic acoustic transducers using distributed point source method

In spite of many advances in analytical and numerical modeling techniques for solving different engineering problems, an efficient solution technique for wave propagation modeling of an electromagnetic acoustic transducer (EMAT) system is still missing. Distributed point source method (DPSM) is a newly developed semi-analytical technique developed since 2000 by Placko and Kundu (2007) [12] that is very powerful and straightforward for solving various engineering problems, including acoustic and electromagnetic modeling problems. In this study DPSM has been employed to model the Lorentz type EMAT with a meander line and flat spiral type coil. The problem of wave propagation has been solved and eddy currents and Lorentz forces have been calculated. The displacement field has been obtained as well. While modeling the Lorentz force the effect of dynamic magnetic field has been considered that most current analyses ignore. Results from this analysis have been compared with the finite element method (FEM) based predictions. It should be noted that with the current state of knowledge this problem can be solved only by FEM.     

计算水下凹面目标散射声场的声束弹跳法

为了解决含有多次散射时水下目标声散射场的计算问题,提出了一种声束弹跳方法。把入射声波划分为若干声束,根据几何声学方法计算每条声束在目标表面的反射方向和能量损失,利用物理声学方法计算最后一次反射的声束所对应的面元的散射场,通过计算所有声束产生的散射场的叠加得到整个目标的散射场。计算了直角凹面圆锥体的散射声场,并对具体模型进行了水池测量实验,理论计算和实验测量结果一致。表明该方法作为一种高频近似的数值计算方法,可以计算存在多次散射时水下目标的散射声场。      

Modal decomposition method for acoustic impedance testing in square ducts

Accurate duct acoustic propagation models are required to predict and reduce aircraft engine noise. These models ultimately rely on measurements of the acoustic impedance to characterize candidate engine nacelle liners. This research effort increases the frequency range of normal-incidence acoustic impedance testing in square ducts by extending the standard two-microphone method (TMM), which is limited to plane wave propagation, to include higher-order modes. The modal decomposition method (MDM) presented includes four normal modes in the model of the sound field, thus increasing the bandwidth from 6.7 to 13.5 kHz for a 25.4 mm square waveguide. The MDM characterizes the test specimen for normal- and oblique-incident acoustic impedance and mode scattering coefficients. The MDM is first formulated and then applied to the measurement of the reflection coefficient matrix for a ceramic tubular specimen. The experimental results are consistent with results from the TMM for the same specimen to within the 95% confidence intervals for the TMM. The MDM results show a series of resonances for the ceramic tubular material exhibiting a monotonic decrease in the resonant peaks of the acoustic resistance with increasing frequency, resembling a rigidly-terminated viscous tube, and also evidence of mode scattering is visible at the higher frequencies.     

On an Integrated Transfer Matrix method for multiply connected mufflers

The commercial automotive mufflers are generally of a complicated shape with multiply connected parts and complex acoustic elements. The analysis of such complex mufflers has always been a great challenge. In this paper, an Integrated Transfer Matrix method has been developed to analyze complex mufflers. Integrated transfer matrix relates the state variables across the entire cross-section of the muffler shell, as one moves along the axis of the muffler, and can be partitioned appropriately in order to relate the state variables of different tubes constituting the cross-section. The paper presents a generalized one-dimensional (1-D) approach, using the transfer matrices of simple acoustic elements, which are available from the literature. The present approach is robust and flexible owing to its capability to construct an overall matrix of the muffler with the transfer matrices of individual acoustic elements and boundary conditions, which can then be used to evaluate the transmission loss, insertion loss, etc. Results from the present approach have been validated through comparisons with the available experimental and three-dimensional finite element method (FEM) based results. The results show good agreement with both measurements and FEM analysis up to the cut-off frequency.     

多元件谐振腔模式的有限元传输矩阵分析方法

建立了多元件谐振腔本征模的有限元传输矩阵模型。提出了模式计算相对误差概念及相应表达式,该表达式在数值上不受菲涅耳数的影响,能够很好反映有限单元划分方案对不同菲涅耳数的谐振腔的模式计算精度的影响。提出了有限单元划分精细度的概念和相应表达式,用以表征有限单元划分的精细程度。该表达式以菲涅耳数作为有限元传输矩阵法对腔镜单元格数划分的相对要求,用镜面实际划分的单元格数与菲涅耳数的比值来表征有限单元划分的精细程度。分析了不同谐振腔参数变化时模式计算相对误差与有限单元划分精细度的关系,建立了3种不同函数形式的经验表达式,并通过比较拟合残差选择了拟合效果较好的表达式。     

Isogeometric finite element analysis of interior acoustic problems

Isogeometric Analysis (IGA) can bridge the gap between geometrical and numerical modeling. To this end, the same basis functions used in Computer Aided Design are applied to represent geometry and approximate physical field in analysis. In this paper, the IGA is firstly introduced to finite element method (FEM) for interior acoustic problems. The domain is parameterized by Non-Uniform Rational B-Spline (NURBS) in the algorithm, which simplifies the mesh generation greatly and furthermore supplies an exact representation of curved boundaries. In addition, the IGA FEM possesses a distinct feature of flexible order-elevation technique without modifying the geometry. Several numerical examples are presented to validate the accuracy and demonstrate the merits of the IGA FEM in the analysis of interior acoustic problems.     

A finite-element method using dispersion reduced spline elements for room acoustics simulation

This paper presents a finite element method (FEM) using hexahedral 27-node spline acoustic elements (Spl27) with low numerical dispersion for room acoustics simulation in both the frequency and time domains, especially at higher frequencies. Dispersion error analysis in one dimension is performed to increase the accuracy of FEM using Spl27 by modifying the numerical integration points of element stiffness and mass matrices. The basic accuracy and efficiency of the FEM using the improved Spl27, which uses modified integration points, are presented through numerical experiments using benchmark problems in both the frequency and time domains, revealing that FEM using the improved Spl27 in both domains provides more accurate results than the conventional method does, and with fewer degrees of freedom. Moreover, the effectiveness of FEM using the improved Spl27 over that using hexahedral 27-node Lagrange elements is shown for time domain analysis of the sound field in a practical sized room.     

Simple method for measuring vibration amplitude of high power airborne ultrasonic transducer: Using thermo-couple

Vibration amplitude of transducer’s elements is the influential parameters in the performance of high power airborne ultrasonic transducers to control the optimum vibration without material yielding. The vibration amplitude of elements of provided high power airborne transducer was determined by measuring temperature of the provided high power airborne transducer transducer’s elements. The results showed that simple thermocouples can be used both to measure the vibration amplitude of transducer’s element and an indicator to power transmission to the air. To verify our approach, the power transmission to the air has been investigated by other common method experimentally. The experimental results displayed good agreement with presented approach.     

非对称阻抗插入管消声器的Chebyshev-变分法建模与求解

针对非对称阻抗插入管消声器三维理论建模与求解问题,提出了一种半解析变分建模和求解方法,试验及有限元结果验证了理论模型和求解结果的正确性,开展了模态频率、声压响应及传递损失等声场特性的预测分析.首先构建插入管消声器内部子声场拉格朗日泛函,基于声压与质点振速连续性条件,得到插入管消声器三维理论模型.随后,将子声场声压展开为...     

多层微穿孔板结构声学性能计算方法对比分析

计算多层微穿孔板结构声学特性方法传统主要用声电类比法,目前出现阻抗转移法和传递矩阵法,对比分析这三种计算方法,同时进行相应的实验验证。结果表明:阻抗转移法和传递矩阵法实质上是相同的,这两种方法计算结果与实验结果吻合良好。声电类比法在空腔较大时计算结果偏离实验值,原因是声电类比法采用集总参数分析,计算多层结构时,空腔单元只考虑声顺,忽略声质量,导致误差。阻抗转移法和传递矩阵法不存在这一误差,计算准确。     

海洋波导中目标声辐射场的计算方法

针对海洋波导中目标声辐射场的计算问题,提出了一种基于波叠加法并在近、远场采用不同水声传播模型的建模方法,可以将近、远场作为一个统一的系统进行高效地分析。该方法通过给定的已知表面振动速度的结构计算出目标内部虚拟点声源的源强,再配合在相应的水声环境中点声源传播模型的Green函数计算出结构外的声辐射场。以Green函数为纽带,在求源强和计算近场声辐射场时采用镜像虚源法,而在计算远场声辐射场时采用简正波法。通过该方法得到的有限水深波导中声速剖面为正梯度、负梯度、负跃层的3种情况下的脉动球、刚体摆动球的声辐射场计算结果与COMSOL的有限元计算结果进行对比,结果表明了该方法在提高计算效率的同时保证了计算精度。      

Loss-improved electroacoustical modeling of small Helmholtz resonators

Modeling of small Helmholtz resonators based on electroacoustical analogies often results in significant disagreement with measurements, as existing models do not take into account some losses that are observed in practical implementations of such acoustical circuits, e.g., in photoacoustic Helmholtz cells. The paper presents a method which introduces loss corrections to the transmission line model, resulting in substantial improvement of simulations. Values of the loss corrections obtained from comparison of frequency responses of practically implemented resonators with computer simulations are presented in tabular and graphical form. A simple analytical function that can be used for interpolation or extrapolation of the loss corrections for other dimensions of the Helmholtz resonators is also given. Verification of such a modeling method against an open two-cavity Helmholtz structure shows very good agreement between measurements and simulations.     

Transient acoustic radiation from impulsively accelerated bodies by the finite element method

Bodies under impulsive motion, immersed in an infinite acoustic fluid, severely put to test any numerical method for the transient exterior acoustic problem. Such problems, in the context of the finite element method (FEM), are not well studied. FE modeling of such problems requires truncation of the infinite fluid domain at a certain distance from the structure. The volume of computation depends upon the extent of this domain as well as the mesh density. The modeling of the fluid truncation boundary is crucial to the economy and accuracy of solution and various boundary dampers have been proposed in the literature for this purpose. The second order damper leads to unsymmetric boundary matrices and this necessitates the use of an unsymmetric equation solver for large problems. The present paper demonstrates the use of FEM with zeroth, first and second order boundary dampers in conjunction with an unsymmetric, out of core, banded equation solver for impulsive motion problems of rigid bodies in an acoustic fluid. The results compare well with those obtained from analytical methods.