Acoustic characteristics analysis of slender cavity system with arbitrary impedance end conditions

A modeling method for the dynamic characteristics analysis of a slender acoustical cavity with impedance end conditions is established. In order to satisfy the continuity requirement at impedance ends for the first order differential of sound pressure, field function is constructed as the standard Fourier series supplemented by boundary smoothed auxiliary polynomials. System characteristic equation is derived by solving the governing differential equation and impedance acoustic boundary of slend...     

考虑任意阻抗壁面条件管腔结构声场特性分析

针对任意阻抗壁面条件一维管腔声学系统建模,对系统动力学特性进行预报。为了满足阻抗边界条件对声压一阶导数连续性要求,管腔声压函数通过在标准傅里叶级数端点位置引入边界光滑辅助多项式进行构建。结合壁面阻抗声学边界和管腔声学Helmholtz控制微分方程得到强形式标准特征值问题,获得相应的声学模态信息。在数值仿真中,通过算例给出各种边界条件下管腔声学模态频率、声压振型、声压和质点振速频率响应曲线,与现有文献中相关结果进行对比,充分验证了本文求解方法的正确性和有效性,证明该方法可对任意阻抗壁面条件管腔系统声学特性进行准确预报。     

Implementation of a constrained Ritz series modeling technique for acoustic cavity-structural systems

A prior study [Ginsberg, J. H. (2010b). J. Acoust. Soc. Am. 127, 2749-2758] used Ritz series in conjunction with Hamilton's principle to derive general equations describing the time domain response of an acoustic cavity bounded by an elastic structure. The equations of motion are supplemented by constraint equations that explicitly enforce velocity continuity at the cavity's surface. These constraints are imposed by the surface traction, which is represented by unknown coefficients of Ritz-type series. The resulting set of equations are differential-algebraic type. Three methods are presented to convert the governing equations to forms that are familiar to structural acoustics, including one that transforms them from differential-algebraic type to the standard ordinary differential equations associated with linear multi-degree-of-freedom vibratory systems. In cases where only the structure is excited, the formulation offers options as to how displacement/velocity boundary conditions on the nonstructural boundary are enforced, as well as whether zero pressure boundary conditions are enforced at all. An example of a one-dimensional waveguide that is closed at one end by an oscillator is used to explore the quality of solutions obtained from each of these options. Results for natural frequencies and mode functions are examined for accuracy and convergence.     

An inherently stable boundary-condition-transfer algorithm for muffler analysis

Wave coupling exists in the wave propagation in multiple interacting ducts within a waveguide. One may use the segmentation approach, decoupling approach, eigenvalue approach, or the matrizant approach to derive the overall transfer matrix for the muffler section with interacting ducts, and then apply the terminal boundary conditions to obtain a two-by-two transfer matrix. In such instances, a boundary condition applied to a vector is given as a linear combination of its components. Spatial dimensions along with parameters like impedance of the perforated interface may yield numerical instability during computation leading to inaccurate prediction of the acoustic performance of mufflers. Here, an inherently stable boundary-condition-transfer approach is discussed to analyze the plane wave propagation in suchlike mufflers and applied to waveguides of variable cross-sectional area. The concept of pseudo boundary conditions applied to the state vector at an intermediate point is outlined. The method is checked for self-consistency and shown to be stable even for extreme geometries.     

声测井中的声压-速度有限差分方法

为了解决薄互储层的声测井问题,提出了声压-速度有限差分方法:用声压和速度矢量做为场变量,分别描述井内流体和井外弹性固体或双相介质。这样选择场变量的优点是:处理脉冲点源(或线源)与套网格技术相比简单得多;在内边界上的差分格式稳定,精度得到了改进;人为边界上的吸收效果较好。用柱坐标分别给出了井壁上流体与弹性固体、流体与双相介质的声压-速度边界条件,并用守恒积分方法处理了井壁上的边界条件。通过用声压-速度有限差分方法模拟弹性固体和双相介质地层的声场,证明了声压-速度有限差分方法的有效性。     

A network approach for analysis of silencers with/without absorbent material

The object of this work is to establish a general approach that can analyze the performance of most of the silencers with/without sound absorbent material. Under the assumption of plane wave propagation, the transfer matrices between the two ends of straight pipe and two-duct perforated section are derived and taken as the basic elements. Based on the conditions of continuity of pressure and of mass velocity, the silencer is modeled as a network formed by the two basic elements. Then the sound attenuation characteristic of the silencers can be investigated. With this scheme the multiply connected acoustic filters can also be analyzed. Further, the porous sound absorbent material is also included in this scheme. The effect of sound absorption material on the performance of silencers is analyzed and discussed.     

Implementation of nonreflecting boundary conditions for the nonlinear Euler equations

Computationally efficient nonreflecting boundary conditions are derived for the Euler equations with acoustic, entropic and vortical inflow disturbances. The formulation linearizes the Euler equations near the inlet/outlet boundaries and expands the solution in terms of Fourier–Bessel modes. This leads to an ‘exact’ nonreflecting boundary condition, local in space but nonlocal in time, for each Fourier–Bessel mode of the perturbation pressure. The perturbation velocity and density are then calculated using acoustic, entropic and vortical mode splitting. Extension of the boundary conditions to nonuniform swirling flows is presented for the narrow annulus limit which is relevant to many aeroacoustic problems. The boundary conditions are implemented for the nonlinear Euler equations which are solved in space using the finite volume approximation and integrated in time using a MacCormack scheme. Two test problems are carried out: propagation of acoustic waves in an annular duct and the scattering of a vortical wave by a cascade. Comparison between the present exact conditions and commonly used approximate local boundary conditions is made. Results show that, unlike the local boundary conditions whose accuracy depends on the group velocity of the scattered waves, the present conditions give accurate solutions for a range of problems that have a wide array of group velocities. Results also show that this approach leads to a significant savings in computational time and memory by obviating the need to store the pressure field and calculate the nonlocal convolution integral at each point in the inlet and exit boundaries.     

Acoustic modelling of exhaust devices with nonconforming finite element meshes and transfer matrices

Transfer matrices are commonly considered in the numerical modelling of the acoustic behaviour associated with exhaust devices in the breathing system of internal combustion engines, such as catalytic converters, particulate filters, perforated mufflers and charge air coolers. In a multidimensional finite element approach, a transfer matrix provides a relationship between the acoustic fields of the nodes located at both sides of a particular region. This approach can be useful, for example, when one-dimensional propagation takes place within the region substituted by the transfer matrix. As shown in recent investigations, the sound attenuation of catalytic converters can be properly predicted if the monolith is replaced by a plane wave four-pole matrix. The finite element discretization is retained for the inlet/outlet and tapered ducts, where multidimensional acoustic fields can exist. In this case, only plane waves are present within the capillary ducts, and three-dimensional propagation is possible in the rest of the catalyst subcomponents. Also, in the acoustic modelling of perforated mufflers using the finite element method, the central passage can be replaced by a transfer matrix relating the pressure difference between both sides of the perforated surface with the acoustic velocity through the perforations. The approaches in the literature that accommodate transfer matrices and finite element models consider conforming meshes at connecting interfaces, therefore leading to a straightforward evaluation of the coupling integrals. With a view to gaining flexibility during the mesh generation process, it is worth developing a more general procedure. This has to be valid for the connection of acoustic subdomains by transfer matrices when the discretizations are nonconforming at the connecting interfaces. In this work, an integration algorithm similar to those considered in the mortar finite element method, is implemented for nonmatching grids in combination with acoustic transfer matrices. A number of numerical test problems related to some relevant exhaust devices are then presented to assess the accuracy and convergence performance of the proposed procedure.     

Prediction of the sound field above a patchwork of absorbing materials

The aim of this paper is to investigate the acoustic performance of sound absorbing materials through a numerical wave based prediction technique. The final goal of this work is to get insight into the acoustic behavior of a combination of sound absorbing patches. In order to address a wide frequency range, a model based on the Trefftz approach is adopted. In this approach, the dynamic field variables are expressed in terms of global wave function expansions that satisfy the governing dynamic equations exactly. Therefore, approximation errors are associated only with the boundary conditions of the considered problem. This results in a computationally efficient technique. The main advantage of this method is the fact that the sound absorbing patches do not have to be locally reacting. In this article, the wave based method is described and experimentally validated for the case of normal incidence sound absorption identification in a standing wave tube. Afterwards, the method is applied to simulate some interesting setups of absorbing materials.     

圆孔非线性声阻抗三维时域仿真与特性分析

为研究有限振幅声波作用下圆孔的非线性声学特性,提出了基于三维时域计算流体动力学(CFD)仿真的圆孔非线性声阻抗提取方法,通过求解层流方程来模拟声信号在圆孔及上下游的传播,以及采用横向周期性边界条件来考虑高穿孔率时圆孔之间相互作用的影响。研究了不同幅值声波作用下孔径、厚度和穿孔率对声阻抗的影响规律,通过对质点振速幅值、频率和板厚等组成的无量纲参量进行非线性回归分析,得到了圆孔非线性声阻抗的拟合公式,并将其转换为可考虑多频声波影响的时域模型。最后结合声阻抗时域模型和有限差分方法计算了直通穿孔管消声器在小振幅和有限振幅声波作用下的传递损失,通过与实验测量结果的比较,验证了拟合公式的准确性和实用性。     

三维润滑问题的数值分析

本文求解了轴承的三维润滑问题。使用格林函数方法,将基本方程化为求解区边界上的积分方程。采用空间曲边三角形单元离散边界,并用六结点等参数无数值求解积分方程,确定了速度场,压力场和边界上的应力。算例与解析解比较表明有较高的精度。其它一些典型问题的计算也给出满意的结果,表明本文方法对数值分析这类问题的有效性。     

ON THE ACOUSTIC ABSORPTION OF MULTI-LAYER ABSORBERS WITH DIFFERENT INNER STRUCTURES

A rigorous finite element analysis procedure is developed to study the effect of the inner structures on the acoustic absorption of multi-layer absorbers. To do this, four types of basic inner structure compartments adopted in the multi-layer absorbers are selected for analysis. These compartments are composed of porous materials inlaid with perforated plates of various shapes, say, triangle, semicircle, convex rectangle and plate shapes. As it is different from the conventional finite element analysis for the acoustic system in the literature, the perforated plates are simulated by appropriate equivalent boundary conditions, depending on their thickness, hole radius, hole pitch and porosity and the air contained in the holes. A large number of total degrees of freedom generated from meshing the air in the holes of perforated plates are thus avoided. The results reveal that the inner structures of the multi-layer absorbers will influence the acoustic absorption at some frequency bands significantly. Based on those features, the multi-layer absorber with a novel inner structure is then designed and manufactured. Both the finite element and experimental results show that its acoustic absorption would be distinctly promoted.     

Acoustic modeling of perforated plates with bias flow for Large-Eddy Simulations

The study of the acoustic effect of perforated plates by Large-Eddy Simulations is reported. The ability of compressible Large-Eddy Simulations to provide data on the flow around a perforated plate and the associated acoustic damping is demonstrated. In particular, assumptions of existing models of the acoustic effect of perforated plate are assessed thanks to the Large-Eddy Simulations results. The question of modeling the effect of perforated plates is then addressed in the context of thermo-acoustic instabilities of gas turbine combustion chambers. Details are provided about the implementation, validation and application of a homogeneous boundary condition modeling the acoustic effect of perforated plates for compressible Large-Eddy Simulations of the flow in combustions chambers cooled by full-coverage film cooling.     

THE FORCED VIBRATION AND BOUNDARY CONTROL OF PRETWISTED TIMOSHENKO BEAMS WITH GENERAL TIME DEPENDENT ELASTIC BOUNDARY CONDITIONS

The governing differential equations and the general time-dependent elastic boundary conditions for the coupled bending-bending forced vibration of a pretwisted non-uniform Timoshenko beam are derived by Hamilton's principle. By introducing a general change of dependent variable with shifting functions, the original system is transformed into a system composed of four non-homogeneous governing differential equations and eight homogeneous boundary conditions. The transformed system is proved to be self-adjoint. Consequently, the method of separation of variables can be used to solve the transformed problem. The physical meanings of these shifting functions are explored. The orthogonality condition for the eigenfunctions of a pretwisted non-uniform beam with elastic boundary conditions is also derived. The relation between the shifting functions and the stiffness matrix is derived. The boundary control of a pretwist Timoshenko beam is studied. The effects of the total pretwist angle, the position of loading and the boundary spring constants on the energy required to control the performance of a pretwisted beam are investigated.     

穿孔板在切向流条件下非线性效应的理论与实验研究

流过声衬表面的切向流和高声压级的声场对于穿孔板共振结构的声学特性有这非常显著的影响。本文从波涡相互作用机制出发,发展了一种旨在研究矩形穿孔板在切向流条件下非线性效应的离散涡模型。同时用双传声器法测量了不同几何参数的穿孔板的声阻抗随偏流速度及声压级的变化情况。将本文的实验与理论结果进行了对比分析,对比的结果表明本文的实验与理论结果符合良好。     

SiO2波导布拉格器件中声表面波及声光相互作用分析

针对SiO2光波导声光布拉格器件,计算了SiO2非对称平板波导TE模式的横向场分布;给出了SiO2/ZnO/Air层状介质结构的性能方程、运动方程和麦克斯韦方程,推导出这种层状结构的特征方程,并结合所满足的边界条件,得到了各层介质的位移及电磁场分布;计算了声表面波所引起的光学相对介质隔离率张量的变化,最后讨论了声光衍射效率和光场与声场的重叠积分、声功率、声频率、声孔径和光波导参数之间的关系。结果表明,在低频范围内光场与声表面波场重叠良好;低阶模的重叠积分始终大于高阶模重叠积分,最低阶模与声表面波相互作用最强,所需声功率最小;当声功率一定时,增加声孔径可以提高衍射效率。     

Variable fluid properties and variable heat flux effects on the flow and heat transfer in a non-Newtonian Maxwell fluid over an unsteady stretching sheet with slip velocity

The effects of variable fluid properties and variable heat flux on the flow and heat transfer of a non-Newtonian Maxwell fluid over an unsteady stretching sheet in the presence of slip velocity have been studied. The governing differential equations are transformed into a set of coupled non-linear ordinary differential equations and then solved with a numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary value problem is based on applying the fourth-order Runge-Kutta method coupled with the shooting technique over the entire range of physical parameters. The effects of various parameters like the viscosity parameter, thermal conductivity parameter, unsteadiness parameter, slip velocity parameter, the Deborah number, and the Prandtl number on the flow and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed. Comparison of numerical results is made with the earlier published results under limiting cases.     

Numerical stability analysis for the explicit high-order finite difference analysis of rotationally symmetric shells

A numerical stability analysis has been formulated to accompany the already developed explicit high-order finite difference analysis of rotationally symmetric shells subjected to time-dependent impulsive loadings. This already developed analysis utilizes a constant nodal point spacing for the spatial finite difference mesh, with the governing field differential equations formulated in terms of the transverse, meridional, and circumferential displacements as the fundamental variables. The remaining quantities which enter into the natural boundary conditions at each edge of the shell are incorporated into the complete system of equations by defining those quantities at each boundary in terms of the displacements. Surface loadings and inertia forces in each of the three displacement directions of the shell have been considered in the governing equations. Ordinary finite difference representations are used for the time derivatives. All loadings and dependent variables in the circumferential direction of the shell are expressed in Fourier series expansions. The complete system of equations is solved implicitly for the first time increment, while explicit relations are used to determine the three primary displacements within the boundary edges of the shell for the second and succeeding time increments. Separate implicit solutions at each boundary are then used to determine the remaining unspecified primary variables on and outside the boundaries. Subsequently, the remaining primary variables within the boundary edges of the shell and all secondary variables are determined explicitly. Numerical stability (or instability) of numerical solutions for given choices of spatial and time increments is determined by evaluation of the eigenvalues of the explicit coefficient matrix and comparing the maximum eigenvalue with the requirements of a stability criterion developed before by the author. Solutions for typical shells and loadings together with results of stability analyses have been included, and comparisons of the stability requirements and solutions with the requirements and solutions based upon ordinary spatial finite difference representations are included.