A hybrid finite element approach to modeling sound radiation from circular and rectangular ducts

A numerical model based on a hybrid finite element method is developed that seeks to join sound pressure fields in interior and exterior regions. The hybrid method is applied to the analysis of sound radiation from open pipes, or ducts, and uses mode matching to couple a finite element discretization of the region surrounding the open end of the duct to wave based modal expansions for adjoining interior and exterior regions. The hybrid method facilitates the analysis of ducts of arbitrary but uniform cross section as well the study of conical flanges and here a modal expansion based on spherical harmonics is applied. Predictions are benchmarked against analytic solutions for the limiting cases of flanged and unflanged circular ducts and excellent agreement between the two methods is observed. Predictions are also presented for flanged and unflanged rectangular ducts, and because the hybrid method retains the sparse banded and symmetric matrices of the traditional finite element method, it is shown that predictions can be obtained within an acceptable time frame even for a three dimensional problem.     

通路时间差与立体声声像定位

通过对双耳声压进行相关分析,探讨了立体声重发时通路时间差对声像定位的影响,并进行了声像定位实验。结果表明,在低频f≤0.6kHz时,通路时间差不能有效地产生声像移动。只有f>0.7kHz时,通路时间差的影响才逐渐明显。并且通路时间差所产生的声像位置明显与频率有关,声像的明晰度、自然度都较差,因而在实际应用中应尽量避免单独利用通路时间差产生立体声声像。     

A comparison of experiment and theory for sound propagation in variable area ducts

An experimental and analytical program has been carried out to evaluate sound suppression techniques in ducts that produce refraction effects due to axial velocity gradients. The analytical program employs a computer code based on the method of multiple scales to calculate the influence of axial variations due to slow changes in the cross-sectional area as well as transverse gradients due to the wall boundary layers. Detailed comparisons between the analytical predictions and the experimental measurements have been made. The circumferential variations of pressure amplitudes and phases at several axial positions have been examined in straight and variable area ducts, with hard walls and lined sections, and with and without a mean flow. Reasonable agreement between the theoretical and experimental results has been found.     

Two-body collisions and time dependent Hartree-Fock theory

The time-dependent Hartree-Fock (TDHF) theory is generalized in order to include the effect of two-body collisions (i.e. the residual interaction). This is achieved by adding a collision integral into the TDHF equations, similar to the one ordinarily used in the Boltzmann equation. It is shown, that two-body collisions arise from the imaginary part of the effective interaction between two nucleons whereas the Hartree-Fock field is associated to the real part of the same interaction. There is thus no double counting when the collisions are added to a single particle field. Various approximations for the collision integral are discussed and their accuracy evaluated. Special effort is made in order to obtain conserving approximations. It is shown that for discrete fields, energy as well as momentum conservation is achieved by off-shell scattering processes. In the light of a previous paper, it is argued that two-body collisions should dominate the irreversible processes above some critical energy (roughly 200 MeV per nucleon). Below this energy the irreversible effects due to the single particle field and the collisions are expected to be of the same order of magnitude.     

Free vibration analysis of stiffened plates using finite difference method

Free vibration characteristics of rectangular stiffened plates having a single stiffener have been examined by using the finite difference method. A variational technique has been used to minimize the total energy of the stiffened plate and the derivatives appearing in the energy functional are replaced by finite difference equations. The energy functional is minimized with respect to discretized displacement components and natural frequencies and mode shapes of the stiffened plate have been determined as the solutions of a linear algebraic eigenvalue problem. The analysis takes into consideration inplane deformation of the plate and the stiffener and the effect of inplane inertia on the natural frequencies and mode shapes. The effect of the ratio of stiffener depth to plate thickness on the natural frequencies of the stiffened plate has also been examined.     

The onset of superconductivity in the time dependent Ginzburg-Landau theory

The fluctuations of the local order parameter above the superconducting transition temperature give rise to singularities in the electrical conductivity and the diamagnetic susceptibility. Using the time dependent Ginzburg-Landau equation the fluctuation of the current density is calculated. By means of the fluctuation-dissipation theorem and a dispersion relation the electromagnetic response function is then determined for small frequencies and wave-numbers. The dynamical conductivity for bulk material, thin films, and thin wires shows an increasing peak at zero frequency the width of which decreases as the transition temperature is approached. This structure should be observable in microwave experiments.     

On the finite settling time and residual vibration control of flexible structures

Rapid end-point positioning of a structure with minimal residual vibration under a single bounded control input is considered. The structure between the actuator and the end point is assumed to be flexible, and is the main cause of positioning error from residual vibration. A standard solution to this problem is offered by the well known bang-bang control. Implementation of such a bang-bang control strategy leads to decreased response time but introduces unwanted vibrations from repeated overshooting of the switching contour, caused by errors in the implementation of the discontinuous control law. An appropriately shaped input function based on minimum energy and bounded control for such end-point positioning systems totally eliminates the residual vibration while making the response time small. The proposed forcing input has two discontinuities at most and therefore does not suffer from the undesirable intermediate discontinuities present in the bang-bang control. This novel control force compares favorably with the bang-bang solution with respect to response time. It also compares favorably with the ramped sinusoidal input force proposed by Meckl and Seering [1] with respect to residual vibration. They shaped the input function by eliminating the resonant frequencies where as the resonant frequencies are retained in the function proposed. As an illustration, the newly shaped forcing input is applied to a rotating thin flexible beam to suppress residual vibration.     

Application of finite strain theory to non-cubic crystals

The application of finite strain theory to a crystal of orthorhombic or higher elastic symmetry, which is subjected to a purely extensional deformation parallel to the crystallographic axes, yields stress-strain relations and effective elastic constants for hydrostatic stresses. Alternative formulations of the theory are obtained when the free energy is written as Taylor series in E, the invariant analogue of the Eulerian strain tensor, or η, the Lagrangian strain tensor. In most cases, the formulation in terms of E provides a better approximation when the Taylor series are truncated at the second or third order. In the case of cubic crystals, the stress-strain relations reduce to the Birch equation. For non-cubic crystals, the P-V relations calculated using the non-cubic and Birch equations will differ due to the effects of elastic anisotropy. A comparison between the second-order approximations of the non-cubic stress-strain relations and the cubic Birch equation suggests that the difference in volume will be less than 1% for most materials. The difference in volume is reduced when the third-order approximations are used. When the third-order terms are retained, the stress-strain relations calculated using the Eulerian formulation agree with measured linear compression data for quartz to 150 kbar $\text{(}\text{P}\text{K}{}_0\text{= 0.4).}$ For zinc, the calculated pressure-volume relation agrees with the shock-wave Hugoniot up to 750 kbar $\text{(}\text{P}\text{K}{}_0\text{= 1.2),}$ although both calculated and Hugoniot P-V relations disagree with X-ray compression data. At pressures greater than 300 kbar, the calculated axial ratio of zinc approaches that for other hexagonal metals $\text{(}\text{c}\text{a}\text{? 1.63).}$     

A setup to study aero-acoustics for finite length ducts with time-varying shape

Elastic ducts with time-varying geometry are a recurrent issue in many engineering and physiological flow or sound production problems. In this study, we present and characterize a setup to study aero-acoustic phenomena through a deformable duct with time-varying geometry. The setup is designed in such a way that experimental control parameters relate directly to input parameters of a quasi-analytical geometrical model (Van Hirtum, 2015). We focus on low Mach number and moderate Reynolds number applications pertinent to physiological problems for which geometrical model input parameters can be related to well defined physiological quantities. Therefore, data gathered using the presented setup allow to study underlying physical phenomena and in addition favor comparison with high performance computational simulations as well as with analytical models for which a limited number of physiological meaningful input parameters are essential. Typical measurements illustrate the impact of geometrical control parameters on the acoustic pressure field in absence and in presence of flow, respectively.     

水中有限长加肋圆柱壳体振动和声辐射近似解析解

加肋圆柱壳体是水下航行器的主要结构形式。将肋骨对壳体的作用简化为只有法向力,本文导出了水中有限长加肋圆柱壳体的振动和声辐射的近似解析解。其中肋骨的作用表现为在无肋的耦合振动方程中增加附加阻抗,因此壳体的振动和声辐射由壳体的机械阻抗、流体的辐射声阻抗和肋骨的附加阻抗所决定。数值计算例子表明,在低频情况下,加肋对辐射声功率影响不大,但将降低表面平均振速,从而增加声辐射效率。     

嵌入式薄片模型在时域有限差分算法中的应用

将一等效薄片模型嵌入到时域有限差分算法（FDTD）中,以快速而有效地解决复合材料薄片在电磁计算中的多尺度问题。在该嵌入式薄片模型中,薄片不需要被剖分网格,而是被嵌入到相邻的网格间,从而可以使用相对较大的网格剖分周围物体,进而可节省大量的计算资源。在这一模型中,薄片被等效为一段传输线,并用其频域的导纳矩阵代替。使用数字滤波器理论以及逆Z变换可将频域的导纳矩阵转换到时域,并将其嵌入到时域有限差分算法中。该嵌入式薄片模型被用来计算一单层碳纤维复合材料薄片的反射以及透射性能,并与其解析解进行对比,从而验证该模型的准确性、收敛性以及高效性。该模型被用来计算三种具有不同电参数的单层碳纤维复合材料薄片的屏蔽性能,以研究各电参数对其屏蔽性能的影响。     

室内声学时域有限差分模拟中的边界条件

给出了时域有限差分法用于室内声学问题模拟中的边界条件,结合声波方程的基本差分格式,模拟并分析了高斯脉冲在4m×4m房间中的波动过程和脉冲响应;模拟了一9m×6m×4m房间的简正频率,并与经典理论计算值进行了对比;模拟了一12m×5m×4m水平地面房间中的坐席吸声低谷效应,并与Joe LoVtri的模拟结果进行了对比;模拟并实际测量了一10.6m×5.8m×3.4m房间在几个受声点的脉冲响应和早期衰变时间EDT,将模拟结果与实际测量结果进行了对比分析,计算程序是用Metlab语言编写的。模拟与经典理论、相关研究、实际测量几方面的对比分析,验证了本边界条件的可靠性。     

Small amplitude limit of the time dependent density matrix theory

The small amplitude limit of the time-dependent density-matrix theory, which is an extension of the time-dependent Hartree-Fock theory, is presented. Its relation to other theories i.e. the random phase approximation (RPA), the second RPA and the shell model is discussed. It is found that the small amplitude limit is a generalization of these theories.     

Source implementation to eliminate low-frequency artifacts in finite difference time domain room acoustic simulation

The finite difference time domain (FDTD) method is a numerical technique that is straight forward to implement for the simulation of acoustic propagation. For room acoustics applications, the implementation of efficient source excitation and frequency dependent boundary conditions on arbitrary geometry can be seen as two of the most significant problems. This paper deals with the source implementation problem. Among existing source implementation methods, the hard source implementation is the simplest and computationally most efficient. Unfortunately, it generates a large low-frequency modulation in the measured time response. This paper presents a detailed investigation into these side effects. Surprisingly, some of these side effects are found to exist even if a transparent source implementation is used. By combing a time limited approach with a class of more natural source pulse function, this paper develops a source implementation method in FDTD that is as simple and computationally as efficient as a hard source implementation and yet capable of producing results that are virtually the same as a true transparent source. It is believed that the source implementation method developed in this paper will provide an improvement to the practical usability of the FDTD method for room acoustic simulation.     

Investigation of long-range sound propagation in surface ducts

Understanding the effect of source-receiver geometry on sound propagation in surface ducts can improve the performance of near-surface sonar in deep water. The Lloyd-mirror and normal mode theories are used to analyze the features of surface-duct propagation in this paper. Firstly, according to the Lloyd-mirror theory, a shallow point source generates directional lobes, whose grazing angles are determined by the source depth and frequency. By assuming a part of the first lobe to be just trapped in the surface duct, a method to calculate the minimum cutoff frequency （MCF） is obtained. The presented method is source depth dependent and thus is helpful for determining the working depth for sonar. Secondly, it is found that under certain environments there exists a layer of low transmission loss （TL） in the surface duct, whose thickness is related to the source geometry and can be calculated by the Lloyd-mirror method. The receiver should be placed in this layer to minimize the TL. Finally, the arrival angle on a vertical linear array （VLA） in the surface duct is analyzed based on normal mode theory, which provides a priori knowledge of the beam direction of passive sonar.     

The simulation of piano string vibration: from physical models to finite difference schemes and digital waveguides

A model of transverse piano string vibration, second order in time, which models frequency-dependent loss and dispersion effects is presented here. This model has many desirable properties, in particular that it can be written as a well-posed initial-boundary value problem (permitting stable finite difference schemes) and that it may be directly related to a digital waveguide model, a digital filter-based algorithm which can be used for musical sound synthesis. Techniques for the extraction of model parameters from experimental data over the full range of the grand piano are discussed, as is the link between the model parameters and the filter responses in a digital waveguide. Simulations are performed. Finally, the waveguide model is extended to the case of several coupled strings.     

A finite difference scheme for acoustic transmission through the walls of distorted circular ducts and comparison with experiment

A numerical method is developed to find the structural response of the walls of cylindrical distorted circular ducts to internal plane acoustic travelling waves, and hence the internal/external sound transmission loss. Comparisons are made between experiment and theory for two “long-seam” air conditioning ducts and a squashed spiral-wound air conditioning duct. In general, reasonable agreement is obtained, when the accuracy of the geometrical specification of the ducts is taken into account. The generality of the computing code allows the method to be applied to cylindrical ducts of virtually any geometry where the radius of curvature and its first and second derivatives can be considered continuous around the duct perimeter. It is concluded that “mode-coupling” effects appear to offer a plausible explanation for the effect of wall distortion in lowering the duct wall transmission loss.