Treatment of frequency-dependent admittance boundary conditions in transient acoustic finite/infinite-element models.

The paper addresses the handling of frequency-dependent, local admittance boundary conditions in acoustic transient finite/infinite-element models. The proposed approach avoids the evaluation of a convolution integral along the related boundary. Based on a similar technique developed in an aeroacoustic/finite difference context, the spatially local boundary condition is rewritten in a discrete form that involves normal accelerations and pressure time derivatives at the current time step and few steps before. The incorporation of such a discrete (in time) boundary condition in a finite/infinite-element context is addressed. The infinite-element scheme selected for that purpose relies on the conjugated Astley-Leis formulation. Implementation aspects cover the handling of frequency-dependent boundary conditions along both finite- and infinite-element edges. Numerical examples (waveguide, single source in a half-space bounded by an impedance plane, diffraction by an acoustically treated screen) are presented in order to demonstrate the efficiency of the proposed approach.     

Diffraction of a sound wave by the open end of a flanged waveguide with impedance walls

Diffraction of a plane sound wave by the open end of an impedance-wall waveguide connected to an opening in an impedance screen is considered. The plane wave is incident on the waveguide from a free half-space. Two versions of the problem are considered: for a semi-infinite waveguide and for a finite-length waveguide with a specified bottom impedance; the impedances of the walls, screen, and waveguide bottom can be different. The finite-length waveguide can be treated as an open cavity in the impedance screen. For the cavity of zero length, the problem is reduced to the diffraction by an impedance insert in the impedance screen. The solution in the external region determines the scattered field; the solution in the internal region allows one to determine the directional pattern of an array of receivers located in the cavity. The problem is solved using the integral Helmholtz equation with a specially selected Green’s function that provides the fulfillment of the boundary conditions. Formally, the problem is reduced to an infinite system of algebraic equations. The computational results obtained for bistatic and monostatic scattering patterns are presented.     

Diffraction of a plane electromagnetic wave by a slot in a conducting screen with a transverse dielectric layer

The problem of diffraction of a plane electromagnetic wave by a slot in a planar perfectly conducting arbitrary thick screen with an infinite planar dielectric layer passing through the slot transversely to the screen is solved rigorously. In each of the field existence domains (two domains on either side of the screen and the interior of the slot), the solution is represented as an expansion in piecewise harmonic or exponential modes that allow for reflection and refraction at the boundaries of the dielectric layer. It is found that a set of functions describing such modes is complete enough to construct a solution satisfying all boundary conditions of the diffraction problem. The procedures of solution construction for the case at hand and for the same diffraction structure without the dielectric layer are compared.     

The effect of impedance on interaural azimuth cues derived from a spherical head model

Recent implementations of binaural synthesis have combined high-frequency pinna diffraction data with low-frequency acoustic models of the head and torso. This combination ensures that the salient cues required for directional localization in the horizontal plane are consistent with psychophysical expectations, regardless of the accuracy or match of the high-frequency cues, or the fidelity of experimental low-frequency information. This paper investigates the effect of a nonrigid boundary condition on the surface pressure and the resulting interaural cues used for horizontal localization. These are derived from an analytical single sphere diffraction model assuming a locally reacting and uniformly distributed impedance boundary condition. Decreasing the magnitude of a purely resistive surface impedance results in an overall decrease in the sphere surface pressure level, particularly in the posterior region. This produces nontrivial increases in both the interaural level and time difference, especially for sound source directions near the interaural axis. When the surface impedance contains a reactive component the interaural cues exhibit further changes. The basic impedance characteristics of human hair and their incorporation into the sphere diffraction model are also discussed.     

Solution of wave diffraction problems by the method of continued boundary conditions

Numerical solution of three-dimensional diffraction problems by the method of continued boundary conditions, which is known to be effective in the case of two-dimensional problems, is discussed. The basic idea of the method is that the boundary condition is imposed at a certain sufficiently small distance from the impedance surface that produces the diffraction field. This procedure reduces the boundary-value problem to the Fredholm integral equation of the first or second kind with a smooth kernel. Results are reported that show how to apply the MCBC most efficiently, depending on particular requirements regarding the accuracy of the solution and number of calculations. Examples illustrating the high efficiency of the approach are presented.     

Piston-type radiator in a soft screen in the pekeris waveguide

A model problem is considered for a radiator in the form of a circular disk with a given pressure jump at its surface. The radiator is inserted in a soft screen coinciding with the upper boundary of the Pekeris waveguide. A series expansion of the sound field in normal modes is obtained. A numerical analysis of the radiation impedance and its components that are responsible for the radiation into the waveguide and into the halfspace is carried out.     

A study on the multi-freedom broadband impedance model for time-domain simulations

The purpose of this paper is to construct a general broadband impedance model, which is suited for predicting acoustic propagation problems in time domain.A multi-freedom broadband impedance model for sound propagation over impedance surfaces is proposed and the corresponding time domain impedance boundary condition is presented.Basing on the extended Helmholtz resonator,the multi-freedom impedance model is constructed through combing with a sum of rational functions in the form of general complex-conjugate pole-residue pairs and it is proved that the impedance model is well posed.The impedance boundary condition can be implemented into a computational aeroacoustics solver by a recursive convolution technique, which results in a fast and computationally efficient algorithm.The two dimensional and three dimensional benchmark problems are selected to validate the accuracy of the proposed impedance model and time domain simulations.The numerical results are in good agreement with the reference solutions.It is demonstrated that the proposed impedance model can be used to describe the broadband characteristics of acoustic liners,and the corresponding time domain impedance boundary condition is viable and accurate for the prediction of sound propagation over broadband impedance surfaces.     

Smooth plasma-sheath transition in a hydrodynamic model

In the hydrodynamic plasma and sheath models, when the two models are treated separately, the use of Bohm's (1949) criterion to obtain boundary conditions at the plasma-sheath interface leads to singularities and discontinuities in some physical quantities. This problem can be overcome by using an appropriate boundary condition; namely, by specifying a particular finite value of the electric field at the plasma-sheath interface. Using such a boundary condition and arbitrary collision parameters, sheath characteristics are then calculated continuously from the collisionless to the collisional sheath. When applied to the plasma model, this new boundary condition takes into account the space-charge effect on the behavior of the plasma at its boundary     

Diffraction of a plane electromagnetic wave by a slot in a conducting screen of arbitrary thickness

A 2D theoretical model of the diffraction of a plane electromagnetic wave by a slot in a perfectly conducting screen is constructed based on the partial domain method. The Tikhonov regularization is used to solve a system of algebraic equations for the slot-mode amplitudes. This makes it possible to extend the domain of applicability of the theory to conducting screens of arbitrary thickness and to significantly increase the accuracy of solution in the cases when the slot width and the screen thickness are comparable to the wavelength of the diffracted radiation. The absence of a continuous passage to the limit of an infinitesimal screen thickness from the case of an arbitrarily small finite thickness is demonstrated. The boundary conditions for the energy-flux vector are considered. A concept of the energy potential that is convenient for the computer calculations of the energy-flux lines of 2D diffraction fields is introduced.     

Scattering from loaded grooves

Electromagnetic scattering from a two-dimensional groove recessed in an arbitrarily thick conducting screen is studied. The groove may be empty or loaded with a lossy material which may or may not completely fill the cavity. For the partially loaded groove, the filling material is assumed electrically dense so that the standard impedance boundary condition is applicable at the top surface of the material. Employing a full-wave analysis, integral equations are derived for the tangential components of the electric field over the aperture. It is shown that the equations are identical for both partially loaded and completely loaded (or empty) cases provided that the aperture admittance of the groove is treated as the equivalent admittance of the internal medium looking into the aperture, thus simplifying the integral equations.When the groove is completely filled by a dense material, the formulation reduces to that corresponding to a direct application of the impedance boundary condition over the aperture.     

Failure of the Ingard-Myers boundary condition for a lined duct: an experimental investigation

This paper deals with experimental investigation of the lined wall boundary condition in flow duct applications such as aircraft engine systems or automobile mufflers. A first experiment, based on a microphone array located in the liner test section, is carried out in order to extract the axial wavenumbers with the help of an "high-accurate" singular value decomposition Prony-like algorithm. The experimental axial wavenumbers are then used to provide the lined wall impedance for both downstream and upstream acoustic propagation by means of a straightforward impedance education method involving the classical Ingard-Myers boundary condition. The results show that the Ingard-Myers boundary condition fails to predict with accuracy the acoustic behavior in a lined duct with flow. An effective lined wall impedance, valid whatever the direction of acoustic propagation, can be suitably found from experimental axial wavenumbers and a modified version of the Ingard-Myers condition with the form inspired from a previous theoretical study [Aure?gan et al., J. Acoust. Soc. Am. 109, 59-64 (2001)]. In a second experiment, the scattering matrix of the liner test section is measured and is then compared to the predicted scattering matrix using the multimodal approach and the lined wall impedances previously deduced. A large discrepancy is observed between the measured and the predicted scattering coefficients that confirms the poor accuracy provided from the Ingard-Myers boundary condition widely used in lined duct applications.     

Vibration of continuous systems with compliant boundaries

A theoretical study of two types of continuous systems with a general form of compliant boundary conditions is presented. The systems considered are elastic beams and circular plates with elastic damped edge constraints. Beam studies are restricted to those with identical boundary conditions at each end. The method of solution consists of formulating the edge condition of the system in terms of the impedance of the compliant boundary material and of using classical solution techniques to solve the equations of motion. The result of matching the boundary conditions of the system with constraining conditions is the system frequency equation in terms of the constraint impedances.A discussion is presented giving the influence of the compliant material on the vibration of the structure. The models give numerically the effect of elasticity and damping of the supports on the resonant frequencies of the systems. Parameters are obtained which indicate when one may assume simply supported or clamped boundaries for the actual case of elastic damped constraints without introducing large errors in the natural frequencies.     

Scattering of plane waves by a wedge with different face impedances

The scattering process of plane waves by a wedge with different face impedances is examined in terms of the closed form series solution. A new boundary condition is derived using the solution of the reflection problem of plane waves by an impedance plane. The series solution is obtained for the wedge problem. The results are investigated numerically.     

Boundary-contact problems of the electromagnetic theory of diffraction

A new class of problems of electromagnetic diffraction associated with the generalized impedance boundary condition (GIBC) is investigated. Methods for obtaining the GIBC and the conditions of its applicability for an arbitrary cylindrical surface are described. The simulation of defects in electromagnetic coatings is studied. A class of problems that can be solved exactly by factorization is isolated. Models of point defects in coatings are constructed and the limits of their applicability are established.St. Petersburg State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 6, pp. 520–542, June, 1993.     

Scattering of waves by an aperture in an impedance screen

The transmission and diffraction of waves by an aperture in an impedance screen is investigated. The Senior's solution of the scattering problem of waves by an impedance half-plane is transformed into a physical optics type integral. The obtained method is applied to the transmission problem of waves by a slit in an impedance screen. The results are compared with the aperture problem in black and conducting screens numerically.     

Cornu's spiral in the Fresnel regime studied using ultrasound: a phase study

A simple experimental technique for measuring the phase and amplitude of diffracting ultrasound wave [A. Hitachi and M. Takata, Am. J. Phys. 78, 678 (2010)] has been applied to diffracting objects with straight edges as a demonstration of the Cornu spiral. Babinet's principle is studied observing the ultrasound field behind a slit and a complementary strip obstacle and is verified directly by comparing vectors (phasors) in the complex plane. The phase of the diffracted wave observed in the geometrical shadow of the straight screen has the form of a cylindrical wave originating at the edge of the straight screen as the boundary diffraction wave proposed by Young. In addition, the incident wave has a phase delay of π/4 behind the wave passing through on the center line of the slit, the plane of symmetry, has been observed as predicted by Huygens-Fresnel diffraction theory.     

微小孔衍射——近场光学理论

推导了圆孔衍射公式，该公式不受孔径大小和到屏距离的限制，可以作为近场光学的理论。它满足麦克斯韦方程标量形式和基尔霍夫边界条件，包括传播波和衰减波。数值计算表明，此结果优于用Ｂｅｔｈｅ模型所得到的近场理论的结果     

阻抗劈绕射对破碎波后向散射特性的影响

海浪的破碎区会导致海面电磁散射特性发生很大改变,导致海尖峰现象的产生.本文结合阻抗劈结构模型分析了劈绕射对破碎波后向散射特性的影响.首先利用基尔霍夫近似求解破碎波的物理光学场;基于Maliuzhinets方法,从波动方程及精确阻抗边界条件出发,由谱函数的积分形式得到阻抗劈的一致性绕射系数,结合物理光学绕射系数导出阻抗劈等效边缘电磁流;利用边缘绕射场修正物理光学场,得到考虑劈绕射效应的破碎波散射总场.数值结果表明,阻抗劈的绕射场在Keller锥内出现HH极化大于VV极化的现象,因此计入绕射场的影响会使得破碎波生长到临近坍塌阶段时,小擦地角逆风观测出现总场的后向散射截面HH极化大于VV极化的现象,说明劈绕射是造成海尖峰现象产生的原因之一.     

Application of the Wiener–Hopf method for describing the propagation of sound in cylindrical and rectangular channels with an impedance jump in the presence of a flow

Exact solutions to problems of the propagation of acoustic modes in lined channels with an impedance jump in the presence of a uniform flow are constructed. Two problems that can be solved by the Wiener- Hopf method—the propagation of acoustic modes in an infinite cylindrical channel with a transverse impedance jump and the propagation of acoustic modes in a rectangular channel with an impedance jump on one of its walls—are considered. On the channel walls, the Ingard–Myers boundary conditions are imposed and, as an additional boundary condition in the vicinity of the junction of the linings, the condition expressing the finiteness of the acoustic energy. Analytical expressions for the amplitudes of the transmitted and reflected fields are obtained.