Arbitrary Wall Impedance Research Articles

Cutoff Frequencies of a Dielectric-Loaded Rectangular Waveguide With Arbitrary Anisotropic Surface Impedance

The coupled transcendental equations describing cutoff frequencies of TE and TM modes are deduced for a rectangular waveguide with arbitrary wall impedance. In the case of TE modes, their generalization is made to a rectangular guiding structure, which possesses both distributed wall impedance and inhomogeneous dielectric loading. Effective impedance is obtained for imperfectly conducting surface incorporating periodic rectangular corrugations along the direction of mode propagation. Circular waveguide bounded by such corrugated surface and rectangular impedance waveguide are considered as numerical examples. For these waveguides, the computations performed to determine the cutoff frequencies of TE guiding modes are validated against the results of the perturbation theory and the finite-element method.

Frequency response of bubble pulsations in tubes with arbitrary wall impedance

A model is presented for the linear pulsation of a small bubble in a tube with locally reactive walls but with otherwise arbitrary wall impedance. The model is based on the normal mode expansion of the Green's function presented by Morse and Ingard [Theoretical Acoustics (McGraw-Hill, 1968), Eq. (9.2.10)]. The specific case of a cylindrical tube is considered. For a bubble that is located in the center of the tube and that is small compared with both tube diameter and wavelength, the radiation impedance on the bubble is given by a summation of the normal modes evaluated in the center of the tube. From the radiation impedance, the frequency response of the bubble to an applied sound field is obtained. For tube walls that are either rigid of pressure release, the solution agrees with the frequency response calculated using the method of images for a square tube having the same cross-sectional area. In tubes with hard walls the resonance frequency decreases as tube radius decreases because of radiation damping. In tubes with very soft walls the radiation damping is negligible below the cutoff frequency of the lowest mode, and the resonance frequency increases slightly as tube radius is decreased.

On the acoustic modes in a cylindrical duct with an arbitrary wall impedance distribution

The present paper considers the propagation of sound in a cylindrical duct, with a wall section of finite length covered by an acoustic liner whose impedance is an arbitrary function of position. The cases of (i) uniform wall impedance, and wall impedance varying along the (ii) circumference or (iii) axis of the duct, or (iv) both simultaneously, are explicitly considered. It is shown that a nonuniform wall impedance couples modes with distinct azimuthal l or axial m wave numbers, so that their radial wave numbers k can no longer be calculated separately for each pair (m,l). The radial wave numbers are the roots of an infinite determinant, in the case when the wall impedance varies either (i) circumferentially or (ii) radially. If the wall impedance varies (iv) both radially and circumferentially, then the radial wave numbers are the roots of a doubly infinite determinant, i.e., an infinite determinant in which each term is an infinite determinant. The infinite determinants specifying the radial wave numbers are written explicitly for sound in a cylindrical nozzle with a uniform axial flow, in which case the radial eigenfunctions are Bessel functions; the method of calculation of the radial wave numbers applies equally well to a cylindrical nozzle with shear flow and/or swirling flows, with the Bessel functions replaced by other eigenfunctions. The radial wave numbers are calculated by truncation of the infinite determinants, for several values of the aspect ratio, defined as the ratio of length to diameter. It is shown that a nonuniform wall impedance will give rise to additional modes compared with a uniform wall impedance. The radial wave numbers specify the eigenfrequencies for the acoustic modes in the duct; the imaginary parts of the eigenfrequencies specify the decay of the sound field with time, and thus the effectiveness of the acoustic liner.

Complex resonance frequencies numerically obtained in the rectangular room with arbitrary wall impedances

Numerical methods to finding the complex resonance frequencies in the rectangular room with arbitrary wall impedances are presented. The eigenvalue equation is written in such a way that allows the unambiguous identification of each Riemann sheet. One numerical procedure applies the Newton method. For each wall-pair mode, the complex resonance frequencies are found, in each Riemann sheet, by small perturbations to the impedances of the wall pair. Another procedure transforms the eigenvalue equation into two differential equations, which are numerically integrated by the homotopic continuation procedure. The latter procedure is faster and finds all possible solutions. From the knowledge of sound decays experimentally obtained in a hard walled rectangular room, the impedances of the hard walls are obtained, which are then used to predict sound decays in the same room with one surface lined with sound absorbing material. It is shown that groups of modes with different reverberation times may collectively produce sound decays not always consistent with the Sabine prediction, and with some experimental results in a rectangular room with the floor covered with sound absorbing material of known acoustic impedance.

Effets d'un fluide en écoulement uniforme sur le comportement vibro-acoustique d'une plaque bafflée couplée à une cavité rectangulaire

The purpose of this work is to develop a general formulation to deal with the vibro-acoustic behavior of a baffled plate, immersed on one side in a mean flow and coupled on the other side to a rectangular cavity with arbitrary wall impedances. The plate is excited by a plane wave convected by the mean flow. The formulation is based on a finite element method for the calculation of the transverse vibrations of the plate and the acoustic field inside the cavity. The external fluid loading is accounted for through the extended Kirchoff-Helmoltz integral equation and the radiation impedance of the plate in the external fluid is computed with a boundary element method. The mean flow effects on the transmission loss of the plate are discussed

Mean flow effects on the vibroacoustic behavior of a plate backed by a cavity in light and heavy fluids

The purpose of this work is to present a general formulation dealing with the vibroacoustic behavior of a baffled plate, immersed on one side in a mean flow and coupled on the other side to a rectangular cavity with arbitrary wall impedances. The plate is excited by a point force, a plane wave convected by the mean flow, or a turbulent boundary layer. The formulation is based on a finite element method for the calculation of the transverse vibrations of the plate. Fluid loading on each side of the plate is taken into account through an impedance matrix approach. The plate–cavity impedance matrix is calculated using a boundary element method. The amount of computation is decreased by using a two indices Green’s function for the rigid cavity. The external impedance matrix accounting for mean flow, is calculated using the extended form of Kirchhoff’s integral equation and a boundary element method. This formulation is compared with a finite element approach for the calculation of the acoustic field inside the cavity. The mean flow effects are investigated through the calculation of different vibroacoustic indicators like the mean-square velocity of the plate, the internal and external acoustic radiated power, the radiation efficiency of the plate inside the cavity and the transmission loss of the plate. Coupling mechanisms are explained in terms of added mass, stiffness, and damping.

Soft and hard horn antennas

Horn antennas with soft and hard boundaries are analyzed. A soft boundary which exists in classical hybrid-mode horns gives zero field intensity at the wall. A hard boundary corresponds to a uniform field distribution over the horn aperture. Soft and hard horn antennas are compared with respect to directivity, sidelobes, and beamwidth. The dependency between the edge taper directivity, and sidelobes is also calculated based on the solution to the spherical hybrid modes in a conical horn with arbitrary wall impedances. This makes it possible to study how to compromise between directivity and sidelobes. Also discussed is how the different wall impedances may be realized, and some preliminary experimental work on hard horns is presented. >

On the fields in a conical horn having an arbitrary wall impedance

The electromagnetic fields propagating up a cone having an arbitrary wall impedance are found using an asymptotic solution. Three special cases are then considered: the smooth-metal wall, the corrugated wall, and the metal wall with a lossy-dielectric lining. The last case, in the form of an absorber-lining is then shown to behave like a corrugated horn since it too provides a highly tapered <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</tex> -plane and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</tex> -plane aperture distribution. Furthermore, it does this over a much larger bandwidth, over 3:1, with negligible gain drop.

Space charge waves in a cylindrical waveguide with arbitrary wall impedance

Properties of the space charge waves in a solid relativistic electron beam propagating in a cylindrical waveguide are investigated, including the important influence of arbitrary wall impedance. The stability analysis is carried out within the framework of the linearized Vlasov–Maxwell equations. In order to examine the influence of axial momentum spread on stability behavior, it is assumed that all electrons have a Lorentzian distribution in the axial canonical momentum. One of the most important features of the analysis is that, for short axial wavelength perturbations, the eigenfunction can be described by a Bessel function. Moreover, the condition for zero phase velocity of the space charge wave is also obtained, in connection with collective ion acceleration. Space charge wave properties for a dielectric loaded waveguide are also investigated. For the appropriate choice of the dielectric constant ε and thickness of the dielectric material, it is shown that strong mode-coupling occurs, exhibiting the growth rate of instability comparable to the beam plasma frequency. The physical mechanism of instability is Cerenkov radiation.

Influence of wall impedance on the electron cyclotron maser instability

The influence of finite-wall impedance on the cyclotron maser instability is investigated for a hollow electron beam. The stability analysis is carried out within the framework of the linearized Vlasov–Maxwell equations, assuming that the beam thickness is much less than the mean radius of the beam. The formal dispersion relation for azimuthally symmetric electromagnetic perturbations including the important influence of arbitrary wall impedance is obtained. One of the most important features of the analysis is that, for a purely resistive wall, the instability growth rate is substantially reduced by a very small wall resistivity. Moreover, the range of axial wavenumbers corresponding to instability increases rapidly as the wall resistivity is increased. Cyclotron maser stability properties for a dielectric loaded waveguide are also investigated. For an appropriate choice of the dielectric constant ε and the thickness of the dielectric material, it is shown that the instability bandwidth can be more than double that for a perfectly conducting waveguide.