Equivalent Impedance Boundary Condition Research Articles

Optimal cavity shape design for acoustic liners using Helmholtz equation with visco-thermal losses

This paper presents a shape optimisation strategy to design a cavity for acoustic liners, that approaches at best a target impedance over a given frequency range, penalising too large shape displacements from an initial guess. A model based on the Helmholtz equation is used, where the visco-thermal losses are taken into account by an equivalent impedance boundary condition. Using an adjoint-based method, the gradient of the cost functional with respect to shape variations is calculated, and regularised by a Sobolev gradient. A finite element method is employed with XFEM cut elements, that allows to consider an immersed boundary which is localised by a level-set function. We show that with this method, we are able to obtain a cavity shape leading to an almost perfect absorption for a frequency in the prescribed optimisation range.

Generalized impedance boundary condition at high frequency for a domain with thin layer: the circular case

Consider a conducting disk surrounded by a thin dielectric layer submitted to an electric field at the pulsation ω. The conductivity of the layer grows like ω1−γ, γ∈[0,1], when the pulsation ω tends to infinity. Using a pseudodifferential approach on the torus, we build an equivalent boundary condition with the help of an appropriate factorization of Helmholtz operator in the layer. This generalized impedance condition approximates the thin membrane in the high frequency limit for small thickness of the layer. L 2-error estimates are given and we illustrate our results with numerical simulations. This work extends, in the circular geometry, previous works of Lafitte and Lebeau (Lafitte O. Lebeau G. 1993, Équations de Maxwell et opérateur d’impédance sur le bord d’un obstacle convexe absorbant. Comptes Rendus de l ' Académic dis Science, Paris, Série I, Mathématiques, 316(11), 1177–1182); (Lafitte O.D., 1999, Diffraction in the high frequency regime by a thin layer of dielectric material. I. The equivalent impedance boundary condition. SIAM Journal on Applied Mathematics, 59(3), 1028–1052 (electronic)) in which γ identically equals zero.

Improvement on the Forward-backward Iterative Physical Optics Algorithm Applied to Computing the RCS of Large Open-ended Cavities

The equivalent impedance boundary condition and the transmission line theory are used to analyze the surface impedance and reflective coefficient of the PEC surface coated with a thin absorber layer. Then, the IPO iterative equation is deduced by combining the surface impedance and reflective coefficient with the asymptotic principles of physical optics. The method of initial value succession is introduced to the forward-backward iterative physical optics (FBIPO) algorithm. The initial residual error is reduced by inheriting the current values. Combined with a relaxation parameter, the method improves the convergence of the FBIPO algorithm for cavity scattering problems. The accuracy of RCS calculation is also enhanced by using a more precise mixed-face model. The RCS of a jet inlet model is calculated, with its results in good agreement with the experimental ones. The method is also used to calculate the RCS reduction of a circular wave guide by coating the inner wall with absorber material.

Determining the equivalent impedance boundary condition for corrugated coatings based on the genetic algorithm

A methodology based on the genetic algorithm (GA) is proposed to determine the equivalent impedance boundary condition (IBC) for corrugated material coating structures. In this approach, rigorous solutions of the reflection coefficients at a number of incident angles are first calculated using a periodic method of moments (MoM) solver. The IBC model is used to predict the reflection coefficients at the same observation angles. The model coefficients are then optimized using the GA so that the difference between the approximated and the MoM predicted reflection coefficients is minimized. The GA proves efficient in obtaining an optimal IBC model. The resulting IBC model can be readily incorporated into an existing computational electromagnetics code to assess the performance of the corrugated coating when mounted on complex platforms.

Diffraction in the high frequency regime by a thin layer of dielectric material I: The equivalent impedance boundary condition

We discuss in this paper a generalized impedance boundary condition that can be used locally to replace a thin layer of material with dielectric absorbing constants. This condition takes into account the curvature of the body and the angle of incidence of the incident wave, which can be more general than a plane wave. We use this condition to obtain a system of equations outside the object equivalent to the system of Maxwell equations.

Theoretical Study of the Input Impedance of a Rectangular Microstrip Antenna

A theoretical study of the input impedance of a rectangular microstrip antenna is presented. The antenna is excited by a coaxial line. Green's function technique and the equivalent impedance boundary condition have been used. The feed pin size, the feed location and the boundary admittance are shown to be important. The expression for the input impedance includes the effect of feed pin size, the feed location, the radiated power and the fringe capacitance. A theoretical curve of the input impedance has been plotted for a specific microstrip antenna.