Incident Wave Number Research Articles

Uniqueness in inverse elastic scattering with finitely many incident waves

We consider the third and fourth exterior boundary value problems of linear isotropic elasticity and present uniqueness results for the corresponding inverse scattering problems with polyhedral-type obstacles and a finite number of incident plane elastic waves. Our approach is based on a reflection principle for the Navier equation.

Improved mutual coupling compensation in compact antenna arrays

A new method for the characterisation of receiving mutual impedances of compact arrays with omni-directional antenna elements is proposed. Based on a large number of incident waves coming from different directions, the new method is able to calculate the receiving mutual impedances of omni-directional antennas based on a system of equations that characterise the received terminal voltages at different incident wave directions. In the new method, the receiving mutual impedances of all the antenna elements are calculated together in a single equation with the scattering effect from all antenna elements in the array being taken into account. Compared to the previous methods for the characterisation of the receiving mutual impedances, the new method preserves the boundary conditions of the original electromagnetic problem and produces much more accurate results on receiving mutual impedances, especially for compact antenna arrays. Direction finding examples based on the new method demonstrate its superior performance over existing methods.

Dynamic stress from a subsurface cavity in a semi-infinite functionally graded piezoelectric/piezomagnetic material

In this paper, an analytical method is applied to investigate the multiple scattering of anti-plane shear waves and dynamic stress around a subsurface cavity in a semi-infinite functionally graded piezoelectric/piezomagnetic composite. The analytical solutions of wave field, electric field and magnetic field are expressed by employing wave function expansion method and the expanded mode coefficients are determined by satisfying the boundary conditions of the cavity. Image method is used to satisfy the free boundary conditions of the semi-infinite structure. According to the analytical expressions of this problem, the numerical solutions of the dynamic stress concentration factor around the cavity are presented. The effects of the piezoelectric and piezomagnetic properties, the buried depth of the cavity, the incident wave number and the nonhomogeneous parameter of materials on the dynamic stress around the cavity are graphically illustrated. Analyses show that the piezoelectric and piezomagnetic properties have great effect on the dynamic stress in the region of intermediate frequency and the effect increases with increasing nonhomogeneous parameter. The effects of the nonhomogeneous parameter of materials on the dynamic stress and electric field are examined. Comparisons with other existing models are also presented.

Scattering of flexural wave in a thin plate with multiple circular holes by using the multipole Trefftz method

The scattering of flexural wave by multiple circular holes in an infinite thin plate is analytically solved by using the multipole Trefftz method. The dynamic moment concentration factor (DMCF) along the edge of circular holes is determined. Based on the addition theorem, the solution of the field represented by multiple coordinate systems centered at each circle can be transformed into one coordinate system centered at one circle, where the boundary conditions are given. In this way, a coupled infinite system of simultaneous linear algebraic equations is derived as an analytical model for the scattering of flexural wave by multiple holes in an infinite plate subject to the incident flexural wave. The formulation is general and is easily applicable to dealing with the problem containing multiple circular holes. Although the number of hole is not limited in our proposed method, the numerical results of an infinite plate with three circular holes are presented in the truncated finite system. The effects of both incident wave number and the central distance among circular holes on the DMCF are investigated. Numerical results show that the DMCF of three holes is larger than that of one, when the space among holes is small and meanwhile the specified direction of incident wave is subjected to the plate.

Dynamic stress from a circular hole in a functionally graded piezoelectric/piezomagnetic material subjected to shear waves

An analytical method is applied to investigate the scattering of magneto-electro-elastic waves and dynamic stress around a circular hole in a functionally graded piezoelectric/piezomagnetic material layer. Analytical solutions of the wave, electric and magnetic fields are expressed by employing a wave function expansion method. Analyses show that the piezoelectric and piezomagnetic properties greatly affect the dynamic stress in the region of the intermediate frequency, and the effect increases with increasing non-homogeneous parameter. The effects of the incident wave number and non-homogeneous parameter of the materials on the dynamic stress and electric field are also examined.

Shadow Theory of Diffraction Grating: A Numerical Example for TE Wave

By use of the shadow theory developed recently, this paper deals with the transverse electric (TE) wave diffraction by a perfectly conductive periodic array of rectangular grooves. A set of equations for scattering factors and mode factors are derived and solved numerically. In terms of the scattering factors, diffraction amplitudes and diffraction efficiencies are calculated and shown in figures. It is demonstrated that diffraction efficiencies become discontinuous at an incident wave number where the incident wave is switched from a propagating wave to an evanescent one, whereas scattering factors and diffraction amplitudes are continuous even at such an incident wave number.

Dynamic anti-plane interaction between an impermeable crack and a circular cavity in an infinite piezoelectric medium

Wave propagation in an infinite elastic piezoelectric medium with a circular cavity and an impermeable crack subjected to steady-state anti-plane shearing was studied based on Green’s function and the crack-division technique. Theoretical solutions were derived for the whole elastic displacement and electric potential field in the interaction between the circular cavity and the impermeable crack. Expressions were obtained on the dynamic stress concentration factor (DSCF) at the cavity’s edge, the dynamic stress intensity factor (DSIF) and the dynamic electric displacement intensity factor (DEDIF) at the crack tip. Numerical solutions were performed and plotted with different incident wave numbers, parameters of piezoelectric materials and geometries of the structure. Finally, some of the calculation results were compared with the case of dynamic anti-plane interaction of a permeable crack and a circular cavity in an infinite piezoelectric medium. This paper can provide a valuable reference for the design of piezoelectric actuators and sensors widely used in marine structures.

Multiple scattering of elastic waves in metal-matrix composite materials with high volume concentration of particles

Abstract A new approach is proposed to investigate the propagation of compressional (P) and shear (SV) waves in metal-matrix composite materials with high volume concentration of particles. The theory of quasicrystalline approximation and Waterman's T matrix formalism are employed to treat the multiple scattering resulting from the particles in composites. The addition theorem for spherical Bessel functions is used to accomplish the translation between different coordinate systems. The analytical expression of the Percus–Yevick correlation function is also given. Closed form solutions for the effective propagation constants and the dynamic effective elastic modulus of materials are obtained in the low frequency limit. At higher frequencies, only numerical results of them are presented. Numerical examples show that the phase velocities of P and SV waves in the composite materials with low volume concentration in the low frequency are in good agreement with the results in previous literatures. The effects of the incident wave number, the volume fraction of particles and the material properties of the particles and matrix on the dynamic effective elastic modulus are also examined.

Sound scattering by a compact circular pore

The aim of this paper is to study the three-dimensional scattering of an oblique wave incident on a flanged circular compact pore of finite depth. The multipole structure with the scattering is resolved by the method of matched asymptotic expansion, where we assume smallness of ε = k * a * , the product of the incident wavenumber k * and the pore radius a * . Two distinguished cases are solved: the rigid boundary condition and the pressure-release boundary condition. The study presents by far the most complete solutions to these problems, with the outer solution up to O ( ε 5 ) and the inner solution up to O ( ε 2 ) . In particular, the sophisticated interplay between the pore depth and the incident angle is revealed in the different orders of solution. It is shown that the leading order of the outer wave field for both cases is O ( ε 3 ) . For the rigid boundaries, there is one dipole dependent on the incident angle and one monopole. Interestingly, the monopole arises from the second-order interaction of the pore volume and the small but non-negligible compressibility in the inner field. This is one of the few examples analytically solvable to demonstrate this property. On the other hand, only one dipole is found for the pressure-release boundary. The next order in the outer solutions for both types of the boundary conditions is of O ( ε 5 ) and is shown to contain quadrupoles and octupoles. The multipole structures for both types of boundaries are tabulated, explicitly with the effects of the incident angle and the pore depth.

Multiple scattering of electro-elastic waves from a buried cavity in a functionally graded piezoelectric material layer

This paper presents a theoretical method to investigate the multiple scattering of electro-elastic waves and the dynamic stress around a buried cavity in a functionally graded piezoelectric material layer bonded to a homogeneous piezoelectric material. The analytical solutions of wave fields are expressed by employing wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary conditions around the cavity. The image method is used to satisfy the mechanical and electrically short conditions at the free surface of the structure. According to the analytical expression of this problem, the numerical solutions of the dynamic stress concentration factor around the cavity are presented. The effects of the piezoelectric property, the position of the cavity in the layer, the incident wave number and the material properties on the dynamic stress around the cavity are analyzed. Analyses show that the piezoelectric property has great effect on the dynamic stress in the region of higher frequencies, and the effect increases with the decrease of the thickness of FGPM layer. If the material properties of the homogeneous piezoelectric material are greater than those at the surface of the structure, the dynamic stress resulting from the piezoelectric property is greater. The effect material properties at the two boundaries of FGPM layer on the distribution of dynamic stress around the cavity is also examined.

Elastic wave scattering from a penny-shaped interface crack in coated materials

This paper is concerned with the elastic wave scattering induced by a penny-shaped interface crack in coated materials. Using the integral transform, the problem of wave scattering is reduced to a set of singular integral equations in matrix form. The singular integral equations are solved by the asymptotic analysis and contour integral technique, and the expressions for the stress and displacement as well as the dynamic stress intensity factors (SIFs) are obtained. Using numerical analysis, this approach is verified by the finite element method (FEM), and the numerical results agree well with the theoretical results. For various crack sizes and material combinations, the relations between the SIFs and the incident frequency are analyzed, and the amplitudes of the crack opening displacements (CODs) are plotted versus incident wavenumber. The investigation provides a theoretical basis for the dynamic failure analysis and nondestructive evaluation of coated materials.

Linear Sampling Method: Physical Interpretation and Guidelines for a Successful Application

The Linear Sampling Method (LSM) is an efiective method to tackle the prob- lem of reconstructing the shape of unknown metallic or dielectric scatterers from the knowledge of single frequency multi-view/multi-static data. Notably, as it just requires to solve a linear problem, its implementation is straightforward and its computational burden almost negligible. However, no results are available in the literature to explain under which operating conditions (e.g., the number of incident waves and receivers which has to be considered) LSM properly works. With respect to the case of dielectric scatterers, in this communication, starting from the physical interpretation of LSM, we provide some guidelines for its successful application. These results are then conflrmed processing experimental data from the \Marseille data-set.

Dynamic effective properties of matrix composite materials with high volume concentrations of particles

A new approach is proposed to investigate the propagation of a plane compressional wave in matrix composite materials with high volume concentrations of particles. The theory of quasicrystalline approximation and Waterman’s T matrix formalism are employed to treat the multiple scattering resulting from the particles in composites. The addition theorem for spherical Bessel functions is used to accomplish the translation between different coordinate systems. The Percus–Yevick correlation function widely applied in the molecular theory of liquids is employed to analyze the interaction of the densely distributed particles. The analytical expression for the Percus–Yevick correlation function is also given. The closed form solution for the effective propagation constant is obtained in the low frequency limit. Only numerical solutions are obtained at higher frequencies. Numerical examples show that the phase velocities in the composite materials with low volume concentration are in good agreement with those in previous literatures. The effects of the incident wave number, the volume fraction and the material properties of the particles and matrix on the phase velocity are also examined.

Dynamic stress of a circular cavity buried in a semi-infinite functionally graded piezoelectric material subjected to shear waves

The paper presents a theoretical method to investigate the multiple scattering of shear waves and dynamic stress around a circular cavity in a semi-infinite functionally graded piezoelectric material. The analytical solutions of wave fields are expressed by employing wave function expansion method and the expanded mode coefficients are determined by satisfying the boundary conditions of the cavity. Image method is used to satisfy the free boundary condition of the semi-infinite structure. According to the analytical expression of this problem, the numerical solutions of the dynamic stress concentration factor around the cavity are presented. The effects of the piezoelectric property, the buried depth of the cavity, the incident wave number and the nonhomogeneous parameter of materials on the dynamic stress around the cavity are analyzed. Analyses show that the piezoelectric property has great effect on the dynamic stress in the region of intermediate frequency and the effect increases with increasing wave number. When the nonhomogeneous parameter of materials is less than zero, it has less influence on the maximum dynamic stress around the cavity; however, it has greater influence on the distribution of the dynamic stress around the cavity. When the nonhomogeneous parameter of materials is greater than zero, it has greater influence on both the maximum dynamic stress and the distribution of dynamic stress around the cavity, especially in the case that the buried depth is comparatively small.

Multiple scattering of shear waves and dynamic stress from a circular cavity buried in a semi-infinite slab of functionally graded materials

Based on the theory of elastodynamics and employing image method, the multiple scattering and dynamic stress in a semi-infinite slab of functionally graded materials with a circular cavity are investigated. The analytical solution of this problem is derived, and the numerical solutions of the dynamic stress concentration factor around the cavity are also presented. The effects of the distance between the cavity and the boundaries of the semi-infinite slab, the incident wave number and the non-homogeneity parameter of materials on the dynamic stress concentration factors are analyzed. Analyses show that the dynamic stress around the cavity increases with increasing non-homogeneity parameter of materials and incident wave number. The boundaries of the semi-infinite slab have great effect on both the maximum dynamic stress and the distribution of dynamic stress around the circular cavity, and the effect increases with increasing incident wave number.

Dynamic effective properties of semi-infinite random unidirectional fiber-reinforced composites subjected to anti-plane shear waves

Based on the theory of elastodynamics, and employing the effective medium method and the image method, the propagation of shear waves in semi-infinite random unidirectional fiber-reinforced composites is investigated. The dispersion relation for the effective wave number in the random composites is derived. The numerical solutions of the dynamic effective properties are obtained by using an iterative scheme. The image method is applied to satisfy the traction free boundary condition of the semi-infinite composite. The effective wave fields are expressed by using the wave function expansion method, and the expanded modal coefficients are determined by satisfying the continuous boundary conditions around the fibers. Analyses show that the variation of the dynamic effective properties in the semi-infinite composite is significantly different from that in the infinite composite. The maximum dynamic effective properties near the surface increase with the increase of the incident wave number, the volume fraction of fibers, and the properties ratio of the two phases.

Strain energy density of a circular cavity buried in a semi-infinite slab of functionally graded materials subjected to anti-plane shear waves

The paper presents a theoretical method to investigate the multiple scattering of shear waves and strain energy density in a semi-infinite slab of functionally graded materials with a circular cavity. The analytical solutions of wave fields are expressed by employing wave function expansion method and the expanded mode coefficients are determined by satisfying the boundary conditions of the cavity. Image method is used to satisfy the free boundary condition of the semi-infinite structure. The analytical solution of the problem is derived, and the numerical solutions of the strain energy density factors around the cavity are also graphically presented. The effects of the distances between the cavity and the boundaries of the semi-infinite slab, the wave number and the non-homogeneous parameter of materials on strain energy density factors are analyzed. Analyses show that the strain energy density around the cavity increases with increasing non-homogeneous parameter of materials and incident wave number. The boundaries of the semi-infinite slab have great effect on both the maximum strain energy density and the distribution around the circular cavity, and the effect increases with increasing incident wave number. When the distance between the semi-infinite boundary and the cavity varies, the effect of the upper and lower boundaries on the distribution of the strain energy density factors around the cavity is also examined.

Internal wave tunnelling through non‐uniformly stratified shear flow

We examine the transmission of internal gravity waves through a non‐uniformly stratified fluid with vertically varying background shear. To quantify wave transmission we show that the appropriate measure is the ratio of the flux of transmitted to incident pseudoenergy, T. We derive an analytic prediction of T for the transmission of waves through a piecewise‐linear shear flow in two cases. In both, the fluid is unstratified over the depth of the shear and uniformly stratified elsewhere. In one study, the density profile is continuous. Such a basic state is unstable but with vanishingly small growth rate as the bulk Richardson number, Ri, becomes large. In the limit of an infinitely large Richardson number (no shear), we recover the tunnelling prediction of Sutherland and Yewchuk (2004). In weak shear, incident waves can transmit weakly, even if the phase speed matches the flow speed within the shear layer (a critical level). However, no transmission occurs when the phase speed of incident waves exactly matches the flow speed on the opposite flank of the shear. In strong shear, with Ri ⋍ 1, a transmission peak occurs where the incident wavenumber and frequency are close to, but different from, those associated with unstable modes. In a second study, the background density profile is discontinuous and representative of a well‐mixed patch within a once uniformly stratified fluid. In this case, no transmission occurs for incident waves with phase speed matching the speed of the flow within the shear layer. However, a transmission spike occurs if the incident waves are resonant with interfacial waves that flank the shear.

Internal Wave Tunnelling Through Non-uniformly Stratified Shear Flow

Abstract We examine the transmission of internal gravity waves through a non‐uniformly stratified fluid with vertically varying background shear. To quantify wave transmission we show that the appropriate measure is the ratio of the flux of transmitted to incident pseudoenergy, T. We derive an analytic prediction of T for the transmission of waves through a piecewise‐linear shear flow in two cases. In both, the fluid is unstratified over the depth of the shear and uniformly stratified elsewhere. In one study, the density profile is continuous. Such a basic state is unstable but with vanishingly small growth rate as the bulk Richardson number, Ri, becomes large. In the limit of an infinitely large Richardson number (no shear), we recover the tunnelling prediction of Sutherland and Yewchuk (2004). In weak shear, incident waves can transmit weakly, even if the phase speed matches the flow speed within the shear layer (a critical level). However, no transmission occurs when the phase speed of incident waves exactly matches the flow speed on the opposite flank of the shear. In strong shear, with Ri ⋍ 1, a transmission peak occurs where the incident wavenumber and frequency are close to, but different from, those associated with unstable modes. In a second study, the background density profile is discontinuous and representative of a well‐mixed patch within a once uniformly stratified fluid. In this case, no transmission occurs for incident waves with phase speed matching the speed of the flow within the shear layer. However, a transmission spike occurs if the incident waves are resonant with interfacial waves that flank the shear.

Accurate Source Number Detection Using Pre-Estimated Signal Subspace

This paper presents a scheme for accurately detecting the number of incident waves arriving at array antennas. The array antenna and MIMO techniques are developing as 4th generation mobile communication systems and wireless LAN technologies, and the accurate estimation of the propagation environment is becoming more important. This paper emphasizes the accurate detection of the number of incident waves; one of the important characteristics in multidirectional communication. There are some recent papers on accurate detection but they have problems of estimation accuracy or computational cost in severe environment like low SNR, small number of snapshots or waves with close angles. Hence, AIC and MDL methods based on statistics and information theory are still often used. In this paper, we propose an accurate estimation method of the number of arrival signals using the orthogonality of subspaces derived from preliminary estimation of signal subspace. The proposed method accurately estimates the number of signals also in severe environments where AIC and MDL methods can hardly estimate. We evaluate the performance of these methods through some computer simulation and experiments in anechoic chamber.