Scattering of elastic waves by multiple elastic circular cylinders with imperfect interface

In the current paper a general method is presented for the rigorous solution for the scattering of elastic waves by a cluster of elastic circular cylinders of infinite length. The interface separating the cylinder from the surrounding media is considered to be homogeneous imperfect. Specifically, the tractions are continuous but the displacements are discontinuous and proportional in terms of interface stiffness parameters to their respective traction components. Using the exact theory of multipole expansion, analytic solutions for the scattered and internal fields excited by an incident plane P-wave, an incident cylindrical P-wave and an incident plane SV-wave are derived.

Numerical results for directivity patterns and scattering cross-sections are presented for a finite hexagonal array of elastic circular inclusions with imperfect interface. The results show that the sequence of maxima and minima in the curves of scattered cross-sections becomes more undistinguishable as the interface becomes more imperfect. Also, the results reveal that large low-frequency peaks of the scattered cross-sections, which correspond to resonance scattering, can be observed for both the low-velocity and high-velocity elastic cylinders with extremely imperfect interface while the small high-frequency peaks of the scattered cross-sections can appear for low-velocity elastic cylinders with relatively perfect interface. Furthermore, the results clearly show that the interaction effects between cylinders cannot be ignored for an incident plane SV-wave as compared to an incident plane P-wave. More importantly is the fact that the reciprocity relations, which hold for elastic wave scattering by a single cylinder, no longer apply for elastic wave scattering by multiple cylinders.     

横向各向同性固体中圆柱状散射体对水平偏振剪切波的散射

给出横向各向同性介质中SH波的标量波动方程,并通过简单的坐标变换,将其化为标准的Helmholtz方程.建立了求解散射问题的积分方程,利用边界单元方法数值计算了横向各向同性固体中圆柱状空洞及刚性散射体对SH波的散射场分布。重点分析了各向异性对空洞散射体散射场指向性的影响.     

Scattering of sound from axisymetric sources by multiple circular cylinders

A general analytic method for calculating the scattering of sound by multiple rigid circular cylinders arranged in an arbitrary parallel configuration is presented. The sound scattered by this collection of cylinders is generated by a time-periodic, spatially distributed, axisymmetric source located within the domain of interest. A Hankel transform method is used to calculate the incident field, while separation of variables is used to obtain the scattered fields from each cylinder in the collection. The unknown scattering coefficients are determined through the use of general addition theorems that allows the various fields to be readily transformed between coordinate systems. The method is validated using various two-, three-, and four-cylinder configurations, and the number of coefficients that must be retained in the truncated series is examined. Benchmark configurations consisting of two- and three-cylinder systems with cylinders of varying radii are also presented. These solutions have been used to validate computational aeroacoustic solvers developed for complex geometries.     

Scattering of antiplane shear waves by layered circular elastic cylinder

An exact analytical solution for the scattering of antiplane elastic waves by a layered elastic circular cylinder is obtained. The solution and its degenerate cases are compared with other simpler models of circular cylindrical scatterers. The effects of the geometrical and physical properties of the interphase are studied. Numerical results confirm the existence of a resonance mode in which the scatterer's core undergoes a rigid-body motion when the outer layer of the scatterer is very compliant. This resonance mode has been attributed [Liu et al., Science 289, 1734 (2000)] to a new mechanism for the band gap formed in the extremely low frequency range for phononic crystals made of layered spherical scatterers. Numerical results also show the existence of a similar resonance mode when the outer layer of the scatterer has very high mass density.     

Scattering of time-harmonic elastic waves by an elastic inclusion with quadratic nonlinearity

This paper considers the scattering of a plane, time-harmonic wave by an inclusion with heterogeneous nonlinear elastic properties embedded in an otherwise homogeneous linear elastic solid. When the inclusion and the surrounding matrix are both isotropic, the scattered second harmonic fields are obtained in terms of the Green's function of the surrounding medium. It is found that the second harmonic fields depend on two independent acoustic nonlinearity parameters related to the third order elastic constants. Solutions are also obtained when these two acoustic nonlinearity parameters are given as spatially random functions. An inverse procedure is developed to obtain the statistics of these two random functions from the measured forward and backscattered second harmonic fields.     

Scattering of Lamb waves by a circular cylinder.

Following our previous attempt at the scattering from a cylinder in a slab to the incidence of a guided shear wave, we hereby discuss the scattering by an elastic cylinder embedded in an isotropic plate for a variety of bonding states to incidence of the fundamental Lamb wave modes S0 and A0 at the low-frequency regime. The plate is divided up into three regions by introducing two imaginary planes located symmetrically some distance from the cylinder and perpendicular to surfaces of the plate. The wave fields in various regions are expanded either into cylinder wave modes or into Lamb wave modes. A system of equations determining the coefficients of expansion is obtained according to the traction-free boundary conditions on the plate walls and the displacement and stress continuity conditions across the virtual planes. By taking an appropriate finite number of terms of the infinite expansion series and some selected points on the two properly chosen imaginary planes and the surfaces of the plate through convergence and precision tests, a matrix equation to numerically evaluate the expansion coefficients is found. Coefficients of the reflection and transmission versus the normalized radius of the cylinder in welded, slip, and cracked interfacial conditions are numerically computed. In the low-frequency range, the relative errors are found to be less than 1%. Contrast curves of the reflection coefficient for the cylinder of nearly all permissible size in perfect and imperfect interfacial bonding are shown and prominent differences are noted.     

Shear waves guided by the imperfect interface of two magnetoelectric materials

In this paper, propagation of shear waves along a weak interface of two dissimilar magnetoelectric or magnetoelectroelastic materials is considered. Two exact dispersion relations are obtained for an imperfect electrode interface and an unelectroded interface, respectively. The existence condition of the interfacial waves is studied. Our results show that the interfacial imperfection strongly affects the velocity of the interfacial shear waves. In particular, for certain bi-magnetoelectric material, the interfacial shear waves may do not exist for a perfect interface and exist only for an imperfect interface. These findings are useful for the design of high-frequency wave devices.     

Scattering of elastic waves in damaged media

The scattering of elastic waves in a medium with damage from microcracking is discussed. The influence of damage from penny-shaped microcracks within a homogeneous medium is considered. The microcracks are assumed to be randomly oriented and uniformly distributed. Explicit expressions are derived for the attenuation of longitudinal and shear elastic waves in terms of the damage parameter and the effective elastic moduli of the medium. A generalized tensor-based approach is used such that the results are coordinate free. The derivation is based upon diagrammatic methods. The problem is formulated in terms of the Dyson equation, which is solved for the mean field response within the limits of the first-order smoothing approximation. The longitudinal and shear attenuations are discussed in terms of their frequency dependence and damage dependence. In particular, the attenuations are shown to scale linearly with the damage parameter.     

Guided waves in a circular duct containing an assembly of circular cylinders

This paper provides an analytical scheme to calculate the admissible acoustic propagation modes of fluid in a circular duct containing an assembly of circular cylinders, as might occur in gas-cooled fast breeder reactors and advanced gas-cooled reactors. The duct wall and cylinders are assumed to be stationary, and their axes are assumed to be parallel to each other. The solution to the acoustic wave equation is expressed in a sum of the partial fluid velocity potentials associated with each rod co-ordinate and duct co-ordinate. The technique of transformation of cylindrical wave functions is then used to solve the boundary value problem. Two kinds of acoustic boundary conditions are considered, acoustically hard and acoustically soft, respectively.     

Time-harmonic torsional waves in a composite cylinder with an imperfect interface

In this paper, the propagation of time-harmonic torsional waves in composite elastic cylinders is investigated. An imperfect interface is considered where tractions are continuous across the interface and the displacement jump is proportional to the stress acting on the interface. A frequency equation is derived for the rod and dispersion curves of normalized frequency as a function of normalized wave number for elastic bimaterials with varying values for the interface constant F are presented. The analysis is shown to recover the dispersion curves for a bimaterial rod with a perfect (welded) interface (F = 0), and has the correct limiting behavior for large F. It is shown that the modes, at any given frequency, are orthogonal, and it is outlined how the problem of reflection of a torsional mode by a planar defect (such as a circumferential crack) can be treated.     

Influence of imperfect bonding on interface waves guided by piezoelectric/piezomagnetic composites

Interface waves, which can be guided by imperfectly bonded piezoelectric and piezomagnetic half-spaces, are studied. The cases of absorbent and permeable interfaces are discussed in detail. It is shown that imperfection of the interface bonding has significant impact on the existence of interface waves and on their velocities of propagation. Some interface waves present in the case of imperfect bonding vanish when the bonding becomes perfect. The waves that are guided by an imperfect interface are shown to be dispersive, although there is no explicit characteristic length in the structure model. The results obtained show that possible imperfections of interface bonding must be considered in the design and fabrication of piezoelectric/piezomagnetic composites.     

Investigation of scattering of elastic waves by cylinders in 1-3 piezocomposites

The scattering behavior of P-waves in piezoelectric composites with 1–3 connectivity is studied. The method of wave function expansion is adopted for the theoretical derivations. Analytical expressions are obtained for the distributions of mechanical displacement in z-direction along the circumferences of piezoelectric cylinders. These solutions are used to study the influence of each element of the stiffness matrix and the piezoelectric matrix on the various resonant modes of vibration. Numerical results obtained indicate that perturbations of the elements c₄₄ and e₁₅ significantly affect resonant frequencies and amplitudes, perturbations of c₁₁ and c₁₂ have pronounced effects on resonant modes of high frequencies also. However, the resonant modes are not so sensitive to the perturbations of c₁₃, e₃₁ and e₃₃. The dynamic characteristics of 1–3 connectivity piezoelectric composites exposed here are meaningful for the design and manufacture of sensor/actuator elements by this kind of composites as well as the on-line health monitoring of the mechanical properties variations of the composites itself.     

Circumferential resonance modes of solid elastic cylinders excited by obliquely incident acoustic waves

When an immersed solid elastic cylinder is insonified by an obliquely incident plane acoustic wave, some of the resonance modes of the cylinder are excited. These modes are directly related to the incidence angle of the insonifying wave. In this paper, the circumferential resonance modes of such immersed elastic cylinders are studied over a large range of incidence angles and frequencies and physical explanations are presented for singular features of the frequency-incidence angle plots. These features include the pairing of one axially guided mode with each transverse whispering gallery mode, the appearance of an anomalous pseudo-Rayleigh in the cylinder at incidence angles greater than the Rayleigh angle, and distortional effects of the longitudinal whispering gallery modes on the entire resonance spectrum of the cylinder. The physical explanations are derived from Resonance Scattering Theory (RST), which is employed to determine the interior displacement field of the cylinder and its dependence on insonification angle.     

On the numerical approximation of high-frequency acoustic multiple scattering problems by circular cylinders

The aim of this paper is to propose a numerical strategy for computing the solution of two-dimensional time-harmonic acoustic multiple scattering problems at high-frequency. The scatterers are assumed to be circular, leading therefore to semi-analytical representation formulae of the scattered field through the solution of a large linear system of equations. Taking advantage of the special block Toeplitz structure of the matrix of the linear system, a fast iterative and preconditioned numerical method yielding large memory savings is proposed. Several numerical experiments for general configurations are presented to show the efficiency of the numerical method.     

Transition radiation of elastic waves at the interface of two elastic half-planes

Radiation of elastic waves is studied that is emitted by a point load that crosses the interface of two elastic half-planes. It is assumed that the load has a constant magnitude, moves along a straight line normal to the interface, and has a constant speed that is smaller than the minimum shear wave speed in the half-planes. In this case the mechanism of excitation of elastic waves is conventionally referred to as transition radiation. The adopted model allows to obtain an analytical expression for the elastic field excited by the load in the frequency-wavenumber domain. Using this expression, the energy of transition radiation is derived in a closed form. It is shown that transition radiation of the body waves occurs at any non-zero velocity of the load. Additionally, transition radiation of interface waves may occur provided that parameters of the half-planes allow existence of Stoneley waves. A parametric analysis of the directivity diagram of radiated body waves is accomplished focusing on dependence of the diagram on the load speed, load direction, and parameters of the half-planes. Using parameters that allow radiation of interface waves, the energy of this radiation is compared to that of the body waves. It is shown that the energy of the interface waves is greater unless the load velocity is close to the lowest body wave velocity.     

Scattering of Rayleigh-Lamb waves by a surface breaking crack in an elastic plate

This work studies the problem of scattering of Rayleigh-Lamb waves by a thin surface-breaking crack. The problem is solved by the projection method, which exploits some orthogonality relations deduced from the reciprocal theorem. Numerical results obtained by the projection method are compared with the results obtained using a finite element method reported by other authors for the case of a flat crack, finding good agreement. From the numerical results it is observed that, as the wave number of the incident wave, so for instance, is smaller, the reflected and transmitted energy corresponding to the converted mode, A0 in this case, are almost equal to each other. An explanation for this result is given, based on the asymptotic nature of the modes S0 and A0 for small wave numbers.