Guided ultrasonic waves in composite cylinders

The ultrasonic nondestructive evaluation of composite cylinders requires a thorough understanding of the propagation of waves in these materials. In this paper, the propagation of flexural and longitudinal guided waves in fiber-reinforced composite (FRC) rods with transversely isotropic symmetry properties is studied. The frequency equations obtained for free cylinders and the effect of increased fiber volume fraction (increased anisotropy) on the dispersion characteristics of the rod are explored. The numerical results reveal a number of previously unnoticed characteristics of dispersion curves for composite cylinders. The mode shapes of longitudinal waves propagating in glass/epoxy cylinders are also plotted. These plots can be used to choose an appropriate strategy for inspecting composite cylinders by ultrasonic nondestructive evaluation techniques. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 3, pp. 411–426, May–June, 2007.     

Effects of functionally graded interlayers on dispersion relations of shear horizontal waves in layered piezoelectric/piezomagnetic cylinders

The effects of functionally graded interlayers on dispersion relations of shear horizontal waves in layered piezoelectric/piezomagnetic cylinders are studied. First, the basic physical quantities of elastic waves in piezoelectric cylinder are derived by assuming that the SH waves propagate along the circumferential direction steadily. Then the transfer matrices of the functional graded interlayer and outer piezomagnetic cylinder are obtained by solving the state transfer equations with spatial-varying coefficients. Furthermore, making use of the electro-magnetic surface conditions of the outer cylinder, the dispersion relations for the shear horizontal waves in layered piezoelectric/piezomagnetic cylinders are obtained and the numerical results are shown graphically. Seven kinds of functionally graded interlayers and four kinds of electro-magnetic surface conditions are considered. It is found that the functionally graded interlayers have evident influences on the dispersion relations of shear horizontal waves in layered piezoelectric/piezomagnetic cylinders. The high order modes are more sensitive to the gradient interlayers while the low order modes are more sensitive to the electro-magnetic surface conditions.     

On the excitation of a closely spaced array by a line source

An infinite row of periodically spaced, identical rigid circularcylinders is excited by an acoustic line source which is parallelto the generators of the cylinders. A method for calculatingthe scattered field accurately and efficiently is presented.When the cylinders are sufficiently close together, Rayleigh–Blochsurface waves that propagate energy to infinity along the arrayare excited. An expression is derived which enables the amplitudesof these surface waves to be computed without requiring thesolution to the full scattering problem.     

Long nonlinear waves in anisotropic cylinders

Small-amplitude plane nonlinear waves in anisotropic cylinders are considered in the case of longitudinal and torsional waves having close velocities. Anisotropy corresponding to this condition can take place in specifically plaited ropes and in the case of anisotropy of other nature. The characteristic velocities are found, and simple waves are studied.     

Second order wave loads on large monolithic offshore structures

This paper considers the wave loads on large monolithic offshore structures. The second order wave force formulae developed by Rahman and Heaps, applicable to large circular cylinders in waves, are extended to evaluate the overturning moments on large circular cylinders. The theory is then applied to square section caissons in waves, to predict the wave loads on these structures. These calculations are performed using the exact form of the second order velocity potential, φ₂, with arbitrary wave number, k₂, and the approximate form of φ₂, with twice the value of the wave number of the first order velocity potential. The second order analytical predictions are compared with available experimental data for various ranges of wave parameters for both circular and square caissons in large amplitude waves.     

Shock Waves in Anisotropic Cylinders

We study small-amplitude longitudinal and torsional shock waves in circular cylinders consisting of an anisotropic medium such that the velocities of the longitudinal and torsional waves are close to each other. Previously, simple waves were considered in the same situation and conditions were found for these waves to overturn and for the corresponding shock waves to form. Here we present the study of shock waves: the shock adiabat and the evolutionary conditions. The results obtained can also be related to shock waves in unbounded media with quadratic nonlinearity.     

Anomalies of Acoustic Wave Propagation in Two Semi-Infinite Cylinders Connected by a Flattened Ligament

Computational Mathematics and Mathematical Physics - We study the propagation of waves in a waveguide which is the union of two semi-infinite cylinders connected by a thin rectangular ligament. It...     

两个垂直圆柱在水波中的水动力相互作用

基于线性势流理论研究了两个垂直圆柱在水波中的水动力相互作用．两个圆柱中的一个固定在底部，另一个铰接在底部且可以在入射波方向以小振幅振动．本文研究了绕射波和辐射波，运用加法定理得到了每个圆柱表面速度势的简单的解析表达式，用级数形式显式表示了圆柱上的波浪激励力和力矩及振动圆柱的附加质量和辐射阻尼系数．级数的系数由代数方程组的解决定．给出了一些数值例子以说明诸如间距、圆柱的相对大小、入射角等各种参数对一阶力、定常二阶力、附加质量和辐射阻尼系数以及振动圆柱的响应等的影响．     

Nonlinear free surface condition due to second order diffraction by a pair of cylinders

An analysis of the non-homogeneous term involved in the free surface condition for second order wave diffraction on a pair of cylinders is presented. In the computations of the nonlinear loads on offshore structures the most challenging task is the computation of the free surface integral. The main contribution to this integrand is due to the nonhomogeneous term present in the free surface condition for second order scattered potential. In this paper, the free surface condition for the second order scattered potential is derived. Under the assumption of large spacing between the two cylinders, waves scattered by one cylinder may be replaced in the vicinity of the other cylinder by equivalent plane waves together with non-planner correction terms. Then solving a complex matrix equation, the first order scattered potential is derived and since the free surface term for second order scattered potential can be expressed in terms of the first order potentials, the free surface term can be obtained using the knowledge of first order potentials only.     

The onset of resonance processes in the Couette–Taylor problem close to the point of codimension-2 bifurcation

The bifurcations on passing around the point of intersection of two neutral curves (points of codimension-2 bifurcation) are considered in the Couette–Taylor problem of the fluid motion between rotating cylinders. The secondary modes in a small neighbourhood of a point of codimension-2 bifurcation are studied using a system of non-linear amplitude equations in a central manifold. The steady-state solutions of the amplitude systems, to which secondary periodic modes of the travelling-wave type, non-linear mixtures of travelling waves and unsteady two-, three- and four-frequency quasiperiodic solutions of the system of Navier–Stokes equations correspond, are analysed. A numerical analysis of the conditions for the existence and stability of irrotationally symmetric steady-state fluid flows between unidirectionally rotating cylinders is carried out.     

Inviscid Limits of the Complex Generalized Ginzburg—Landau Equations

1 IntroductionDerivative Ginzburg-Landau equation appeared in many physical problem. It was derivedfor instability waves in hydrodynamic such as the nonlinear growth of Rayleigh-Benard convectiverolls, the appearance of Taylor Vortices in the couette flow between counter-rotating cylinders.This paper is concerning with the generalized derivative Ginzburg-Landau equations given by     

Dynamic torsion of viscoelastic cylindrical rods

An exact solution of the problem of the propagation of torsional waves in semiinfinite and finite circular cylinders is obtained within the framework of the linear theory of viscoelasticity. Concrete examples are discussed, and estimates are given for the stresses near the wave front. All the solutions are obtained in series; it is shown that these series converge absolutely for any finite time.     

Electromagnetic scattering from a right-circular cylinder using a surface radiation condition

The scattering of plane, harmonic electromagnetic waves fromperfectly conducting right-circular cylinders is studied bymaking use of a surface radiation condition. Using sphericalpolar coordinates, the surface profile of the cylinder is describedand the particular form taken by the surface radiation conditonis determined. A numerical scheme is outlined and the problemscaused by the discontinuity of curvature across the surfaceare discussed. The results produced are then favourably comparedwith those produced by the numerical electromagnetics code andphysical optics.     

Hypersingular integral equations for the diffraction of electromagnetic waves on homogeneous magneto-dielectric bodies

It is shown that hypersingular integral equations may be used for numerical solution of diffraction problems for electromagnetic waves on magneto-dielectric bodies. The problem is reducible to surface equations with simple kernels, which permit applying numerical schemes previously developed for ideally conducting objects. Examples of numerical solution of diffraction problems on circular or square dielectric cylinders obtained from equations of different kinds are reported. __________ Translated from Prikladnaya Matematika i Informatika, No. 20, pp. 5–15, 2005.     

High-frequency asymptotics of acoustic pressure for bounded wave beam scattering by an elastic sphere

Asymptotic high-freqeuncy estimates are obtained for the amplitudes of specular and non-specular reflections with extraction of the contribution of sound reradiation into the surrounding medium by Rayleigh type surface elastic waves. The conditions are found that govern the magnification of scattering in the opposite direction. The theoretical explanation of the book reflection effect /1/ for bounded sound beam incidence on the plane interface of a fluid-elastic solid is given by many authors in different situations (/12/, say). As for non-specular reflection of a plane sound wave by bounded elastic bodies (plates, cylinders, rods, and shells enclosed in a screen), studied most thoroughly in /3–9/, this effect is a consequence of satisfying the space-time resonance conditions between the incident acoustic wave and the normal surface waves excited in an elastic solid under total internal reflection.     

A new approximation method for scattering by long finite arrays

The scattering of water waves by a long array of evenly spaced,rigid, vertical circular cylinders is analysed under the usualassumptions of linear theory. These assumptions permit the reductionof the problem to that of solving the Helmholtz equation intwo dimensions, with appropriate circular boundaries. Our primarygoal is to show how solutions obtained for semi-infinite arrayscan be combined to provide accurate and numerically efficientsolutions to problems involving long, but finite, arrays. Theparticular diffraction problem considered here has been chosenboth for its theoretical interest and for its applicability.The design of offshore structures supported by cylindrical columnsis commonplace and understanding how the multiple interactionsbetween the waves and the supports affect the field is clearlyimportant. The theoretical interest comes from the fact that,for wavelengths greater than twice the geometric periodicity,the associated infinite array can support Rayleigh–Blochsurface waves that propagate along the array without attenuation.For a long finite array, we expect to see these surface wavestravelling back and forth along the array and interacting withthe ends. For particular sets of parameters, near-trapping haspreviously been observed and we provide a quantitative explanationof this phenomenon based on the excitation and reflection ofsurface waves by the ends of the finite array.     

Robust and high-order effective boundary conditions for perfectly conducting scatterers coated by a thin dielectric layer

A new approach is considered to construct effective boundaryconditions for the solution of problems related to the scatteringof electromagnetic waves by perfectly conducting cylinders coatedby a thin dielectric shell. These boundary conditions aim tobe both robust and of high order while remaining set in termsof surface differential operators involving at most second-orderderivatives. Error estimates yield a theoretical basis for theuse of these boundary conditions in practical computations.Some numerical experiments at frequencies beyond the range ofvalidity of the usual impedance boundary conditions validatethe efficiency of the approach.     

Wave diffraction from multiple truncated cylinders of arbitrary cross sections

Many marine structures are supported by piles or caissons which, from a mathematical point of view, can be assimilated to an array of truncated cylinders of arbitrary cross sections. The focus of this paper is such an array subjected to harmonic waves of small steepness. We develop an analytic method based on linear potential flow theory to solve the diffraction problem and evaluate the excitation forces and moments acting on each cylinder. The water domain is divided into the interior regions below each cylinder and an exterior region extending to infinity in the horizontal plane. A series of eigen-functions are applied to express the velocity potential in each region. The Fourier series method combined with the eigen-function expansion matching method is used to satisfy the wetted surface body conditions and continuity conditions between adjacent regions. The analytic model is validated by comparing its results with numerical modelling results and published data. It is then applied to two truncated cylinders with caisson cross sections, and results are given for the excitation forces and moments on each cylinder for different values of incident wave direction and spacing between the cylinders, and for different configurations.     

Trapped modes of oscillation of a liquid for surface-piercing bodies in oblique waves

The linear problem of the harmonic oscillations of an ideal incompressible heavy liquid with a free surface in the presence of two and more infinitely long partially submerged cylindrical bodies of arbitrary cross-section is considered. It is proved that there are configurations of the bodies which provide examples of the non-uniqueness of the boundary-value problem in the case of an arbitrary frequency of the oscillations and an arbitrary non-zero angle between the generatrix of the cylinders and the direction of propagation of the surface waves. In the case of these configurations, the homogeneous boundary-value problem has non-trivial solutions with a finite energy integral, which describe trapped modes of oscillation of the liquid.     

Localized modes at defects in sonic composites

The paper discusses a sonic composite consisting of an array of silicone rubber coated hollow steel cylinders embedded in an epoxy matrix, with linear defects. Such structures allow localization of modes in the vicinity of the line defect with propagation along this line. The material in the vicinity of the line behaves like frequency-specific mirrors. The mirrors localize waves within a finite region of the line defect, and modes are quantized into discrete frequencies. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)