Modeling nonlinear Rayleigh wave fields generated by angle beam wedge transducers—A theoretical study

Nonlinear Rayleigh wave fields generated by an angle beam wedge transducer are modeled in this study. The calculated area sound sources underneath the wedge are used to model the fundamental Rayleigh sound fields on the specimen surface, which are more accurate than the previously used line sources with uniform or Gaussian amplitude distributions. A general two-dimensional nonlinear Rayleigh wave equation without parabolic approximation is introduced and the solutions are obtained using the quasilinear theory. The second harmonic Rayleigh wave due to material nonlinearity is given in an integral expression with these fundamental Rayleigh waves radiated by the wedge transmitter acting as a forcing function. Multi-Gaussian beam (MGB) models are employed to simplify these integral solutions and to extract the diffraction and attenuation correction terms explicitly. The effect of nonlinearity of generating sources on the second harmonic Rayleigh wave fields is taken into consideration; simulation results show that it will affect the magnitude and diffraction correction of the second harmonic waves in the region close to the Rayleigh wave sound sources. This research provides a theoretical improvement to alleviate the experimental restriction on analyzing the effects of diffraction, attenuation and source nonlinearity when using angle beam wedge transducers as transmitters.     

A Representation Formula for the Velocity Part of 3D Time-Dependent Oseen Flows

We prove a representation formula for the solution of an initial-boundary value problem associated with the 3D time-dependent Oseen system. This formula involves the solution of an integral equation on the lateral boundary of the space-time cylinder. The key point of this article is that the assumptions on the data are chosen in such a way that the formula in question may be used in a theory of the asymptotic behaviour of solutions to the nonstationary 3D Navier–Stokes system with Oseen term (incompressible viscous flow in an exterior domain with nonzero velocity at infinity).     

Diffraction of a sound wave by a slit

The diffraction of a sound wave by a slit in an unbounded plane is analyzed as an initial-boundary-value problem with a moving boundary for the two-dimensional wave equation. The initial-boundary-value problem is solved by the formation and inversion of Volterra integral equations. A solution is obtained in closed form in quadratures for an arbitrary angle of inclination of the incident wave front relative to the plane. The solution is presented in the form of recursion formulas, which take into account the influence of diffraction waves occurring in succession at the boundaries of the slit.     

High-frequency surface currents induced on a spherical reflector by the edge-diffraction of obliquely incident waves

An explicit expression of the high-frequency surface current excited on a perfectly conducting spherical cap by the edge-diffraction of an obliquely incident wave is derived. The result is given in the GTD terminology and shows the influence of the incidence angles on the transfer functions. To this end the real (physical) space is embedded into a twofold extended abstract space in which an equivalent canonical problem is established. This latter yields a system of dual integral equations whose kernels were not previously treated. By inverting these new kernels, the system of dual equations is reduced to two independent Wiener-Hopf problems. From the asymptotic solutions of these problems, one derives the expression of the edge-excited current along with the known geometrical optics term. The resutlt can be used directly in practical applications. If the incident ray becomes normal to the edge, then the resulting expressions are reduced to the already known expressions. The basic idea and general formulas used here can also be used to solve other diffraction problems with similar geometry.     

Induction by an oscillating magnetic dipole over a two layer ground

Summary An expression for the mutual electromagnetic coupling between two small loops over a two-layer ground is derived. The result is expressed in a form which is suitable for calculation by a digital computer. When the heights or separation of the loops are large compared to the skin depth in the ground, simple asymptotic formulas for the fields can de developed. The results are employed to obtain a convenient formula for the self-impedance of a loop over a two-layer ground.     

Rays,modes and beams for plane wave coupling into a wide open-ended parallel-plane waveguide

A plane wave incident obliquely onto the open end of a wide parallel-plane waveguide generates an interior field that resembles a geometric optical sheet beam whose initially well-defined shape gets diffused after undergoing multiple reflection. This behavior can be confirmed, but not physically well explained, from numerical results obtained by summing over the aperture-excited guided modes. A phenomenologically incisive representation is obtained by subjecting the guided mode sum to partial Poisson summation that yields an exact hybrid field comprising the multiple reflected geometric optical beam, some multiple reflected edge-diffracted rays, some guided modes, plus remainder terms. Asymptotic approximations reduce these exact forms to the wave constituents of the nonuniform and, when required, uniformized geometrical theory of diffraction. Numerical results presented for various parameter regimes delineate the ranges of applicability of the asymptotic forms and also the relative importance of the individual wave contributions. In the parameter range where geometrical features of the field can still be resolved, the hybrid form is not only physically appealing but also numerically more efficient than alternatives involving only rays or only modes.     

Efficient computation of steady solitary gravity waves

An efficient numerical method to compute solitary wave solutions to the free surface Euler equations is reported. It is based on the conformal mapping technique combined with an efficient Fourier pseudo-spectral method. The resulting nonlinear equation is solved via the Petviashvili iterative scheme. The computational results are compared to some existing approaches, such as Tanaka’s method and Fenton’s high-order asymptotic expansion. Several important integral quantities are computed for a large range of amplitudes. The integral representation of the velocity and acceleration fields in the bulk of the fluid is also provided.     

Shape analysis and damped oscillatory solutions for a class of nonlinear wave equation with quintic term简

This paper aims at analyzing the shapes of the bounded traveling wave solu- tions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of planar dynamical systems are used to make a qualitative analysis to the planar dynamical system which the bounded traveling wave solutions of this equation correspond to. The shapes, existent number, and condi- tions are presented for all bounded traveling wave solutions. The bounded traveling wave solutions are obtained by the undetermined coefficients method according to their shapes, including exact expressions of bell and kink profile solitary wave solutions and approxi- mate expressions of damped oscillatory solutions. For the approximate damped oscillatory solution, using the homogenization principle, its error estimate is given by establishing the integral equation, which reflects the relation between the exact and approximate so- lutions. It can be seen that the error is infinitesimal decreasing in the exponential form.     

Anti-plane wave motion in a cylindrically orthotropic elastic solid containing a stress-free crack

A cylindrically orthotropic elastic solid is excited by a point impulsive body force. The solid contains a semi-infinite stress-free crack. The resulting wave motion is anti-plane. An eigenfunction solution to the problem is obtained in the form of an infinite series. The series is summed into two parts. The first part contains the incident and reflected wave pulses while the second part gives the diffraction integral. Wave front patterns are presented with an application to wood.     

Simulation of elastic wave diffraction by multiple strip-like cracks in a layered periodic composite

The problem of numerical simulation of the steady-state harmonic vibrations of a layered phononic crystal (elastic periodic composite) with a set of strip-like cracks parallel to the layer boundaries is solved, and the accompanying wave phenomena are considered. The transfer matrix method (propagator matrix method) is used to describe the incident wave field. It allows one not only to construct the wave fields but also to calculate the pass bands and band gaps and to find the localization factor. The wave field scattered by multiple defects is represented by means of an integral approach as a superposition of the fields scattered by all cracks. An integral representation in the form of a convolution of the Fourier symbols of Green’s matrices for the corresponding layered structures and a Fourier transform of the crack opening displacement vector is constructed for each of the scattered fields. The crack opening displacements are determined by the boundary integral equation method using the Bubnov-Galerkin scheme, where Chebyshev polynomials of the second kind, which take into account the behavior of the solution near the crack edges, are chosen as the projection and basis systems. The system of linear algebraic equations with a diagonal predominance of components arising when the system of integral equations is discretized has a block structure. The characteristics describing qualitatively and quantitatively the wave processes that take place under the diffraction of plane elastic waves by multiple cracks in a phononic crystal are analyzed. The resonant properties of a system of defects and the influence of the relative positions and sizes of defects in a layered phononic crystal on the resonant properties are studied. To obtain clearer results and to explain them, the energy flux vector is calculated and the energy surfaces and streamlines corresponding to them are constructed.     

非均匀介质散射问题的体积分方程数值解法

将非均匀介质视为某一均匀背景介质中的扰动，可建立用均匀背景介质格林函数作基本解的体积分方程．给出了配置法求解体积分方程的数值方法，首先解得扰动域内各点以速度扰动为权的波场函数，然后回代计算得到观测面上各接收点的散射波场．与边界元法和Ｂｏｒｎ近似法计算结果比较表明该方法具有很高的精度，可得到穿过非     

直接计算应力强度因子的扩展有限元法

系统地给出了直接计算应力强度因子的扩展有限元法。该方法以常规有限元法为基础,利用单位分解法思想,通过在近似位移表达式中增加能够反映裂纹面的不连续函数及反映裂尖局部特性的裂尖渐进位移场函数,间接体现裂纹面的存在,从而无需使裂纹面与有限元网格一致,无需在裂尖布置高密度网格,也不需要后处理就可以直接计算出应力强度因子,并且大大简化了前后处理工作。最后通过两个简单算例验证了该方法的精度,分析了影响计算结果的因素,并与采用J积分计算的应力强度因子作了对比,得出了两种方法计算精度相当的结论。     

Transient wave propagation of isotropic plates using a higher-order plate theory

Transient wave propagation of isotropic thin plates using a higher-order plate theory is presented in this paper. The aim of this investigation is to assess the applicability of the higher-order plate theory in describing wave behavior of isotropic plates at higher frequencies. Both extensional and flexural waves are considered. A complete discussion of dispersion of isotropic plates is first investigated. All the wave modes and wave behavior for each mode in the low and high-frequency ranges are provided in detail. Using the dispersion relation and integral transforms, exact integral solutions for an isotropic plate subjected to pure impulse load and a number of wave excitations based on the higher-order theory are obtained and asymptotic solutions which highlight the physics of waves are also presented. The axisymmetric three-dimensional analytical solutions of linear wave equations are also presented for comparison. Results show that the higher-order theory can predict the wave behavior closely with exact linear wave solutions at higher frequencies.     

Acoustic scattering of a plane wave by a circular penetrable cone

The paper is devoted to the diffraction of a plane wave by an acoustically transparent semi-infinite cone. The problem of diffraction is reduced to a singular integral equation in the framework of the incomplete separation of variables. The Fredholm property and regularization of the integral equation are discussed. Some important integral representations of the wave field are considered. The detailed study of the far-field asymptotics is given. Expressions for the diffraction coefficient of the spherical wave scattered from the vertex of the cone are considered. The reflected from the conical surface waves and those transmitted across the surface are also discussed.     

Wave forces on stationary slender bodies

A theory is presented for the prediction of the wave forces on ships and the pressure field on slender bodies vibrating in an acoustic medium. In both radiation and diffraction the flow in the near field is approximated by a sequence of two-dimensional problems supplemented with homogeneous components which account for longitudinal flow interactions. These are matched to three-dimensional far-field approximations represented by axial source distributions and two integral equations are solved for their strengths. The theory is valid from the incompressible long-wavelength limit to wavelengths comparable to the body beam. Comparisons of wave forces and the acoustic radiation impedance pressure are in very good agreement with exact solutions. It is shown that the asymptotic matching conserves energy.     

Strain-field investigations with plane diffraction gratings

The development of means for producing small, separate, plane diffraction gratings as integral parts of the surfaces of flat metal specimens has led to modification of the method of Bell and to the investigation of strain fields by study of diffraction phenomena. Choice of a particular diffraction-strain relationship and the use of master gratings in conjunction with diffraction gratings to be used as strain gages permits use of simple optical instrumentation. The diffraction phenomena from multiple gages at the same orientation may be photographed simultaneously during loading for subsequent analysis, and instrumentation in the form employed permits resolving strain increments of magnitude 0.0008 in the range 0.0030 to 0.030.     

Solution of electromagnetic scattering and radiation problems using a spectral domain appoach–a review

In this paper we present a brief review of some recent developments on the use of the spectral-domain approach for deriving high-frequency solutions to electromagnetics scattering and radiation problems. The spectral approach is not only useful for interpreting the well-known Keller formulas based on the geometrical theory of diffraction (GTD), it can also be employed for verifying the accuracy of GTD and other asymptotic solutions and systematically improving the results when such improvements are needed. The problem of plane wave diffraction by a finite screen or a strip is presented as an example of the application of the spectral-domain approach.     

The study of wave motion in the Talbot interferometer with a lens

We present the study of the wave motion in the Talbot interferometer with an additional element such as a lens for all related audiences. Our solutions are in the analytic form. A general principle of the Talbot effect, which is the optical near-field effect, is the Fresnel diffraction. The Fresnel integral is rather complicated. We therefore introduce an alternative method which is based on the wave propagation through the transmission functions of the grating and the lens. Our method has been proved by a simple experimental setup.