Diffraction of Love waves by a stress-free crack of finite width in the plane interface of a layered composite

A rigorous theory of the diffraction of Love waves by a stress-free crack of finite width in the interface of a layered composite is presented. The incident wave is taken to be either a bulk wave or a Love-wave mode. The resulting boundary-value problem for the unknown jump in the particle displacement across the crack is solved by employing the integral equation method. The unknown quantity is expanded in terms of a complete sequence of expansion functions in which each separate term satisfies the edge condition. This leads to an infinite system of linear, algebraic equations for the coefficients of the expansion functions. This system is solved numerically. The scattering matrix of the crack, which relates the amplitudes of the outgoing waves to the amplitudes of the incident waves, is computed. Several reciprocity and power-flow relations are obtained. Numerical results are presented for a range of material constants and geometrical parameters.     

半平面问题远域辐射阻尼的时域边界元法模拟研究

辐射阻尼在岩石基坑爆破开挖、边坡稳定、结构抗震以及结构-地基动力相互作用等实际工程问题中具有重要意义.为了模拟半平面问题的远域辐射阻尼,以时域边界元法(TD-BEM)理论为基础,根据应力波在弹性介质中的传播特性,在时域内提出了一种新的单元,即自适应半无限边界单元,专门用于离散远域半无限边界.该单元外侧节点是一个始终处于应力波波前位置的动态节点,保证计算区域在任何情况下都恰好包含应力波的影响范围,从而模拟远域辐射阻尼.最后,分别采用近场和远场动力荷载作用下的弹性半平面算例进行验证,并将结果与有限元法FEM和常规TD-BEM结果进行综合对比.结果 表明,采用自适应半无限单元的TD-BEM满足半无限域的辐射条件,较好地解决了远域辐射阻尼的模拟问题,且在计算时间成本与常规TD-BEM几乎相同的前提下,具有更高的计算精度.     

Reflection and transmission of obliquely incident Rayleigh surface waves by a viscoelastic interphase

The reflection and transmission of obliquely incident Rayleight surface waves by an interphase between two quarter spaces of identical or different materials, have been investigated. The mechanical behavior of the interphase is represented by a thin viscoelastic layer. By using the full space Green's functions due to a spatially harmonic line load, the mathematical statement of the 3-dimension problem is reduced to a 2-dimension system of singular integral equations. The far-field behavior of the scattered waves leads to the definition of reflection and transmission coefficients,R andT. The system of the singular integral equations are solved forR andT with the boundary element method. The results are presented for selected values of the elastic constants of the joined quarter spaces, the parameters of the interphase and the incident angles of Rayleigh surface waves.     

Scattering of flexural waves by a cracked Mindlin plate of soft ferromagnetic material in a uniform magnetic field

Consider the impingement of time harmonic flexural waves on a through crack in a soft ferromagnetic plate the surface of which is subjected to a uniform magnetic field at normal incidence. Mindlin's plate theory is used to account for the magneto-elastic interaction. For an incident wave that gives rise to moments symmetric about the crack plane, Fourier transforms are applied reducing the mixed boundary value problem to a Fredholm integral equation that can be solved numerically. The dynamic moment intensity factor versus frequency is computed to exhibit the influence of the magnetic field.     

Regular wave integral approach to numerical simulation of radiation and diffraction of surface waves

A regular wave integral method is developed in the discretisation of a linear hydrodynamic problem on radiation and diffraction of surface waves by a floating or submerged body. The velocity potential of the problem is expressed as a solution of a body boundary integral equation involving the pulsating free surface Green function or pulsating free surface sources distributed on the body surface. With the use of a discretisation on the regular wave integral rather than discretisations on the singular wave integral of the Green function as in earlier investigations, the singular wave integral is approximated as an expansion of regular (or nonirregular) wave potentials. Influence coefficients between pulsating free surface source points are computed by the approximate expansion together with Hess–Smith panel integral formulas. Thus the velocity potential solution is evaluated by a boundary element algorithm. The numerical results produced from the proposed method agree well with semi-analytic solution results.     

Numerical simulation of fully nonlinear irregular wave tank in three dimension

A fully nonlinear irregular wave tank has been developed using a three‐dimensional higher‐order boundary element method (HOBEM) in the time domain. The Laplace equation is solved at each time step by an integral equation method. Based on image theory, a new Green function is applied in the whole fluid domain so that only the incident surface and free surface are discretized for the integral equation. The fully nonlinear free surface boundary conditions are integrated with time to update the wave profile and boundary values on it by a semi‐mixed Eulerian–Lagrangian time marching scheme. The incident waves are generated by feeding analytic forms on the input boundary and a ramp function is introduced at the start of simulation to avoid the initial transient disturbance. The outgoing waves are sufficiently dissipated by using a spatially varying artificial damping on the free surface before they reach the downstream boundary. Numerous numerical simulations of linear and nonlinear waves are performed and the simulated results are compared with the theoretical input waves. Copyright © 2006 John Wiley & Sons, Ltd.     

Diffraction of an elastic wave by an embedded quarter-space

A method of matching asymptotic fields has recently been applied to the problem of the diffraction of a plane time-harmonic acoustic wave by an embedded quarter-space with different acoustic properties from the rest of space. The method is here applied to the equivalent problem of elastic waves. The normal to the incident wavefront is perpendicular to the apex of the quarter-space and so the problem is two-dimensional in plane strain.Exact expressions are found for the far-field on the boundary of the quarter-space, neglecting those terms which decay faster than the inverse half power of the distance. The main case of interest is where the incident wave propagates parallel to one of the interfaces.The method, unfortunately, does not lead to any information about the amplitude of any interface (Stoneley or Rayleigh) wave which may exist.     

Acoustic radiation force on a rigid cylinder in an off-axis Gaussian beam near an impedance boundary

The exact equations of the axial and transverse acoustic radiation force functions of a Gaussian beam arbitrarily incident on an infinite rigid cylinder close to an impedance boundary and immersed in an ideal fluid are deduced by expressing the incident wave, the scattering wave and the boundary reflected wave in terms of the cylindrical wave function. The effects of the beam waist, the sound reflection coefficient, the cylinder position and the distance from the impedance boundary on the acoustic radiation force are studied using numerical simulations. The simulation results show that the amplitude of the acoustic radiation force function increases with beam width. Moreover, the values of the acoustic radiation force in both the axial and transverse directions reach those of a plane wave when the beam width is considerably larger than the wavelength of the Gaussian beam. The properties of the impedance boundary and the position of the cylinder in the Gaussian beam have a considerable effect on the magnitude and direction of the force. The simulation results, particularly in the case of a transverse force, indicate the presence of a negative acoustic radiation force that is related to the nondimensional frequency and position of the cylinder in the Gaussian beam.     

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.     

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.     

A note on the diffraction of an obliquely incident surface wave by a partially immersed fixed vertical barrier

The problem of the diffraction of surface waves, obliquely incident on a partially immersed fixed vertical barrier in deep water, is solved approximately by reducing it to the solution of an integral equation, for small angle of incidence of the incident wave. The corrections to the reflection and transmission coefficients over their normal incidence values for small angle of incidence are obtained and presented graphically for some intermediate values of wave numbers.     

A time-domain energy theorem for the scattering of plane elastic waves

A time-domain energy theorem for the scattering of plane elastic waves by an obstacle of bounded extent is derived. The obstacle is embedded in a homogeneous, isotropic, perfectly elastic medium. As to the elastodynamic behavior of the obstacle no assumptions have to be made; so, lossy, non-linear and time-variant behavior is included. As to the wave motion, three different kinds of time behavior are distinguished: (a) transient, (b) periodic, and (c) pertuating, but with finite mean power flow density. For these cases, the total energy (case (a)) or the time-averaged power (cases (b) and (c)) that is both absorbed and scattered by the obstacle is related to a certain time interaction integral of the incident plane wave (P or S) and the spherical-wave amplitude of the scattered wave of the same type (P or S) in the far-field region, when observed in the direction of propagation of the incident wave.     

Reflection of a beam of elastic waves by a periodic surface profile

Reflection of elastic waves from a traction-free solid-air boundary of periodic saw-tooth profile is investigated analytically and experimentally. For an incident plane wave the surface displacements on the profile are computed as the solution of a singular integral equation. The reflected field is subsequently obtained by using an integral representation. Incident beams of finite width are represented by Fourier superpositions of plane waves. The dependence of the reflected signal spectra on the incident beam width is examined closely near the fundamental surface resonance frequency. Experimental spectra which were obtained using two different diameter transducers, are compared to the corresponding theoretical spectra. It is found that the depth of the spectral minima depends on the incident beam width. Both analytical and experimental results exhibit the splitting of an incident beam of elastic waves into two reflected beams. The beam splitting is more pronounced for a narrower incident beam and for frequencies close to a resonance frequency of the profile.     

有限散射信号下二维缺陷形状识别的罚函数方法

研究在有限照射角度和频带宽度下二维缺陷的形状识别问题。首先,通过引进介质参数扰动函数,建立介质参数扰动函数和弹性波散射场之间的非线性关系,并将所关心的缺陷的形状识别问题转化为关于扰动函数的反演;然后,利用变分技术和优化方法求解,为了弥补散射数据的不足,在总的目标函数中,采用附加度量函数作为罚函数;最后,对后场散射远场测量时有限照射角度和频带宽度下几种典型缺陷进行了模拟识别,表明了;表明了罚函数法的有效性。     

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.     

Three dimensional shock wave/boundary layer interactions

An investigation into a three-dimensional, curved shock wave interacting with a three-dimensional, curved boundary layer on a slender body is presented. Three different nose profiles mounted on a cylindrical body were tested in a supersonic wind tunnel and numerically simulated by solving the Navier–Stokes equations. The conical and hemispherical nose profiles tested were found to generate shock waves of sufficient strength to separate the boundary layer on the cylinder, while the shock wave generated by the ogival profile did not separate the boundary layer. For the separated flow, separation was found to occur predominantly on the windward side of the cylinder with the lee-side remaining shielded from the direct impact of the incident shock wave. A thickening of the boundary layer on the lee-side of all the profiles was observed, and in the conical and hemispherical cases this leads to the re-formation of the incident shock wave some distance away from the surface of the cylinder. A complex reflection pattern off the shock wave/boundary layer interaction (SWBLI) was also identified for the separated flow cases. For comparative purposes, an inviscid simulation was performed using the hemispherical profile. Significant differences between the viscous and inviscid results were noted including the absence of a boundary layer leading to a simplified shock wave reflection pattern forming. The behaviour of the incident shock wave on the lee-side of the cylinder was also affected with the shock wave amalgamating on the surface of the cylinder instead of away from the surface as per the viscous case. Test data from the wind tunnel identified two separation lines present on the cylindrical surface of the hemispherical SWBLI generator. The pair of lines were not explicitly evident in the original CFD simulations run, but were later identified in a high-resolution simulation.     

Reflection and Transmission of Elastic Waves from the Interface of a Fluid-saturated Porous Solid and a Double Porosity Solid

The reflection and transmission characteristics of an incident plane P1 wave from the interface of a fluid-saturated single porous solid and a fluid-saturated double porosity solid are investigated. The fluid-saturated porous solid is modeled with the classic Biot’s theory and the double porosity medium is described by an extended Biot’s theory. In a double-porosity model with dual-permeability there exist three compressional waves and a shear wave. The effects of the incident angle and frequency on amplitude ratios of the reflected and transmitted waves to the incident wave are discussed. Two boundary conditions are discussed in detail: (a) Open-pore boundary and (b) Sealed-pore boundary. Numerical results reveal that the characteristics of the reflection and transmission coefficients to the incident angle and the frequency are quite different for the two cases of boundary conditions. Properties of the bulk waves existing in the fluid-saturated porous solid and the double porosity medium are also studied.     

Diffraction of a sound wave by a nonmoving plate

The problem of determining the velocity field excited by a sound wave impinging on a plate at rest is analyzed as an initial- and boundary-value problem with a movable boundary for the two-dimensional wave equation. The latter problem is solved by the formulation and inversion of integral equations of the Volterra type. The solution is obtained in closed form for any angle of inclination of the incident wave relative to the plate surface and is represented by recursion relations allowing for the influence of any number of diffracted waves generated in succession at the plate boundary.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 123–130, March–April, 1972.     

Oscillatory line source for water waves in shear flow

The linearized water-wave radiation problem for the oscillating 2D submerged source in an inviscid shear flow with a free surface is investigated analytically. The vorticity is uniform, with zero velocity at the free surface. Then there will be at most two emitted waves, and no Doppler effects. Exact far-field waves are derived, with radiation conditions applied at infinity. An upstream wave will always exist, whereas the downstream wave exists only when the angular frequency of oscillation exceeds the vorticity. The wave radiation problem is solved also for oscillating vortex and dipoles. The amplitudes and energy fluxes are calculated.