Water-wave transmission through barriers with small gaps

Summary The problem of the transmission of water waves through gaps inn arbitrary barriers is solved under the assumption that both the gaps and the barrier thicknesses are small. Closed-form expressions for the transmission and reflection coefficients are derived for the special case ofn equally-spaced identical barriers and gaps.     

Water-wave Scattering by an Ice-strip

The problem of water-wave scattering by a strip of ice-cover floating on the surface of deep water is investigated here. The ice-cover is modelled as a thin elastic plate of very small thickness. The problem is reduced to that of solving two singular integral equations of Carleman type over a semi-infinite range and are solved approximately by casting them into two separate Riemann-Hilbert problems by assuming the strip width to be large. The reflection and transmission coefficients are derived approximately. Numerical results for the reflection coefficient are presented graphically against the wave number and also against the ice-cover parameter. The oscillatory nature of the reflection coefficient against the wave number as well as the ice-cover parameter is found to be one of the main features of the curves. It is also seen that, in the limiting case when the ice-cover parameter tends to zero (i.e., the ice-cover is almost absent), the amount of reflection is negligible     

Wave propagation through engineering materials; assessment and monitoring of structures through non-destructive techniques

Elastic wave propagation has been used for decades for assessment of the structural integrity of engineering materials. The advantage it offers is the direct connection to elastic properties, the relatively easy application through commercial equipment as well as numerous empirical correlations between pulse velocity and material strength or quality in general. Advanced features like frequency dependence of wave parameters may further improve the characterization capacity. Concrete materials due to their inherent microstructure, which is enhanced by the existence of damage-induced cracking, exhibit a complicated behavior concerning the propagation of pulses of different frequencies. The different wave lengths interact with inhomogeneities according to their size and therefore, leave their signature on the phase velocity and attenuation versus frequency curves. Although experimental measurements are troublesome in concrete structures, mainly due to attenuation of high frequencies, it is suggested that, whenever possible, application of different frequencies can provide a more detailed insight on the internal condition of the structure. Apart from classical elastic wave studies, the scattering microstructure of concrete exercises strong influence on the elastic signals emitted after cracking events, distorting therefore crucial acoustic emission parameters used for the characterization of the structural integrity. In the present paper experimental evidence of dispersion and examples on how it can be utilized in concrete non destructive inspection are presented and discussed.     

Fluid flow through an array of fixed particles

Slow flow of an incompressible viscous fluid is studied in an array of a great number of small fixed solid particles. The particles size ? and the distance η between two neighbouring solids are such that $\text{??η?1}$. Using perturbation methods it is proved that Brinkman's law occurs really for a critical size of particles; for larger particles the fluid filtration is governed by the Darcy's law and smaller solids do not influence the flow. The 3 and 2-dimensional cases are studied.     

Wave propagation through scattering structures made by cascading screens of finite thickness

In a genuine three-dimensional context, we study analytically the scattering properties of a cascading structure made by plane, parallel and equi-spaced screens, each one having the same (periodic) distribution of identical openings of rectangular shape. Differently from previous paper, the screens are supposed to have a common non-null thickness, which implies a double number of governing equations and systems. By using suitable approximations involving physical and geometrical parameters, we get explicit representations with respect to frequency for the scattered wave field and the relevant parameters. To show and discuss the peculiar properties of the structure, some figures are finally provided.     

In-plane problem for wave propagation through elastic solids with a periodic array of cracks

Summary In the context of wave propagation in damaged (elastic) solids, an analytical method previously introduced for scalar problems, is now applied to study the (vector) problem for normal penetration of a longitudinal plane wave into a periodic array of collinear cracks. Reduced the problem to an integral equation holding over the openings, an approximation of one-mode type leads to analytical solutions and then to explicit representations for the wave fields and the scattering parameters. Some graphs will finally compare our results with the numerical ones by other authors.     

The stress intensity factors of a star-shaped array of cracks in an infinite elastic solid

The problem of determining the stress intensity factors and crack formation energy of a radial system of line cracks in an infinite elastic solid is reduced to the solution of a singular integral equation. The equation is solved numerically for the special case in which the cracks are opened by a constant pressure.     

Omnidirectional guided wave inspection of large metallic plate structures using an EMAT array

The design of an electromagnetic acoustic transducer (EMAT) array device for the inspection of large areas of metallic plate-like structures using the S0 guided wave mode is described. The reasons for using the S0 mode are discussed and it is shown how the choice of mode determines the nature of the EMAT array elements. A novel array construction technique is shown to be necessary whereby the EMAT coils for adjacent elements are overlapped in order to achieve the required element density. Results are presented that illustrate the operation of the device on steel and aluminum plate specimens in the thickness range from 5 to 10 mm. An area of at least 10 m2 can be inspected from a single location. Spurious signals in the results are caused both by the unwanted A0 mode and by S0 sidelobes, the latter occurring at the same radial distance from the array as the genuine S0 signal from a reflector, but in the wrong direction. The signal-to-coherent noise performance of the complete system is determined by the amplitude ratio of the largest genuine S0 signal to the largest spurious signal. This is typically around 30 dB. The sensitivity of the device to artificial defects and genuine corrosion patches is demonstrated and the limitations of its operation are discussed. The feasibility of using the device with the S1 guided wave mode to inspect a 20 mm thick plate is also demonstrated.     

The longitudinal shear problem for an array of cracks at the edge of a circular hole in an infinite elastic solid

Summary A Mellin-type transform technique reduces the longitudinal shear problem for a set of cracks at the edge of a circular hole in an infinite elastic solid to that of solving a system of integral equations. The stress intensity factors and crack formation energy are calculated. Three special cases are considered in detail and graphical results given.     

The linear-wave response of a periodic array of floating elastic plates

The problem of an infinite periodic array of identical floating elastic plates subject to forcing from plane incident waves is considered. This study is motivated by the problem of trying to model wave propagation in the marginal ice zone, a region of ocean consisting of an arbitrary packing of floating ice sheets. It is shown that the problem considered can be formulated exactly in terms of the solution to an integral equation in a manner similar to that used for the problem of wave scattering by a single elastic floating plate, the key difference here being the use of a modified periodic Green function. The convergence of this Green function in its original form is poor, but can be accelerated by a transformation. It is shown that the results from the method satisfy energy conservation and that in the particular case of a fixed rigid rectangular plate which spans the periodicity uniformly the solution reduces to that for a two-dimensional rigid dock. Solutions for a range of elastic-plate geometries are also presented.     

Dynamic wave propagation in infinite saturated porous media half spaces

From a macroscopic perspective, saturated porous materials like soils represent volumetrically interacting solid–fluid aggregates. They can be properly modelled using continuum porous media theories accounting for both solid-matrix deformation and pore-fluid flow. The dynamic excitation of such multi-phase materials gives rise to different types of travelling waves, where it is of common interest to adequately describe their propagation through unbounded domains. This poses challenges for the numerical treatment and demands special solution strategies that avoid artificial and numerically-induced perturbations or interferences. The present paper is concerned with the accurate and stable numerical solution of dynamic wave propagation problems in infinite half spaces. Proceeding from an isothermal, biphasic, linear poroelasticity model with incompressible constituents, finite elements are used to discretise the near field and infinite elements to approximate the far field. The transient propagation of the poroacoustic body waves to the infinity is thereby modelled by a viscous damping boundary, which, for stability reasons, necessitates an appropriate treatment of the included velocity-dependent damping forces.     

Numerical simulation of the dynamic response of floating structures

This paper summarizes a computational procedure for the simulation of wave-structure interactions. The procedure combines the Boundary Element Method (BEM) for potential flows and a predictor-corrector scheme for the time-integration of the nonlinear free-surface condition. In order to have a good representation of a domain of infinite extent, a significant part of the procedure deals with the formulation of a nonreflecting boundary condition for multidirectional waves. This formulation is based on generalizations of modal-superposition in a least-squares sense. In spite of the assumption that the linearized free-surface condition is satisfied in the far field, the proposed nonreflecting boundary condition gives reasonably good performance in absorbing the nonlinear free-surface waves from the interior. The verification and validation of the time–domain computations show very good agreement between the numerical and experimental data from a physical wave basin. Financial support for this research, provided by the Offshore Technology Research Center and the Texas Advanced Research Program, is gratefully acknowledged. Computing resources have been made available by the Offshore Technology Research Center and the Department of Civil Engineering at The University of Texas at Austin.     

Beam propagation constants for a radial laser array

The beam quality of a radial laser array, quantified in terms of the M(2) propagation constant, is determined as a function of array element configuration. A lower bound on array M(2) is estimated for both phase-locked and nonphase-locked conditions. It is shown that, to achieve near-unity M(2) array, either aperture filling or spatial filtering is required in addition to phase locking. An aperture-filling method suitable for radial arrays of CO(2) slab lasers is presented.     

Effects of phase lags on wave propagation in an infinite solid due to a continuous line heat source

The present work is concerned with the wave propagation in a homogeneous, isotropic and unbounded solid due to a continuous line heat source under the theory of thermoelasticity with three phase-lags (Roychoudhari in J Therm Stress 30:231?C238, 2007). For the solution of the problem, we employ a potential function approach together with Laplace and Hankel transform method. Analytical expressions for the distributions of different fields like temperature, displacement and stresses inside the medium are derived by inverting Laplace transforms in an approximate manner for small values of time. The problem is illustrated by computing numerical values of the field variables for a particular material. The theoretical as well as numerical results are compared with the corresponding results for other theories of thermoelasticity reported earlier.     

A photoacoustic imager with light illumination through an infrared-transparent silicon CMUT array

A novel hardware design and preliminary experimental results for photoacoustic imaging are reported in this paper. This imaging system makes use of an infrared-transparent capacitive micromachined ultrasonic transducer (CMUT) chip for ultrasound reception and illuminates the image target through the CMUT array. The cascaded arrangement between the light source and transducer array allows for a more compact imager head and results in more uniform illumination. Taking advantage of the low optical absorption coefficient of silicon in the near infrared spectrum as well as the broad acoustic bandwidth that CMUTs provide, an infrared-transparent CMUT array has been developed for ultrasound reception. The center frequency of the polysilicon-membrane CMUT devices used in this photoacoustic system is 3.5 MHz, with a fractional bandwidth of 118% in reception mode. The silicon substrate of the CMUT array has been thinned to 100 μm and an antireflection dielectric layer is coated on the back side to improve the infrared-transmission rate. Initial results show that the transmission rate of a 1.06-μm Nd:Yag laser through this CMUT chip is 12%. This transmission rate can be improved if the thickness of silicon substrate and the thin-film dielectrics in the CMUT structure are properly tailored. Imaging of a metal wire phantom using this cascaded photoacoustic imager is demonstrated.     

Light propagation through anisotropic turbulence

A wealth of experimental data has shown that atmospheric turbulence can be anisotropic; in this case, a Kolmogorov spectrum does not describe well the atmospheric turbulence statistics. In this paper, we show a quantitative analysis of anisotropic turbulence by using a non-Kolmogorov power spectrum with an anisotropic coefficient. The spectrum we use does not include the inner and outer scales, it is valid only inside the inertial subrange, and it has a power-law slope that can be different from a Kolmogorov one. Using this power spectrum, in the weak turbulence condition, we analyze the impact of the power-law variations α on the long-term beam spread and scintillation index for several anisotropic coefficient values ?. We consider only horizontal propagation across the turbulence cells, assuming circular symmetry is maintained on the orthogonal plane to the propagation direction. We conclude that the anisotropic coefficient influences both the long-term beam spread and the scintillation index by the factor ?(2-α).     

Love波在电磁弹性多层结构中的频散特性

在电磁弹性多层结构模型的基础上, 通过本构方程和场方程推导出Love 波在电磁弹性介质中的波动方程。利用传递矩阵方法, 给出了一定边界条件下Love 波在该结构中的频散方程。通过对算例进行分析, 得出了Love 波在电磁弹性多层结构中传播的一些特性。      

非对称周期结构中耦合波的传播特性

为了揭示周期结构中纵向波和弯曲波的耦合作用,设计了对称和非对称周期结构。考虑子结构中的纵向和弯曲耦合运动,利用导纳法和传递矩阵法,得到了周期单元的传递方程。由于结构中存在多种波的耦合作用,在求解周期单元的传播系数时将出现变态矩阵,采用波型分组法,求得了周期结构中多种波型的传播系数。推导了半无限长和有限长周期结构在纵向力、横向力和弯矩作用下的动态响应。数值计算结果表明,对称周期结构中纵向波和弯曲波的带隙结构相互独立;非对称周期结构中纵向波和弯曲波的耦合明显改变了两种波的带隙结构,只有在两种波阻带重叠的频段内结构上的振动响应才存在衰减。     

Penny-shaped crack in an infinite elastic cylinder bonded to an infinite elastic material surrounding it

This paper concerns with the state of stress in a long elastic cylinder, with a concentric penny-shaped crack, bonded to an infinite elastic medium. The crack is assumed to be opened by an internal pressure and that the plane of the crack is perpendicular to the axis of the cylinder. The elastic constants of the cylinder and the semi-infinite medium are assumed to be different. The problem is reduced to the solution of a Fredholm integral equation of the second kind. Closed form expressions are obtained for the stress-intensity factor and the crack energy. The integral equation is solved numerically and results are used to obtain the numerical values of the stress-intensity factor and the crack energy which are graphed.