SH-wave propagation and resonance phenomena in a periodically layered composite structure with a crack

This paper presents a dynamic analysis of time-harmonic plane SH-waves propagating in periodically multilayered elastic composites with a strip-like crack. The total wave field in the multilayered elastic structure is described as a sum of incident wave field modeled by the transfer matrix method and the scattered wave field governed by an integral representation containing the crack-opening-displacement. The integral equation derived from the boundary conditions on the crack-faces is solved numerically by a Galerkin method. The paper focuses on resonant and non-resonant regimes of anti-plane wave motion in a stack of elastic layers weakened by a single strip-like crack and wave localization in the vicinity of the crack. The scattered extra displacement induced by the presence of the crack is investigated in detail for both situations of high and low contrast in material properties. Numerical results for the average crack-opening-displacement, the transmission coefficient, the stress intensity factor and the average energy flow are presented and discussed to reveal wave resonance and localization phenomena within the band-gaps and the pass-bands.     

Surface acoustic oscillations in a periodically layered medium

The existence of surface acoustic waves at the interface between a periodically layered and a homogeneous half-space is predicted. The reason for the arisal of such waves is the violation of the transnational symmetry pertinent to the periodic structure. The properties of the surface waves at a free boundary and a boundary with an elastic half-space are considered.     

Reaction-diffusion fronts in periodically layered media

We compute the effective wavefront speeds of reaction-diffusion equations in periodically layered media with coefficients that have small-amplitude oscillations around a uniform mean state. We compare them with the corresponding wavefront speeds in the uniform state. We analyze a one-dimensional model where wave propagation is along the layering direction of the medium and a two-dimensional shear flow model where wave propagation is othogonal to the layering direction. We find that the effective wave speed is smaller in the one-dimensional model and is larger in the two-dimensional model for both bistable cubic and quadratic nonlinearities of the Kolmogorov-Petrovskii-Piskunov form. We derive approximate expressions for the wave speeds in the bistable case.Dedicated to Jerry Percus on the occasion of his 65th birthday.     

Investigation of nonstationary models of laser pulse propagation through a homogeneous scattering layer

Using three nonstationary models of radiation transfer in two versions (diffusion-based and axial), the absorption and scattering coefficients of homogeneous scattering media are found from experimental temporal distributions of an ultrashort laser pulse transmitted through the scattering layer of different thickness. These optical characteristics are found to be dependent on the scattering layer thickness, which contradicts physical considerations. The reason for the discovered effect is related to incomplete taking into account of the properties of the scattering indicatrix in the used approximate models. The validity of this interpretation is supported by a Monte Carlo simulation, which yielded similar dependences. Recommendations on the correct use of the approximate radiation transfer models are given.     

Statistics of amplified light in periodically correlated layered systems with randomness

Abstract

We study the statistics of reflection and transmission coefficients of light in randomly layered amplifying media that are periodic on average. We are interested in one-dimensional universal scaling behaviours in such systems. Our study shows that while a homogeneous medium boundary condition is capable of reproducing universal scaling at low frequencies, a periodic medium boundary condition is necessary for high frequencies. Although the statistics depends on the boundary condition, the saturation length, where the reflection coefficient reaches a stationary distribution, and the localization length do not. Implications of these results are discussed.     

Scaling and decay in periodically driven scattering systems

We investigate irregular scattering in a periodically driven Hamiltonian system of one degree of freedom. The potential is asymptotically attracting, so there exist parabolically escaping scattering orbits, i.e. orbits with asymptotic energy E(out)=0. The scattering functions (i.e. the asymptotic out-variables as functions of an asymptotic in-variable) show a characteristic algebraic scaling in the vicinity of these orbits. This behavior is explained by asymptotic properties of the interaction. As a consequence, the number N(Deltat) of temporarily bound particles decays algebraically with the delay time Deltat, although no KAM scenario can be found in phase space. On the other hand, we find the number N(n) of temporarily bound particles to decay exponentially with the number n of zeros of x(t).     

周期性加隔板有限长圆柱壳声散射

研究内部真空周期性加隔板圆柱壳在水中的声散射特性.壳体振动用薄壳理论的Donnell方程描述,隔板振动用相互独立的薄板纯弯曲振动和平面应力状态下的振动方程描述.考虑轴向、切向、径向三个方向的力和弯矩共同作用导出了散射声场的解析表达式.数值计算给出远场收发合置情况下的角度-频率谱图,并据此进行机理分析.通过与内部周期性加环肋圆柱壳声散射的角度-频率谱图比较发现,除周期加肋产生的Bragg散射波与弯曲Bloch-Floquet波外,加隔板的情况还存在明显的隔板共振亮线,并且发生隔板共振与壳体弹性波、Bragg散射波、弯曲Bloch-Floquet波耦合的现象.通过实验对理论进行了验证,在实验的频率范围内,Bragg散射亮线与理论符合得很好,部分Bloch-Floquet波散射亮线和隔板共振散射亮线也与理论符合.     

Propagation of SH-wave in a corrugated viscous sandy layer sandwiched between two elastic half-spaces

The present paper attempts to investigate the effect of sandiness, corrugated boundary surfaces, heterogeneity, and gravity on phase velocity and attenuation of SH-wave propagating in a viscous sandy layer with corrugated upper and lower boundary surfaces sandwiched between an upper heterogeneous elastic half-space and lower viscoelastic half-space under gravity. Heterogeneity associated with the upper half-space is due to exponentially varying density which is a function of depth; but the rigidity is constant. The closed form of dispersion relation is established and found to be in complex form. Real part and imaginary part of the dispersion relation correspond to dispersion curve and attenuation curve, respectively. One of the salient points of present study is the use of DEBYE asymptotic expansion to establish that the obtained dispersion relation is in well-agreement with the classical Love wave equation in isotropic case. The effect of presence and absence of corrugated boundary surfaces, measured by initial flatness parameter, on dispersion and attenuation curves have been meticulously examined. Moreover, the substantial effect of heterogeneity, sandiness, internal friction, and Biot’s gravity parameter on phase velocity and attenuation coefficient of SH-wave has been studied and demonstrated by means of graphical illustration and numerical computations.     

Brillouin scattering in layered structures

Theoretical and experimental results on Brillouin scattering in inhomogeneous materials are presented: Normal elastic modes and Brillouin intensities have been calculated for a periodic layer system. Measurements on semicrystalline polybutene-1 are discussed in terms of the theoretical results. Both theory and experiment yield several Brillouin lines in VV scattering instead of the one peak characteristic for homogeneous specimens.     

Magnetoelectric effect in layered composites with arc shape

Magnetoelectric (ME) layered Ni/PZT/Ni composites with arc shape have been prepared by using electroless deposition. The ME effect is measured by applying both constant and alternating magnetic fields in longitudinal and transverse directions. The longitudinal ME voltage coefficient is much larger than the transverse one. With the increase of arc length or decrease of curvature, the resonance frequency of layered arc Ni/PZT/Ni composites gradually decreases, while the maximum of the ME voltage coefficient of the composites increases monotonously. The influence of the arc length and the curvature on ME coupling is discussed. The flat interface between the ferromagnetic and the piezoelectric phases in layered ME composites is believed to provide large ME voltage coefficient.     

Detonation propagation across a stratified layer with a diffuse interface

A study was conducted to examine detonation propagation in a stratified layer of hydrogen-oxygen-nitrogen above an inert gas in a horizontal narrow channel. The stratified layer was produced by a gravity current, generated by retracting a door initially separating a hydrogen-oxygen-nitrogen mixture in the predetonator and a heavier inert gas in the test-section. A steady detonation wave generated in the predetonator was transmitted into the stratified layer. The reactivity of the predetonator mixture was varied via the hydrogen-oxygen equivalence ratio and the amount of nitrogen dilution. Schlieren photography was used to visualize the detonation front in the test-section, and soot foils were used to obtain the cellular structure. Schlieren imaging showed a curved detonation front that decoupled at about mid channel height, into a shock wave and trailing contact surface. Both the hydrogen-oxygen-nitrogen reactivity and the type of inert gas initially in the test-section affected the distance travelled by the detonation wave in the stratified layer. The mixture composition distribution within the test-section before ignition was obtained via a three-dimensional CFD simulation. The lateral extent of the cellular structure captured on the soot foil, coincided with the calculated inert gas mole fraction contour that corresponds to a sharp increase in the ZND induction zone length, e.g., 70% argon dilution for a stoichiometric hydrogen-oxygen predetonator mixture.     

Love wave propagation in piezoelectric layered structure with dissipation

We investigate analytically the effect of the viscous dissipation of piezoelectric material on the dispersive and attenuated characteristics of Love wave propagation in a layered structure, which involves a thin piezoelectric layer bonded perfectly to an unbounded elastic substrate. The effects of the viscous coefficient on the phase velocity of Love waves and attenuation are presented and discussed in detail. The analytical method and the results can be useful for the design of the resonators and sensors.     

Interference effects in wave propagation in periodically inhomogeneous media

Radiophysics Scientific-Research Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 32, No. 9, pp. 1144–1151, September, 1989.     

Sound scattering by a body in a planar layered waveguide

In the framework of the theory of integral equations, the problem of sound diffraction by pressure-release and acoustically stiff inhomogeneities of an oceanic waveguide is considered. The iteration method is used to obtain recurrent relations for the surface currents. The relations describe the diffraction process as a sequence of interactions between the body and the waveguide boundaries (multiple reflections). The validity condition for the zero-order approximation, which ignores multiple reflections, is formulated and physically justified.     

Wave propagation and vibration response of a periodically supported pipe conveying fluid

Propagation of free harmonic waves, in a periodically supported infinite pipe, has been studied. The presence of the Coriolis term in the equation of motion renders the phase velocity different for the positive and the negative going waves. Hence no classical normal modes (in the sense of standing modes) exist. Natural frequencies of a periodically supported finite pipe have been obtained by using the wave approach. The response of the infinite pipe to a convected harmonic pressure field has also been obtained. Owing to the difference in the phase velocities of the positive and the negative going free waves, the coincidence frequency depends on the direction of the convected loading. The static buckling or the divergence instability of such pipes has also been considered from the wave approach.     

Formulation and validation of a Ritz-based analytical model of high-frequency periodically layered isolators in compression

Periodically layered isolators exhibit transmissibility “stop bands” or frequency ranges in which there is very low transmissibility. A two-dimensional axisymmetric model was developed to accurately predict the location of these stop bands for isolators in compression. A Ritz approximation method was used to model the axisymmetric elastic behavior of layered cylindrical isolators. A modal analysis was performed for a single elastomer and metal layer combination or cell. A modal synthesis approach was then used to obtain a model of an n-celled isolator, from which overall isolator modal properties are determined. This model of the dynamic behavior of layered isolators was validated with experiments. Analytical and experimental transmissibilities are compared for test specimens having identical elastomer components, but different geometries and different numbers of cells. In all cases, experimental and analytical transmissibilities are in close agreement at frequencies ranging from zero to those associated with the initial roll-off of the stop bands. For three and four cell cases, minimum stop band analytical transmissibilities lie below the minimum experimental measurements, although an experimental noise floor imposed a minimum transmissibility measurement of approximately 1.4×10⁻⁴. Experiment suggests a practical isolator design could limit the minimum number of cells to three or four to ensure a pronounced stop band attenuation effect. In addition, analytical and experimental transmissibilities are compared for geometrically similar test specimens with differing elastomeric damping properties. The analytical and experimental results show that stop band effectiveness is not appreciably affected by the addition of modest damping.     

Dielectric response of a crystal with a damaged surface layer in the longitudinal-transverse splitting region

A model of the dielectric function of a surface layer formed under the mechanical treatment of the crystal surface is considered in the range of the lattice optical vibrations. An approach is proposed based on the continuous distribution of the dipole-active modes in order to take into account the dislocation effect. It is demonstrated that the model used allows one to describe satisfactorily the decrease in the reflectivity of polished SiC6H samples in the vicinity of the frequency of the transverse optical phonon.     

Localization in frequency for periodically kicked light propagation in a dispersive single-mode fiber

We show a special effect of localization in the temporal frequency domain of light pulses that propagate in a dispersive single-mode fiber in the presence of a time-periodic phase modulation that is repeatedly applied at equally spaced locations along the fiber. The effect is analogous to the dynamical localization that occurs for the quantum kicked rotor, which is similar to Anderson localization in disordered solids. The wave behavior eliminates the diffusive spread of sidebands (harmonics). The light propagation, which is described by a Schr?dinger-like propagation equation, can provide a new testing ground for the investigation of localization besides shedding light on technologically important pulse propagation in fibers and mode-locked lasers.