Three-dimensional non-linear coupling and dynamic tension in the large-amplitude free vibrations of arbitrarily sagged cables

This paper presents a model formulation capable of analyzing large-amplitude free vibrations of a suspended cable in three dimensions. The virtual work-energy functional is used to obtain the non-linear equations of three-dimensional motion. The formulation is not restricted to cables having small sag-to-span ratios, and is conveniently applied for the case of a specified end tension. The axial extensibility effect is also included in order to obtain accurate results. Based on a multi-degree-of-freedom model, numerical procedures are implemented to solve both spatial and temporal problems. Various numerical examples of arbitrarily sagged cables with large-amplitude initial conditions are carried out to highlight some outstanding features of cable non-linear dynamics by accounting also for internal resonance phenomena. Non-linear coupling between three- and two-dimensional motions, and non-linear cable tension responses are analyzed. For specific cables, modal transition phenomena taking place during in-plane vibrations and ensuing from occurrence of a dominant internal resonance are observed. When only a single mode is initiated, a higher or lower mode can be accommodated into the responses, making cable spatial shapes hybrid in some time intervals.     

Non-linear vibrations of cables in three dimensions,part I: Non-linear free vibrations

Analysis and results for non-linear free vibrations of both horizontal and inclined cables in three dimensions are presented. Sag-to-span ratios of the cables are not limited to being small. Computed results are presented for various geometrical and material parameters. The major findings are that the geometrical non-linearity may be of the stiffening type or the softening type, depending on the sag-to-span ratio, and the stiffness of out-of-plane vibrations is affected by the corresponding in-plane vibration near a resonant frequency due to non-linear coupling between out-of-plane and in-plane vibrations.     

Non-linear vibrations of cables considering loosening

A cable cannot resist the axial compressive force that may be induced during large amplitude vibrations. In this paper, the effect of cable loosening on non-linear vibrations of flat-sag cables is discussed by using the finite difference method that can express cable loosening. In the present method, flexural rigidity and damping of the cable are considered in the equations of motion of a cable in order to handle the numerical instability. The effect of cable loosening is evaluated explicitly in the present paper. Furthermore, non-linear vibration properties are evaluated for various parameters under periodic and step vertical loading. The effect of cable loosening on response under vertical periodic time-varying load is small and it is possible for the sag-to-span ratio to roughly equal the ratio for modal transition. The loosening under the vertical step loading in the direction opposite to the gravity appears at almost the same sag-to-span ratio.     

Double Loops and Pitchfork Symmetry Breaking Bifurcations of Optical Solitons in Nonlinear Fractional Schrödinger Equation with Competing Cubic-Quintic Nonlinearities

Symmetry breaking bifurcations of solitons are investigated in framework of a nonlinear fractional Schrödinger equation (NLFSE) with competing cubic-quintic nonlinearity. Some prototypical characteristics of the symmetry breaking, featured by transformations of symmetric and antisymmetric soliton families into asymmetric ones, are found. Stable asymmetric solitons emerge from unstable symmetric and antisymmetric ones by way of two different symmetry breaking scenarios. A twisting branch, featured with double loops bifurcation, bifurcates off from the base branch of symmetric soliton solutions and crosses it, then merges into the base branch driven by the competitive nonlinear effect. A supercritical pitchfork bifurcation is bifurcated from the branch of antisymmetric soliton solutions and gives rise to a supercritical pitchfork bifurcation. Stability of the soliton families is explored by linear stability analysis. With the increase of the Lévy index, stability region induced by the twisting loops bifurcation is expanded. However, stability region of the pitchfork bifurcation is shrunk on the parameter plane of the Lévy index and the soliton power.     

Surface solitons in trilete lattices

Fundamental solitons pinned to the interface between three semi-infinite one-dimensional nonlinear dynamical chains, coupled at a single site, are investigated. The light propagation in the respective system with the self-attractive on-site cubic nonlinearity, which can be implemented as an array of nonlinear optical waveguides, is modeled by the system of three discrete nonlinear Schrödinger equations. The formation, stability and dynamics of symmetric and asymmetric fundamental solitons centered at the interface are investigated analytically by means of the variational approximation (VA) and in a numerical form. The VA predicts that two asymmetric and two antisymmetric branches exist in the entire parameter space, while four asymmetric modes and the symmetric one can be found below some critical value of the inter-lattice coupling parameter—actually, past the symmetry-breaking bifurcation. At this bifurcation point, the symmetric branch is destabilized and two new asymmetric soliton branches appear, one stable and the other unstable. In this area, the antisymmetric branch changes its character, getting stabilized against oscillatory perturbations. In direct simulations, unstable symmetric modes radiate a part of their power, staying trapped around the interface. Highly unstable asymmetric modes transform into localized breathers traveling from the interface region across the lattice without significant power loss.     

Free vibration analysis of cantilever plates by the method of superposition

The method of superposition is employed to analyze the first five symmetric and antisymmetric free vibration modes of a cantilever plate for a wide range of aspect ratios. It is shown that this method provides a simple, straightforward and highly accurate means of solution for this family of problems. Convergence to exact values is shown to be remarkably rapid. The first two symmetric and antisymmetric modal shapes for a square plate are accurately described by means of contour line drawings. The numerous advantages of this method over previously used methods are discussed. It is shown that it lends itself readily to the entire family of rectangular plates with classical edge conditions: i.e., clamped, simply supported, and free. Its applicability to a wide family of rectangular plates with boundary conditions other than the classical type is also discussed.     

Photogalvanic current in a double quantum well

A double quantum well affected by external alternating electric field with in- and out-of-plane components is studied. This field causes transitions between near-degenerate states located in different wells. The phototransitions are accompanied by the in-plane momentum nonconservation caused by the impurity scattering. We study the in-plane stationary current due to the lack of the in-plane symmetry of these indirect phototransitions. It is shown that the value and direction of the current are determined by the polarization of light. The linear and circular photogalvanic coefficients are found. When the photon energy approaches the distance between subbands these coefficients have their symmetric and antisymmetric resonance behaviors, respectively.     

各向异性表面张力对定向凝固中共晶生长形态稳定性的影响

研究各向异性表面张力对定向凝固中共晶生长形态稳定性的影响.应用多重变量展开法导出了共晶界面表达式和扰动振幅的变化率满足的色散关系.结果表明,共晶生长系统有两种整体不稳定性机理:由非震荡导致的"交换稳定性"机理和由震荡导致的"整体波动不稳定性"机理.震荡有四种典型模式,即:反对称-反对称(AA-),对称-反对称(SA-)、反对称-对称(AS-)和对称-对称(SS-)模式.稳定性分析表明:共晶界面形态稳定性取决于Peclet数ε的某一个临界值ε_*,当ε大于临界值ε_*时,共晶界面形态不稳定;当ε小于临界值ε_*时,共晶界面形态稳定.随着各向异性表面张力增大,对应于AA-,SA-和SS-模式的临界值ε_(aa*),ε_(sa*)和ε_(ss*)随之减小,表明各向异性表面张力减小这三种模式的稳定性区域;然而,随着各向异性表面张力增大,对应于AS-模式的临界值ε_(as*)随之增大,表明各向异性表面张力增大AS-模式的稳定性区域.     

Damage detection in composite panels based on mode-converted Lamb waves sensed using 3D laser scanning vibrometer

This paper introduces damage identification approach based on guided ultrasonic waves and 3D laser Doppler vibrometry. The method is based on the fact that the symmetric and antisymmetric Lamb wave modes differ in amplitude of the in-plane and out-of-plane vibrations. Moreover, the modes differ also in group velocities and normally they are well separated in time. For a given time window both modes can occur simultaneously only close to the wave source or to a defect that leads to mode conversion. By making the comparison between the in-plane and out-of-plane wave vector components the detection of mode conversion is possible, allowing for superior and reliable damage detection. Experimental verification of the proposed damage identification procedure is performed on fuel tank elements of Reusable Launch Vehicles designed for space exploration. Lamb waves are excited using low-profile, surface-bonded piezoceramic transducers and 3D scanning laser Doppler vibrometer is used to characterize the Lamb wave propagation field. The paper presents theoretical background of the proposed damage identification technique as well as experimental arrangements and results.     

Symmetric and antisymmetric vector solitons for the fractional quadric-cubic coupled nonlinear Schrödinger equation

The fractional quadric-cubic coupled nonlinear Schrödinger equation is concerned, and vector symmetric and antisymmetric soliton solutions are obtained by the square operator method. The relationship between the Lévy index and the amplitudes of vector symmetric and antisymmetric solitons is investigated. Two components of vector symmetric and antisymmetric solitons show a positive and negative trend with the Lévy index, respectively. The stability intervals of these solitons and the propagation constants corresponding to the maximum and minimum instability growth rates are studied. Results indicate that vector symmetric solitons are more stable and have better interference resistance than vector antisymmetric solitons.     

SUPER AND COMBINATORIAL HARMONIC RESPONSE OF FLEXIBLE ELASTIC CABLES WITH SMALL SAG

The paper deals with the analysis of cables in stayed bridges and TV-towers, where the excitation is caused by harmonically varying in-plane motions of the upper support point with the amplitude U. Such cables are characterized by a sag-to-chord-length ratio below &0uml;02, which means that the lowest circular eigenfrequencies for in-plane and out-of-plane eigenvibrations, ω₁and ω₂, are closely separated. The dynamic analysis is performed by a two-degree-of-freedom modal decomposition in the lowest in-plane and out-of-plane eigenmodes. Modal parameters are evaluated based on the eigenmodes for the parabolic approximation to the equilibrium suspension. Superharmonic components of the ordern , supported by the parametric terms of the excitation and the non-linear coupling terms, are registered in the response for circular frequency ω?ω₁/n. At moderate U, the cable response takes place entirely in the static equilibrium plane. At larger amplitudes the in-plane response becomes unstable and a coupled whirling superharmonic component occurs. In the paper a first order perturbation solution to the superharmonic response is performed based on the averaging method. For ω?(m/n)ω₁, m<n, the geometrical non-linear restoring forces gives rise to a substantial combinatorial harmonic component with the circular frequency (n/m)ω. Both entirely in-plane and coupled in-plane and out-of-plane responses occur. Based on an initial frequency analysis of the response, an analytical model for these vibrations is formulated with emphasis on superharmonics of the order n=3 and combinatorial harmonics of the order (n, m)=(3,2). All analytical solutions have been verified by direct numerical integration of the modal equations of motion.     

Trapped states and transitions between them in double-well pseudopotentials

We analyze a model of a double-well pseudopotential (DWPP), based in the 1D Gross-Pitaevskii equation with a spatially modulated self-attractive nonlinearity. In the limit case when the DWPP structure reduces to the local nonlinearity coefficient represented by a set of two delta-functions, analytical solutions are obtained for symmetric, antisymmetric and asymmetric states. In this case, the transition from symmetric to asymmetric states, i.e., a spontaneous-symmetry-breaking (SSB) bifurcation, is subcritical. Numerical analysis demonstrates that the symmetric states are stable up to the SSB point, while emerging asymmetric states (together with all antisymmetric solutions) are unstable in the delta-function model. In a general model, which features a finite width of the nonlinear-potential wells, the asymmetric states quickly become stable, simultaneously with the switch of the bifurcation into the supercritical type. Antisymmetric solutions may also enjoy stabilization in the finite-width DWPP structure, demonstrating a bistability involving the asymmetric states. The symmetric states require a finite norm for their existence. A full diagram for the existence and stability of the trapped states is produced for the general model.     

Applying a Mode Selector to Improve the Pulse-Compression Performance of Asymmetric-Coupled-Waveguide-Based Dispersion Compensators

An InGaAsP slab-type asymmetric-coupled-waveguide-based dispersion compensator with a mode selector has been designed and fabricated. The mode selector is necessary to select either a symmetric [with a positive group-velocity dispersion (GVD)] or antisymmetric (with a negative GVD) supermode. These supermodes exist simultaneously in the dispersion-compensation region of the device. Pulse-compression experiments were used to test the dispersion compensator, evaluating the function of the mode selector. A theoretical study of the experimental results shows that the mode selector obtains a very strong selectivity (nearly 100%) for the antisymmetric supermode.     

Solitons in a system of three linearly coupled fiber gratings

We introduce a model of three parallel-coupled nonlinear waveguiding cores equipped with Bragg gratings (BGs), which form an equilateral triangle. The most promising way to create multi-core BG configuration is to use inverted gratings, written on internal surfaces of relatively broad holes embedded in a photonic-crystal-fiber matrix. The objective of the work is to investigate solitons and their stability in this system. New results are also obtained for the earlier investigated dual-core system. Families of symmetric and antisymmetric solutions are found analytically, extending beyond the spectral gap in both the dual- and tri-core systems. Moreover, these families persist in the case (strong coupling between the cores) when there is no gap in the systems linear spectrum. Three different types of asymmetric solitons are found (by means of the variational approach and numerical methods) in the tri-core system. They exist only inside the spectral gap, but asymmetric solitons with nonvanishing tails are found outside the gap as well. Stability of the solitons is explored by direct simulations, and, for symmetric solitons, in a more rigorous way too, by computation of eigenvalues for small perturbations. The symmetric solitons are stable up to points at which two types of asymmetric solitons bifurcate from them. Beyond the bifurcation, one type of the asymmetric solitons is stable, and the other is not. Then, they swap their stability. Asymmetric solitons of the third type are always unstable. When the symmetric solitons are unstable, their instability is oscillatory, and, in most cases, it transforms them into stable breathers. In both the dual- and tri-core systems, the stability region of the symmetric solitons extends far beyond the gap, persisting in the case when the system has no gap at all. The whole stability region of antisymmetric solitons (a new type of solutions in the tri-core system) is located outside the gap. Thus, solitons in multi-core BGs can be observed experimentally in a much broader frequency band than in the single-core one, and in a wider parameter range than it could be expected. Asymmetric delocalized solitons, found outside the spectral gap, can be stable too.Received: 13 August 2003PACS: 42.81.Dp Propagation, scattering, and losses; solitons - 42.65.Tg Optical solitons; nonlinear guided waves - 05.45.Yv Solitons     

Experimental evidence of surface-plasmon coupling in anisotropic hollow nanoparticles

We report on the investigation of surface-plasmon excitation of anisotropic WS(2) hollow nanoparticles in a near-field geometry by means of a scanning transmission electron microscope. The shell thickness influence on the electron-energy-loss-spectroscopy spectra is experimentally observed and is analyzed within a classical dielectric formalism. As for the isotropic case, we evidence one symmetric (tangential) and one antisymmetric (radial) mode. We point out the intriguing fact that, for the anisotropic case, one can relate these modes to the interband transition of the in-plane component of the dielectric tensor and to the bulk-plasmon energy of the out-of-plane component.     

Lamb wave propagation in magnetoelectroelastic plates

Based on the three-dimensional linear elastic equations and magnetoelectroelastic constitutive relations, propagation of symmetric and antisymmetric Lamb waves in an infinite magnetoelectroelastic plate is investigated. The coupled differential equations of motion are solved, and the phase velocity equations of symmetric and antisymmetric modes are obtained for both electrically and magnetically open and shorted cases. The dispersive characteristic of wave propogation is explored. The mechanical, electric and magnetic responses of the lowest symmetric and antisymmetric Lamb wave modes are discussed in detailed. Obtained results are valuable for the analysis and design of broadband magnetoelectric transducer using composite materials.     

Absorption of zero Lamb waves in an elastic layer by mechanical resonators with friction

The propagation of zero Lamb waves in a plate with mechanical resonators attached to its surfaces is studied. It is shown that, in a plate that is single-mode for symmetric (antisymmetric) waves, the zero symmetric (antisymmetric) Lamb wave can be absorbed by mechanical resonators with a certain friction. The single-mode (for symmetric or antisymmetric waves) plate can be not thin compared to the wavelength of the transverse wave.     

Photogalvanic current in electron gas over a liquid helium surface

We study the stationary surface photocurrent in 2D electron gas near the helium surface. Electron gas is assumed to be attracted to the helium surface due to the image attracting force and an external stationary electric field. The alternating electric field has both vertical and in-plane components. The photogalvanic effect originates from the periodic transitions of electrons between quantum subbands in the vertical direction caused by a normal component of the alternating electric field accompanied by synchronous in-plane acceleration/deceleration due to the electric field in-plane component. The effect needs vertical asymmetry of the system. The problem is considered taking into account a friction caused by the electron-ripplon interaction. The photocurrent resonantly depends on the field frequency. The resonance occurs at field frequencies close to the distance between well subbands. The resonance is symmetric or antisymmetric depending on the kind (linear or circular) of polarization.     

Families of spatial solitons in a two-channel waveguide with the cubic-quintic nonlinearity

We present eight types of spatial optical solitons which are possible in a model of a planar waveguide that includes a dual-channel trapping structure and competing (cubic-quintic) nonlinearity. The families of trapped beams include “broad” and “narrow” symmetric and antisymmetric solitons, composite states, built as combinations of broad and narrow beams with identical or opposite signs (“unipolar” and “bipolar” states, respectively), and “single-sided” broad and narrow beams trapped, essentially, in a single channel. The stability of the families is investigated via the computation of eigenvalues of small perturbations, and is verified in direct simulations. Three species-narrow symmetric, broad antisymmetric, and unipolar composite states-are unstable to perturbations with real eigenvalues, while the other five families are stable. The unstable states do not decay, but, instead, spontaneously transform themselves into persistent breathers, which, in some cases, demonstrate dynamical symmetry breaking and chaotic internal oscillations. A noteworthy feature is a stability exchange between the broad and narrow antisymmetric states: in the limit when the two channels merge into one, the former species becomes stable, while the latter one loses its stability. Different branches of the stationary states are linked by four bifurcations, which take different forms in the model with the strong and weak coupling between the channels.     

Helimagnetism in MnP-type compounds: MnP,FeP, CrAs and CrAs1−xSbx mixed crystals

The solid solution CrAs_1?xSb_x has been investigated by neutron diffraction at various temperatures. The phase boundary between mixed crystals with MnP-structure and those with NiAs-structure moves from 59 mol% CrAs at room temperature to 48 mol% CrAs at liquid helium temperature. The mixed crystals with NiAs-type structure at 4.2K have the collinear magnetic structure of CrSb. Samples having the MnP-type structure exhibit a “double spiral” spin structure like CrAs. The variation of the magnetic moment and the spiral structure have been studied. Using neutron diffraction data for the magnetic propagation vector and the phase difference of the two helices, the signs and the ratios of the exchange integrals are discussed in a Heisenberg model. The stability regions in parameter space are determined by a matrix method for the ferromagnetic mode observed in MnP above 50 K and for the helical modes observed in MnP below 50 K, and in FeP, CrAs and CrAs_1?xSb_x. We have also considered the possibility of antisymmetric and symmetric exchange between nearest neighbours only, using a group theoretical approach.The high ratios of antisymmetric to symmetric exchange would be necessary to explain the observed helical structures preclude however antisymmetric exchange as a dominant factor.