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1.
The chaotic escape of a nonlinearly damped oscillator excited by a periodic string of symmetric pulses from a cubic potential
well is investigated. Analytical (Melnikov analysis) and numerical results show that chaotic escapes are typically induced
over a wide range of parameters by hump-doubling of an external excitation which is initially formed by a periodic string
of single-humped symmetric pulses. The role of a nonlinear damping term, proportional to the nth power of the velocity, on the hump-doubling scenario is also discussed. 相似文献
2.
In this paper N-soliton propagations for the Calogero–Bogoyavlenskii–Schiff (CBS) equation in an inhomogeneous media which describes the long nonautonomous waves are obtained. Here attention is focused to study the effect of the dispersion coefficient on the propagation solitons waves. It is found that N-bright-dark solitons are produced by periodic or coupled periodic and pulses waves. Solitons waves are propagated for two and three pulses with periodic oscillating. Further, the double-periodic and solitary waves are dispersive to broken-solitons waves for the graded-index with oscillating reflection components. These results are useful for the application for long-distance telecommunication and optical fiber. 相似文献
3.
We investigate the stabilization of periodic orbits of one-dimensional discrete maps by using a proportional feedback method
applied in the form of pulses. We determine a range of the parameter μ values representing the strength of the feedback for which all positive solutions of the controlled equation converge to
a periodic orbit. 相似文献
4.
5.
A pulsed Rayleigh surface wave of prescribed shape is incident on a cylindrical cavity which is parallel to both the plane free surface and the plane wave front. Multiple reflections at the cylindrical and plane free surface are considered and the resulting displacements and stress components are calculated in the surrounding of the cavity by approximately summing infinite double sums. Use is made of the stationary loading case simulated by a periodic train of wave pulses and its time Fourier series representation and of expansions of all incident and reflected waves in terms of cylindrical wave functions. For reflection, the free surface of the half-space is approximated by a fictitious convex (or concave) cylindrical surface of “large” radius. The wave pattern due to a single pulse loading is constructed from the stationary solution by enforcing homogeneous initial conditions in the half-space ahead of the single loading pulse and by prescribing a wide spacing in the periodically set-forth train of pulses. The numerical results for stresses and dynamic stress magnification factors are especially useful for the interpretation of recent measurements in dynamic photoelasticity. 相似文献
6.
7.
K.-W.Chow 《Acta Mechanica Sinica》2011,27(5):620-626
Exact doubly periodic standing wave patterns of the Davey-Stewartson (DS) equations are derived in terms of rational expressions of elliptic functions.In fluid mechanics,DS equations govern the evolution of weakly nonlinear,free surface wave packets when long wavelength modulations in two mutually perpendicular,horizontal directions are incorporated.Elliptic functions with two different moduli (periods) are necessary in the two directions.The relation between the moduli and the wave numbers constitutes the dispersion relation of such waves.In the long wave limit,localized pulses are recovered. 相似文献
8.
The aim of this work is to study the transmission of stress waves in an impulsively forced semi-infinite repetitive system of linear layers which are coupled by means of strongly nonlinear coupling elements. Only primary pulse transmission and reflection at each nonlinear element is considered. This permits the reduction of the problem to an infinite set of first-order strongly nonlinear ordinary differential equations. A subset of these equations is solved both analytically and numerically. For a system possessing clearance nonlinearities it is found that the primary transmitted pulse propagates to only a finite number of layers, and that further transmission of energy to additional layers can occur only through time-delayed secondary pulses or does not occur at all. Hence, clearance nonlinearities in a periodic layered system can lead to energy entrapment in the leading layers. An alternative continuum approximation methodology is also outlined which reduces the problem of primary pulse transmission to the solution of a single strongly nonlinear partial differential equation. The use of the continuum approximation for studying maximum primary pulse penetration in the system with clearance nonlinearities is discussed. 相似文献
9.
In this paper, convergent, multi-infinite, series solutions are derived for the homoclinic orbits of a canonical fourth-order ODE system, in both reversible and non-reversible cases. This ODE includes traveling-wave reductions of many important non-linear PDEs or PDE systems, for which these analytical solutions would correspond to regular or localized pulses of the PDE. As such, the homoclinic solutions derived here are clearly topical, and they are shown to match closely to earlier results obtained by homoclinic numerical shooting. In addition, the results for the non-reversible case go beyond those that have been typically considered in analyses conducted within bifurcation-theoretic settings. We also comment on generalizing the treatment here to parameter regimes where solutions homoclinic to exponentially small periodic orbits are known to exist, as well as another possible extension placing the solutions derived here within the framework of a comprehensive categorization of ALL possible traveling-wave solutions, both smooth and non-smooth, for our governing ODE. 相似文献
10.
One-dimensional pulse propagation in composite materials modelled as interpenetrating solid continua
Matthew F. McCarthy 《Wave Motion》1982,4(3):221-242
Modulated simple wave theory is used to study the propagation of one dimensional, finite amplitude, high frequency pulses in composites which are modelled as interpenetrating solid continua with two identifiable constituents. The equations which govern the propagation of high frequency pulses are derived and their properties are studied in detail. Particular attention is paid to small amplitude high frequency pulses and results for pulses propagating into composites of a rather general nature are presented. The special results which hold for pulses which propagate into uniform regions are discussed in detail. The influence of the structure of the composite on pulse propagation is also assessed by examining pulse propagation in a number of different types of composite. 相似文献
11.
J. I. Ramos 《国际流体数值方法杂志》1995,21(9):735-761
Perturbation methods are used to obtain the one-dimensional, asymptotic equations that govern the fluid dynamics of slender, thin, inviscid, incompressible, axisymmetric, irrotational, annular liquid jets from the Euler equations. It is shown that, depending on the magnitude of the Weber number, two flow regimes are possible: an inertia-dominated one corresponding to large Weber numbers, and a capillary regime for Weber numbers of the order of unity. The steady equations governing these two regimes have analytical solutions for the liquid's axial velocity component and require a numerical integration to determine the jet's mean radius for inertia-dominated jets. The one-dimensional equations derived in this paper are shown to be particular cases of a hydraulic model for annular liquid jets, and this model is used to determine the effects of gravity modulation on the unsteady fluid dynamics of annular liquid jets in the absence of mass injection into the volume enclosed by the jet and mass absorption. It is shown that both the convergence length and the pressure coefficient are periodic functions of time which have the same period as that of the gravity modulation, but undergo large variations as the amplitude, frequency and width of gravitational pulses is varied. 相似文献
12.
The determination of periodic solutions is an essential step in the study of dynamic systems. If some of the generalized coordinates
describing the configuration of a system are angular positions relative to certain reference axes, the associated periodic
motions divide into two types: oscillatory and rotary periodic motions. For an oscillatory periodic motion, all the generalized
coordinates are periodic in time. On the other hand, for a rotary periodic motion, some angular coordinates may have unbounded
magnitude due to the persistent circulation about their pivots. In this case, although the behaviour of the system is periodic
physically, those angular coordinates are not periodic in time. Although various effective methods have been developed for
the determination of oscillatory periodic motion, the rotary periodic motion can only be determined by brute force integration.
In this paper, the incremental harmonic balance (IHB) method is modified so that rotary periodic motions can be determined
as well as oscillatory periodic motions in a unified formulation. This modified IHB method is applied to a practical device,
a rotating disk equipped with a ball-type balancer, to show its effectiveness. 相似文献
13.
Matthew F. McCarthy 《Archive for Rational Mechanics and Analysis》1992,120(3):285-303
The propagation of finite pulses of high-frequency in a suspension composed of a distribution of incompressible particles in an incompressible fluid is examined by using the technique of modulated simple-wave theory. The differential equation which governs the propagation of high-frequency pulses is derived and its consequences are examined. The properties of small amplitude high-frequency pulses are examined in detail. 相似文献
14.
Numerical simulations of the evolution equation [14] for thickness of a film flowing down a vertical fiber are presented. Solutions with periodic boundary conditions on extended axial intervals develop trains of pulse-like structures. Typically, a group of several interacting pulses (or a solitary pulse) is bracketed by spans of nearly uniform thinned film and is virtually isolated: The evolution of such a section is modeled as a solution with periodic boundary conditions on the corresponding, comparatively short, interval. Single-pulse sections are steady-shape traveling waveforms (cells of shorter-period solutions). The collision of two pulses can be either a particle-like elastic rebound, or—and only if a control parameter S (proportional to the average thickness) exceeds a certain critical value, S
c 1—a deeply inelastic coalescence. A pulse which grows by a cascade of coalescences is associated with large drops observed in experiments by Quéré [39] and our S
c is in excellent agreement with its laboratory value.This research was supported in part by U.S. DOE under Grant DE-FG05-90ER14100. 相似文献
15.
Li Fengming Wang Yuesheng Chen Ali 《Acta Mechanica Solida Sinica》2006,19(1):50-57
The wave propagation in periodic and disordered periodic piezoelectric rods is studied in this paper. The transfer matrix between two consecutive unit cells is obtained according to the continuity conditions. The electromechanical coupling of piezoelectric materials is considered. According to the theory of matrix eigenvalues, the frequency bands in periodic structures are studied. Moreover, by introducing disorder in both the dimensionless length and elastic constants of the piezoelectric ceramics, the wave localization in disordered periodic structures is also studied by using the matrix eigenvalue method and Lyapunov exponent method. It is found that tuned periodic structures have the frequency passbands and stopbands and localization phenomenon can occur in mistuned periodic structures. Furthermore, owing to the effect of piezoelectricity, the frequency regions for waves that cannot propagate through the structures are slightly increased with the increase of the piezoelectric constant. 相似文献
16.
The propagation of longitudinal and flexural waves in axisymmetric circular cylindrical shells with periodic circular axial curvature is studied using a finite element method previously developed by the authors. Of primary interest is the coupling of these wave modes due to the periodic axial curvature which results in the generation of two types of stop bands not present in straight circular cylinders. The first type is related to the periodic spacing and occurs independently for longitudinal and flexural wave modes without coupling. However, the second type is caused by longitudinal and flexural wave mode coupling due to the axial curvature. A parametric study is conducted where the effects of cylinder radius, degree of axial curvature, and periodic spacing on wave propagation characteristics are investigated. It is shown that even a small degree of periodic axial curvature results in significant stop bands associated with wave mode coupling. These stop bands are broad and conceivably could be tuned to a specific frequency range by judicious choice of the shell parameters. Forced harmonic analyses performed on finite periodic structures show that strong attenuation of longitudinal and flexural motion occurs in the frequency ranges associated with the stop bands of the infinite periodic structure. 相似文献
17.
《European Journal of Mechanics - A/Solids》2002,21(2):333-346
The questions of a dynamical stability and instability of soliton-like solutions (solitary pulses) of the Hamiltonian equations, describing planar waves in nonlinear elastic composites are considered, both in the presence as well as in the absence of the anisotropy. In the anisotropic case one has the slow and the fast two-parametric soliton families on the background of the quiescent state. In the absence of the anisotropy these two families coalesce into the unique three parametric family. It was shown recently that solitary pulses of the slow family in the anisotropic composite and pulses in the isotropic composite are stable when their speeds lie inside a certain range, the so-called range of stability. In the present paper, on the basis of numerical solving of the Cauchy problem for the basic governing equations, the classification is given of the types of instability of solitary pulses from the fast family for all range of speeds as well as in the case of the slow family and in the isotropic case, when the speeds of the pulses lie without the range of stability. The first type of instability is the blow-up instability for the slow anisotropic and isotropic pulses, living without the range of stability and also for high amplitude fast anisotropic pulses. The second type of instability is the instability resulting in energy exchange between the components of strain tensor for low amplitude fast anisotropic solitary pulses. The reasons of the both types of instability are discussed in detail.The interaction between the pairs of solitary pulses of different nature is investigated both analytically as well as numerically. It is found out that solitary pulses having the different polarization, i.e. different sign of amplitudes, can form bound states, oscillating about the common center, subjected to a motion with a constant speed, approximately equal to the average of speeds of two pulses when they are far apart. 相似文献
18.
Interaction of forced and self-sustained vibrations of one disk rotor is described by nonlinear finite-degree-of-freedom dynamical system. The shaft of the rotor is supported by two journal bearings. The combination of the shooting technique and the continuation algorithm is used to study the rotor periodic vibrations. The Floquet multipliers are calculated to analyze periodic vibrations stability. The results of periodic motions analysis are shown on the frequency response. The quasi-periodic motions are investigated. These nonlinear vibrations coexist with the periodic forced vibrations. 相似文献
19.
A novel dynamic compressive experimental technique has been developed based on a split Hopkinson pressure bar. This new method
dynamically loads the ceramic specimen by two consecutive stress pulses. The first pulse determines the dynamic response of
the intact ceramic materiaal and then crushes the specimen, and the second pulse determines the dynamic compressive constitutive
behavior of the ceramic rubble. Precise pulse shaping ensures that the specimen deforms at nearly constant strain rates under
dynamic stress equilibrium during the loading by both stress pulses. Pulse shaping also controls the amplitudes of loading
pulses, the values of strain rates, the maximum strains in the rubble specimens, and the proper separation time between the
two loading pulses. The feasibility of the new technique is demonstrated by the experimental results obtained on an AD995
alumina. 相似文献
20.
In this paper, the effect of impulsive perturbation on enzyme kinetics is investigated. The impulsive perturbation is affected by introducing periodic constant input. The dynamical behavior of system is simulated and bifurcation diagrams are obtained. The results show that impulsive perturbation can easily give rise to complex dynamics, which includes: quasi-periodic oscillation, periodic doubling cascade, periodic halving cascade, attractor crisis and chaotic bands with periodic windows. 相似文献