23,614 research outputs found

    Solitary waves on a ferrofluid jet

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    The propagation of axisymmetric solitary waves on the surface of an otherwise cylindrical ferrofluid jet subjected to a magnetic field is investigated. An azimuthal magnetic field is generated by an electric current flowing along a stationary metal rod which is mounted along the axis of the moving jet. A numerical method is used to compute fully-nonlinear travelling solitary waves and predictions of elevation waves and depression waves by Rannacher & Engel (2006) using a weakly-nonlinear theory are confirmed in the appropriate ranges of the magnetic Bond number. New nonlinear branches of solitary wave solutions are identified. As the Bond number is varied, the solitary wave profiles may approach a limiting configuration with a trapped toroidal-shaped bubble, or they may approach a static wave (i.e. one with zero phase speed). For a sufficiently large axial rod, the limiting profile may exhibit a cusp

    Coupling of Highly Nonlinear Waves with Linear Elastic Media

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    This paper reports a fundamental study of the coupling between highly nonlinear waves, generated in a one dimensional granular chain of particles, with linear elastic media, for the development of a new Non Destructive Evaluation and Structural Health Monitoring (NDE/SHM) paradigm. We design and use novel acoustic actuators to excite compact highly nonlinear solitary waves in a one-dimensional linear elastic rod and investigate the pulse propagation across the interface. To model the actuator and rod system we use Finite Element Analysis (Abaqus) and obtain excellent agreement between the experimental observations and the numerical results. We also study the response of the system to the presence of defects (cracks) in the steel rod, by comparing the wave propagation properties in pristine and cracked test objects. The obtained results encourage the use of highly nonlinear waves as an effective tool for developing a new, viable NDE/SHM method

    Non-sinusoidal magnetoelastic waves in structural members

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    The paper discuses propagation of longitudinal waves in a homogeneous nonlinear superconducting rod placed in strong magnetic field. By using the nonlinear Bishop model the equations of magnetoelasticity for the rod performing longitudinal oscillations has been derived. The evolution of nonlinear magnetoelastic waves is studied. As a result the conditions of formation of intense periodic magnetoelastic waves and magnetoelastic solitons are established

    H¹-PERTURBATIONS OF SMOOTH SOLUTIONS FOR A WEAKLY DISSIPATIVE HYPERELASTIC-ROD WAVE EQUATION

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    We consider a weakly dissipative hyperelastic-rod wave equation (or weakly dissipative Camassa-Holm equation) describing nonlinear dispersive dissipative waves in compressible hyperelastic rods. By fixed a smooth solution, we establish the existence of a strongly continuous semigroup of global weak solutions for any initial perturbation from H1(R)H^1({\mathbb R}). In particular, the supersonic solitary shock waves [8] are included in the analysis

    Traveling waves for a dissipative modified KdV equation

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    AbstractIn this paper we consider a dispersive–dissipative nonlinear equation which can be regarded as a dissipation perturbed modified KdV equation, governing the evolution of long waves in an elastic rod immersed inside a viscoelastic medium. Using geometric singular perturbation theory, a construction of traveling waves for the equation is shown. This also is illustrated by presenting some numerical calculations

    Coupling of Highly Nonlinear Waves with Linear Elastic Media

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    This paper reports a fundamental study of the coupling between highly nonlinear waves, generated in a one dimensional granular chain of particles, with linear elastic media, for the development of a new Non Destructive Evaluation and Structural Health Monitoring (NDE/SHM) paradigm. We design and use novel acoustic actuators to excite compact highly nonlinear solitary waves in a one-dimensional linear elastic rod and investigate the pulse propagation across the interface. To model the actuator and rod system we use Finite Element Analysis (Abaqus) and obtain excellent agreement between the experimental observations and the numerical results. We also study the response of the system to the presence of defects (cracks) in the steel rod, by comparing the wave propagation properties in pristine and cracked test objects. The obtained results encourage the use of highly nonlinear waves as an effective tool for developing a new, viable NDE/SHM method

    Propagation of extensional waves in a piezoelectric semiconductor rod

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    We studied the propagation of extensional waves in a thin piezoelectric semiconductor rod of ZnO whose c-axis is along the axis of the rod. The macroscopic theory of piezoelectric semiconductors was used which consists of the coupled equations of piezoelectricity and the conservation of charge. The problem is nonlinear because the drift current is the product of the unknown electric field and the unknown carrier density. A perturbation procedure was used which resulted in two one-way coupled linear problems of piezoelectricity and the conservation of charge, respectively. The acoustic wave and the accompanying electric field were obtained from the equations of piezoelectricity. The motion of carriers was then determined from the conservation of charge using a trigonometric series. It was found that while the acoustic wave was approximated by a sinusoidal wave, the motion of carriers deviates from a sinusoidal wave qualitatively because of the contributions of higher harmonics arising from the originally nonlinear terms. The wave crests become higher and sharper while the troughs are shallower and wider. This deviation is more pronounced for acoustic waves with larger amplitude
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