Journal ArticleDOI
Resonantly forced surface waves in a circular cylinder
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In this paper, a weakly nonlinear, weakly damped response of the free surface of a liquid in a vertical circular cylinder that is subjected to a simple harmonic, horizontal translation is examined by extending the corresponding analysis for free oscillations.Abstract:
The weakly nonlinear, weakly damped response of the free surface of a liquid in a vertical circular cylinder that is subjected to a simple harmonic, horizontal translation is examined by extending the corresponding analysis for free oscillations. The problem is characterized by three parameters, α, β, and d/a, which measure damping, frequency offset (driving frequency–natural frequency), and depth/radius. The asymptotic (t↑∞) response may be any of: (i) harmonic (at the driving frequency) with a nodal line transverse to the plane of excitation (planar harmonic); (ii) harmonic with a rotating nodal line (non-planar harmonic); (iii) a periodically modulated sinusoid (limit cycle); (iv) a chaotically modulated sinusoid. It appears, from numerical integration of the evolution equations, that only motions of type (i) and (ii) are possible if 0.30 < d/a < 0.50, but that motions of type (iii) and (iv) are possible for all other d/a in some interval (or intervals) of β if α is sufficiently small. Only motion of type (i) is possible if α exceeds a critical value that depends on d/a.read more
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Book ChapterDOI
Liquid Sloshing Dynamics: Weakly nonlinear lateral sloshing
TL;DR: The linear theory of liquid sloshing is adequate for determining the natural frequencies and wave height of the free surface under translational excitation, but it does not take into account the important vertical displacement of the center of gravity of the liquid for large amplitudes of free-surface motion as discussed by the authors.
Book ChapterDOI
Liquid Sloshing Dynamics: Nonlinear interaction under external and parametric excitations
Journal ArticleDOI
Parametric resonance in low-frequency magnetic stirring
TL;DR: In this article, the effect of an alternating magnetic field of low frequency ω on a cylindrical tank of liquid metal was analyzed and the stability regions associated with this system were discussed and it was shown that the most easily excited transition to a non-axisymmetric mode is subharmonic.
Journal ArticleDOI
Nonlinear liquid oscillation in a cylindrical tank with an eccentric core barrel
TL;DR: In this paper, the nonlinearity of the liquid surface oscillation is considered in the response analysis of the sloshing motion in a partially filled cylindrical tank with an eccentric core barrel.
Journal ArticleDOI
On a periodically forced, weakly damped pendulum. Part 2: Horizontal forcing
Peter J. Bryant,John W. Miles +1 more
TL;DR: In this paper, phase-locked solutions of the differential equation governing planar motion of a weakly damped pendulum driven by horizontal, periodic forcing of the pivot with maximum acceleration eg and dimensionless frequency ω are considered.
References
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Journal ArticleDOI
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Journal ArticleDOI
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TL;DR: In this article, the weakly nonlinear, resonant response of a damped, spherical pendulum (length l, damping ratio δ, natural frequency ω 0 ) to the planar displacement e l cos ω t (e ⪡ 1) of its point of suspension is examined in a four-dimensional phase space in which the coordinates are slowly varying amplitudes of a sinusoidal motion.
Journal ArticleDOI
Stability of forced oscillations of a spherical pendulum
TL;DR: In this paper, the equations of motion for a lightly damped spherical pendulum that is subjected to harmonic excitation in a plane are approximated in the neighborhood of resonance by discarding terms of higher than the third order in the amplitude of motion.
Journal ArticleDOI
Internally resonant surface waves in a circular cylinder
TL;DR: In this article, the two dominant, linearly independent surface-wave modes in a circular cylinder, which differ only by an azimuthal rotation of ½π and have equal natural frequencies, are nonlinearly coupled, both directly and through secondary modes.