Journal ArticleDOI
Resonantly forced surface waves in a circular cylinder
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TLDR
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
Citations
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Surface Waves in a Square Container Due to Resonant Horizontal Oscillations
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Sloshing simulation of standing wave with time-independent finite difference method for Euler equations
Zhi-qiang Luo,Zhi-Min Chen +1 more
TL;DR: In this article, the numerical solutions of standing waves for Euler equations with the nonlinear free surface boundary condition in a two-dimensional (2D) tank are studied. And the results show very clear nonlinear and beating phenomena.
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Experimental analysis of one-dimensional Faraday waves on a liquid layer subjected to horizontal vibrations
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Resonant motion of a spherical pendulum
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.
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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.