Publication Date:
1991-06-01
Description:
The motion of subharmonic resonant modes of surface waves in a rectangular container subjected to vertical periodic oscillation is studied based on the weakly nonlinear model equations derived by both the average Lagrangian and the two-timescale method. Explicit estimates of the nonlinearity of some specific modes are given. The bifurcations of stationary states including a Hopf bifurcation are examined. Numerical calculations of the dissipative dynamical equations show periodic and chaotic attractors. Theoretical parameter-space diagrams and numerical results are compared in detail with Simonelli & Gollub’s (1989) surface-wave mode-competition experiments. It is shown that the average Hamiltonian system for the present 2:1:1 external-internal resonance with suitable coefficients has homoclinic chaos, which was mathematically proven by Holmes (1986) for the specific case of 2:1:2 external-internal resonance. © 1991, Cambridge University Press. All rights reserved.
Print ISSN:
0022-1120
Electronic ISSN:
1469-7645
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Physics
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