Chaotic motion and internal resonance of forced surface waves in a water-filled circular basin

The objectives of this paper are to investigate the chaotic motions and int ernal resonance of nonlinear surface waves generated by a harmonic vibratio n applied to the side wall of a water-filled circular basin. The harmonic f orcing consists of a component with a frequency near twice a fundamental re sonance frequency of the basin and a smaller component with a frequency nea r the fundamental frequency. The amplitude equation for the excited eigenmo de corresponding to the fundamental frequency is derived and the existence of chaotic motion of this equation is studied by Melnikov method. At certai n critical radii of the basin, twice the fundamental frequency is also a re sonance frequency and the so-called internal resonance takes place. Eigenmo de corresponding to this resonance frequency can also be excited. (C) 2000 Elsevier Science B.V. All rights reserved.