应用数学和力学(英文版)
應用數學和力學(英文版)
응용수학화역학(영문판)
APPLIED MATHEMATICS AND MECHANICS(ENGLISH EDITION)
2003年
10期
1194-1207
,共14页
vertically forced oscillation%nonlinear%Faraday wave%singular perturbationexpansion%amplitude equation
In the cylindrical coordinate system, a singular perturbation theory of multiple-scale asymptotic expansions was developed to study single standing water wave mode bysolving potential equations of water waves in a rigid circular cylinder, which is subject to avertical oscillation. It is assumed that the fluid in the circular cylindrical vessel is inviscid ,incompressible and the motion is irrotational, a nonlinear amplitude equation with cubicand vertically excited terms of the vessel was derived by expansion of two-time scales withoutconsidering the effect of surface tension. It is shown by numerical computation that differentfree surface standing wave patterns will be formed in different excited frequencies andamplitudes. The contours of free surface waves are agreed well with the experimental resultswhich were carried out several years ago.
