Nonlinear analysis of an interesting phenomenon of the Chinese cultural relic --- Dragon Washbasin (Fish Washbasin) (Q1814714)

The authors discuss properties of a famous Chinese antique known as the dragon washbasin. The basin has two handles, or ears. When these ears are rubbed, an interesting sound is produced and beads of water spurt upward from specific four or six regions of the basin. Once it was believed that it was a simple resonance, but studies by one of the authors (Wang) indicate that these phenomena are self-excited vibrations of fluid-solid coupled system caused by dry friction. Vibrations of the shell of the dragon washbasin are described by a system of differential equations of the type \(L_1(u,v,w)+\rho h\partial^2u/\partial t^2=q_u\), \(L_2(u,v,w)+\rho h\partial^2v/\partial t^2=q_v\), \(L_3(u,v,w)+\rho h\partial^2w/\partial t^2=q_w\), with appropriate description of the dynamic loads \(q_u\), \(q_v\), \(q_w\). \(L_i\) are the operators of thin shell theory. Specific modes of vibration are computed. The authors show that the basin is divided into four or six regions with nodes separating them. This is confirmed by observing the behavior of this interesting historical relic.