A droplet vibration is a very effective experimental model in order to clarify nonlinear phenomenon. We have developed a measuring system of a droplet vibration using surface acoustic wave (SAW), and the experimental results of free vibration and nonlinear vibration of the droplet have been reported. For the free vibration, we have also reported that exact solution using spherical droplet model in partial contact with spherical bowl and experimental result agreed well. In this study, we report on the theory of nonlinear vibration of the droplet. As the model which did not contradict the exact solution, the spring-mass-dashpot system model was introduced, and two nonlinear equations are proposed on the basis of this. Those are Duffing equation with the negative nonlinear spring and a nonlinear equation considering fluidic nonlinearity. Using those equations, whether it could explain various nonlinear phenomenon obtained in the measurement was examined. As the result, it was proven that both equations together corresponded to the experimental results.
展开▼
