Abstract: The numerical simulation based on finite element is used to study the vibration of liquid droplets which hang on the needle in the second mode. The results show that there is a linear relationship between the natural vibration frequency of the hanging droplets and that of the weightless free droplets. The linear relationship is related to the liquid surface tension coefficient，liquid density and needle diameter，and is independent of the liquid viscosity and“the ratio of the liquid surface tension coefficient and density”. Under the excitation of a sound field， the displacement resonance curves of the hanging droplets fit the normal velocity resonance curves of the forced vibration in shape，and the damping coefficient is positively correlated with the liquid viscosity，the liquid surface tension coefficient and the needle diameter，while negatively correlated with the liquid density and“the ratio of the liquid surface tension coefficient and density”. Finally，the simulation results are compared with the experimental data，and the two are in well agreement.

Key words: droplets, forced vibration, numerical simulation, measurement