A self-consistent fluid model is proposed for describing collisionless radio-frequency ~rf! sheaths driven by a sinusoidal current source. This model includes all time-dependent terms in ion fluid equations, which are commonly ignored in some analytical models and numerical simulations. Moreover, an equivalent circuit model is introduced to determine self-consistently the relationship between the instantaneous potential at a rf-biased electrode and the sheath thickness. The time-dependent voltage wave form, the sheath thickness and the ion flux at the electrode as well as the spatiotemporal variations of the potential, the electric field and the ion density inside the sheath are calculated for various rf powers and ratios of the rf frequency to the ion plasma frequency. The ion energy distributions ~ IEDs! impinging on the rf-biased electrode are also calculated with the ion flux at the electrode. The numerical results show that the frequency ratio is a crucial parameter determining the spatiotemporal variations of the rf sheath and the shape of the IEDs.