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Trapped vortices can contribute significantly to a residual surface resistance of superconducting radio frequency (SRF) cavities but the nonlinear dynamics of flexible vortex lines driven by strong rf currents has not been yet investigated. Here we report extensive numerical simulations of large- amplitude oscillations of a trapped vortex line under the strong rf magnetic field. The rf power dissipated by an oscil- lating vortex segment driven by the rf Meissner currents was calculated by taking into account the nonlinear vortex line tension, vortex mass and a nonlinear Larkin-Ovchinnikov viscous drag force. We calculated the field dependence of the residual surface resistance R i and showed that at low frequencies R i (H) increases with H but as the frequency increases, R i (H) becomes a nonmonotonic function of H which decreases with H at higher fields. These results sug- gest that trapped vortices can contribute to the extended Q(H) rise observed on the SRF cavities.