A nonlinear dynamic model of a vibration isolator is presented where influences of precompression and dynamic amplitude are investigated within the frequency domain. It is found that the dynamic stiffness at the frequency of a harmonic displacement excitation is strongly dependent on those parameters. The problems of simultaneously modeling the elastic, viscous and friction forces are removed by additively splitting them, where the elastic force is modeled by a nonlinear, shape factor based approach, the viscous force by a fractional derivative model while the friction force is modeled by a generalized friction element. The dynamic stiffness magnitude is shown to increase with static precompression and frequency while decreasing with dynamic excitation amplitude, with its loss angle displaying a maximum at an intermediate amplitude. The dynamic stiffness at a static precompression, using a linearized elastic force response model, is shown to agree with the fully nonlinear model except at the highest dynamic amplitudes. The latter model is displaying an increased stiffness magnitude at the highest amplitudes due to nonlinear elastic effects. Furthermore, a harmonic displacement excitation is shown to result in a force response containing the excitation frequency and all higher-order harmonics, whereas every other higher-order harmonics vanish for the elastically linearized case.