Numerical simulations of fully developed turbulence driven by a modulated energy input rate or driving force are performed within two dynamical cascade models, the Gkedzer-Ohkitani-Yamada shell model and a reduced wave vector set approximation of the Navier-Stokes equation. The frequency behavior of the system response is studied and compared with predictions from a variable range mean-field theory, which excludes turbulent fluctuations. In agreement with the mean-field approach, we find a constant response amplitude for low driving frequencies and a 1/omega decay of the amplitude for high frequencies. In the mean-field theory, the finite cascade time scale had led to an oscillating behavior of the response amplitude as a function of the driving frequency. In the simulations of both models we observe the main maximum. The higher maxima and minima are completely washed out by fluctuations, though the statistical properties of the fluctuations are different in the two models.