In the present study, Dust Acoustic(DA) waves are investigated in the presence of periodic force for an unmagnetized quantum dusty plasma consisting of degenerate electrons, ions and negatively charged dust grains. Using quantum hydrodynamic (QHD) model and employing reductive perturbation technique, a forced Korteg-de Vries (KdV) equation is derived for DA waves and an analytical solution for these waves is derived in the presence of periodic force. It is found that the presence of external periodic force affects the amplitude and width of DA waves. A dynamical system is formed to explore the periodic and quasiperiodic structures of DA waves in model plasma through phase portrait and time series analysis. It is found that in the presence of external periodic perturbation, the perturbed KdV equation shows quasiperiodic behavior which is confirmed by a torus in phase plane. It is noted that, quasiperiodic motion is represented by a dynamical system having a finite number of incommensurable frequencies, and the trajectory in the phase space winds around on a torus filling its surface. The results will be helpful in laboratory plasmas as well as in space plasma environments.