The generalized expression for the polarization force (which mainly arises due to the polarization of plasma ions around the dust grains) acting on charge fluctuating dust grains has been derived. The effect of such generalized polarization force on the propagation of the dust-acoustic waves in such dusty plasma has been also examined. It has been found that both the real and imaginary parts of the dust-acoustic wave frequency are significantly modified by this generalized polarization force. The implications of our results in some real situations of space and laboratory dusty plasmas are briefly discussed.
