According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified way proposed by Luo, some basic principles in the dynamic theory of viscoelastic materials with voids can be established systematically. In this paper, an important integral relation in terms of convolutions is given, which can be considered as the generalized principle of virtual work in mechanics. Based on this relation, it Is possible not only to obtain the principle of virtual work and the reciprocal theorem, but also to derive systematically the complementary functionals for the eight-field, six-field, four-field simplified Gurtin-type variational principles and the potential energy-functional for the two-field one in the dynamic theory of viscoelastic materials with voids by the generalized Legendre transformations given in this paper. Furthermore, with this approach, the intrinsic relationship among various principles can be explained clearly.