According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified way proposed by Luo(1987), some unconventional Hamilton-type variational principles for dynamics of Reissner sandwich plate can be established systematically. The unconventional Hamilton-type variation principle can fully characterize the initial-boundary-value problem of this dynamics. In this paper, an important integral relation 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 in dynamics of Reissner sandwich plate, but also to derive systematically the complementary functionals for five-field, two-field and one-field unconventional Hamilton-type variational principles by the generalized Legender transformations. Furthermore, with this approach, the intrinsic relationship among the various principles can be explained clearly.