Using a refined theory of three-layer plates and shells developed for analysis dynamic deformations of high variability of parameters, we study problems on free and eigen vibrations for a three-layer plate of infinite width. The plate is of symmetrical structure in the transversal direction. The results obtained are compared with results for similar problems solved earlier for the case when we used non-simplified equations of the theory of elasticity for a core. We establish that the equations proposed are of high degree of accuracy when are used for dynamic problems of three-layer structures with a core of moderate thickness. We also indicate the possible ways for refinement equations under consideration.