On vibrations of plates under periodically distributed inertial loadings

The aim of the paper is twofold. Firstly, it is the application of equations of the refined macro-dynamics of microperiodic plates to calculation of the resonance frequencies of Kirchhoff or Hencky-Reissner periodic plates and comparing the obtained results. Secondly, some from the above results will be compared to those obtained from the known approximation methods and hence we shall prove that the proposed refined models lead to the physically correct results. The presented modelling approach to the linear-elastic plates, having microperiodic structure in planes parallel to the midplane, is based on the assumptions given by Baron and Woźniak (1995) (for the Hencky-Reissner plate theory) and Jędrysiak and Woźniak (1995) (for the Kirchhoff plate theory), and describes the effect of the microstructure length dimensions on the plate macro-behaviour.