On dynamic behaviour of medium-thickness plates with uniperiodic structure

An averaging 2-D model of a rectangular plate with unidirectional microperiodic structure is presented in this paper. The approach is partly based on the results exposed in [7]. The model describes the length-scale effect, i.e. the influence of the size of microstructure on the overall dynamic plate behaviour. This effect has not yet been considered in the literature on asymptotic homogenized models of periodic plates. The equations of motion of the elastic plate are introduced according to the Hencky-Bolle assumptions. It is demonstrated that the dynamics of plates with unidirectional periodic structure cannot be treated as a specific case of those with bidirectional periodicity. A lower frequency of free vibrations of a linear - elastic plate band has been determined and compared with the numerical results obtained by the FEM, revealing the consistence of the proposed method. However, a higher free vibration frequency depends in this contribution on the length-scale and cannot be derived using the homogenized plate model.