On vibrations of thin plates with one-dimensional periodic structure

A new approach to problems of thin plates with a periodic structure along one direction in the planes parallel to the prate midplane is proposed. The model is a certain generalisation of the length-scale models for periodic plates, which make it possible to take into account the effect of periodicity cell size on the dynamics of prates with two-dimensional periodic structure [J. Jedrysiak, C. Wozniak, J. Theoret. Appl. Mech. 33 (1995) 337-349; J. Jedrysiak, Eng. Trans. 46 (1998) 73-87]. In order to describe this effect in stationary processes, e.g., a prate stability, and non-stationary processes for one-dimensional periodic plates the generalised model is presented in this paper. In order to show differences between governing equations of the extended model and the model for plates with two-dimensional periodic structure or the homogenised model vibrations problems of one-dimensional periodic plates will be analysed. (C) 2000 Elsevier Science Ltd. All rights reserved.