Similitudes for the structural response of flexural plates

This article presents an investigation into exact and distorted similitudes and the related scaling laws for the analysis of the dynamic response of rectangular flexural plates. The response of a given model in similitude is determined from a generalization of the modal approach, which allows the use the mode shapes and natural frequencies in order to establish scaling laws. Analytical models of simply supported rectangular plates are used to produce both the original and distorted model responses. Some highlights about the distribution of the natural frequencies, the forced response and the energy response are given. The results show that, with the proposed methodology, it is possible to reproduce with good confidence the response of the reference plate, even if distorted models are used.