An application of multi-scale vibration analysis of thin plate with a dense system of ribs in the detection of micro-scale imperfections

Abstract

In this paper the analytical multi-scale vibration analysis of the periodic thin plate with a dense system of ribs is performed. It is assumed that the considered structure is burdened with certain imperfections, which can affect its dynamic behaviour. Eventually, basing on the free vibration analysis and short wave propagation issue, it is proved, that the presented averaged models are capable of detecting the small scale imperfections. It should be noticed, that such analysis is not possible with other known methods of analysis of periodic structures, such as the homogenisation method. The presented results prove both the correctness of the shown transformations and the superiority of the solution.