Vibration response of perforated thin plates

Abstract

The vibration behavior of perforated metal thin plates is studied here. In order to highlight specific phenomena, a rather simple experiment has been researched. While covering a large range of frequencies, a sinusoidally varying point force has been applied to a free boundary circular plate at its midpoint. In that case, the plate vibrations obtained are of an axial symmetry type; for that geometry the first symmetrical modes only are excited. The driving-point mechanical impedance is measured. For a plane stress problem, the perforated plate vibration response is evaluated by assimilating perforated plates to equivalent solid thin plates whose effective elastic constants are determined with the help of Meijers’ theory [Ph.D. thesis, University of Delft, Holland, 1967]. First of all, the numerical simulation is validated by comparing theoretical impedance results to those obtained experimentally. Then, the use of double exposure holographic laser interferometry permits one to verify that modes observed on photographs correspond in general to theoretical ones. Initially developed for the study of perforated plate static behavior, that theory can certainly be used for the dynamic study of various geometry perforated plates.