An experimental investigation of vibrating plates in similitude and the possibility to replicate the responses using sensitivity-based scaling laws

Scaling laws are a general engineering tool that utilize a scaled model to estimate the system responses of the original system, provided that the original system and the scaled model are similar in terms of the similitude theory. Therefore, scaling laws allow for (1) investigating systems on a laboratory scale and subsequently transferring the obtained results to the original system or (2) investigating systems that are available in several sizes, so-called size ranges, e.g., a size range of gear boxes. In this paper, a finite element (FE) model of a vibrating rectangular plate with simply supported boundary conditions is used to directly obtain the scaling laws from a sensitivity analysis (sensitivity-based scaling laws). The sensitivity-based scaling laws are validated by applying them to measured vibration responses of simply supported rectangular plates. Therefore, a test stand for experimental analyses of simply supported rectangular plates with various geometrical dimensions is set up. In a first step, the similitude of the scaled plates is analyzed based on the mode shapes of the plates and on their modal damping. The modal response and the frequency response of the rectangular plates are measured using a scanning laser Doppler vibrometer. In a second step, the sensitivity-based scaling laws obtained from the FE model are used to transfer the natural frequencies and the mean squared transfer admittance from the parent to the replicas. In this paper not only scaled plates that are in complete similitude to the original are investigated, but also an outlook on scaling the vibration responses of rectangular plates that are not completely similar to the original is given (incomplete similitude). Therefore, the vibration responses of plates that are scaled by different factors in length, width, and thickness are considered as well.