Experimental realization and three-dimensional vibration analysis of simply supported rectangular plates

Abstract

This study presents a theoretical, numerical, and experimental investigation into the vibration characteristics of rectangular elastic plates under simply supported boundary conditions. A three-dimensional state-space formulation is used to obtain the vibration characteristics of the simply supported plate. The calculated natural frequencies are compared with finite element simulations and experimental measurements, and the theoretical mode shapes agree well with the finite element results. In the experiment, a separable V-groove support system combined with elastic adhesive materials is proposed to emulate simply supported boundary conditions. This method provides vertical support to the plate edges while allowing rotational freedom and maintaining operational flexibility and good repeatability. The effects of different adhesive media are systematically examined. The results indicate that neutral silicone performs the best. For the thin plate, the discrepancies in natural frequencies between the experimental measurements and theoretical analysis are within 1.6%. For the thick plate, the proposed method accurately captures the first two natural frequencies, with errors <2.6%. The main contribution is a nondestructive experimental method for realizing simply supported boundaries, validated by analytical and numerical results.