Parametric Study on Transverse Vibration of Thin Rectangular Plate with Bonded Elastic Patch

In this work, transverse vibration of a thin rectangular plate with bonded high density and high modulus patch has been undertaken with simply supported boundary conditions at its edges. Plate material properties, patch thickness and patch area influence the transverse vibration of the host plate. Therefore, these effects must be accounted to correctly determine the natural frequencies of the plate in transverse vibration. The equation of motion for transverse vibration of the plate has been derived by taking into account of the patch material elasticity in the moment and force equations. The displacement function of the transverse vibration has been represented by a double Fourier series to solve the equation of motion for a composite plate with bonded elastic patch. Influence of dimensionless material and geometry parameters on the natural frequencies of the composite plate have been investigated. For material parameters, the flexural rigidity ratio and density ratio of the patch and the host plate have been considered. For geometrical parameters, area ratio and thickness ratio of the patch and the host plate have been considered. The location of the bonded elastic patch has been offset to study the influence of geometry on the modal frequencies. It has been found that these parameters significantly influence the modal frequencies. The results have shown that the shift in the fundamental mode frequency for the case of a central patch is larger than that of the offset patch. For a given area of the patch, the modal frequencies first increase and then decrease for an increase in the patch thickness.