Effect of concentrated masses with rotary inertia on vibrations of rectangular plates

Abstract

The effect of attached masses on free vibrations of rectangular plates is studied by considering rotary inertia of concentrated masses and geometric imperfections of the plate. Experiments are performed to understand the changes in natural frequencies and mode shapes. In order to validate and better understand the experiments, numerical results are also presented. Boundary conditions at the plate edges are those of simply supported plate with additional rotational springs at the plate edges. By tuning the stiffness of these springs, any boundary conditions comprised between simply supported and clamped edges can be simulated. Numerical results are successfully compared to experiments performed on a stainless-steel plate with an attached mass of different translational and rotary inertia. In particular, it is shown that a small mass placed on the diagonal of a square thin plate is enough to transform the shape of modes with one nodal line parallel to the edge, into diagonal modes, i.e. modes with diagonal nodal lines. Rotary inertia of concentrated masses reduces significantly natural frequencies. Moreover, additional modes due to the presence of large rotary inertia of concentrated masses arise, which do not appear if rotary inertia is neglected. Finally it is shown that masses placed only on one side of the plate or symmetrically (with respect to the mid-plane) placed on both sides give similar results.