Natural frequency analysis of simply supported thin centrally attached hole rectangular plate with attached concentrated masses

Abstract

In the present work, free vibration response of a simply supported rectangular plate with attached concentrated masses has been analysed. The plate material is linearly elastic, homogenous and isotropic. Galerkin method is used for finding fundamental frequencies of plate with attached concentrated masses. The candidate mode shape of plate is approximated by the sine series, which satisfy the boundary conditions of simply supported at all the edges of the plate. The modal values obtained by Galerkin method are compared with that of obtained by ANSYS. The result obtained by Galerkin method is in good agreement with those of ANSYS for concentrated mass upto 6.7% of the plate mass. It has been shown that by using one term of approximation for candidate mode in Galerkin method, the error in natural frequency of the plate is less than 0.06% when attached concentrated mass is less than 6.7% of plate mass. This saves a lot of computation.