A generalized approach for implementing general boundary conditions in the GDQ free vibration analysis of plates

Abstract

A new approach for implementing general boundary conditions in the GDQ free vibration analysis of rectangular plates is presented in this paper. The proposed approach directly couples the boundary conditions with the governing equations and is referred to as the CBCGE approach. It can be applied to any combination of simply supported, clamped, and free boundary conditions. The generality and accuracy of the CBCGE approach are demonstrated through its application to the vibration analysis of a rectangular plate with various combinations of free edges and corners. In particular, the effect of grid point distribution on the numerical results for plates with free boundary conditions is discussed, and a new grid point distribution is suggested.