Implementation of clamped and simply supported boundary conditions in the GDQ free vibration analysis of beams and plates

In this paper, a new methodology for implementing the clamped and simply supported boundary conditions is presented for the free vibration analysis of beams and plates using the generalized differential quadrature (GDQ) method. The proposed approach directly substitutes the boundary conditions into the governing equations and is referred to as SBCGE approach. The SBCGE approach is presented to overcome the drawbacks of previous approaches in treating the boundary conditions. A comparison of the SBCGE approach with the method of modifying weighting coefficient matrices (MWCM) is made by their application to the vibration analysis of beams and plates with combinations of simply supported and clamped boundary conditions. Some details of the GDQ method are also described in the paper. ~i 1997 Elsevier Science Ltd. All rights reserved.