Free Vibration Analysis Tapered Box Grider using Grillage Analogy and Finite Element Methods


A general method using the theory of thin-walled structures is given for determining the natural frequencies and mode shape for box –girder of varying depth having closed section, subjected to torsion and bending using a grillage method and finite element method (Plate /Shell, MSC, NASTRAN). Consistent mass matrices related to torsion and bi-moment effects have been derived using shape function corresponding to an assumed polynomial deflection configuration, also stiffness and consistent mass matrices for flexural behavior including the effect of shear deformation and rotary inertia in bending. The stiffness matrix for beam element under non-uniform torsion is presented by using the differential equation of equilibrium.A special computer program is written to perform the free vibration analysis starting from the element stiffness and consistent mass matrices. The results have been compared with those obtained from MSC/NASTRAN package. Numerical examples are presented to show the effect of cell number and effect of variation for (span/width) ratio.