Galerkin Analysis of Effect of Dead Load on Natural Frequencies of Box Beam

Based on Hamilton’s principle, a nonlinear differential equation considering the effect of dead loads is formulated for box beams. By using Galerkin method, the effect of dead load on the natural frequencies of box beams with various restraint conditions being simply supported, fixed at both ends, cantilevered and fixed at one end and simply supported at the other end is studied. The effects of major physical parameters, including the magnitude of dead load, sectional inertia moment and inertia radius, span length, and restraint conditions are discussed, and the natural frequencies are presented for these box beams, with the nonlinear effect of dead load taken into account. The results show that the deterrent effect of dead loads has significant effect on the increase of the natural frequencies of box beams. It is further observed that this behavior is more apparent at lower-order natural frequencies; the varying deterrent effect of dead loads relates to the stiffness of structures and is more significant for more flexible structures.