Two new approximate methods for analyzing free vibration of structural components

Two approximate methods, which have not previously been used for structural dynamics problems, are applied to the free vibration analysis of various structural components. The first method is a new version of the complementary energy method. It is shown to be considerably more accurate than the conventional Rayleigh and Rayleigh-Schmidt methods when applied to spatially one-dimensional free vibration problems: prismatic and tapered bars, prismatic beams, and axisymmetric motion of circular membranes. The second method is the differential quadrature method introduced by Bellman and his associates. It is applied successfully here to all of the problems mentioned plus square membranes and circular and square plates.