Solution Methods of Inherent Characteristics of Plane Beam with Arbitrary Boundary Conditions

A semi-analytical method and a two-direction expansion method, have been presented and used to find the natural vibration characteristics of two-dimension beam with arbitrary boundary conditions. In these two methods there are no any assumptions on the transverse and the longitudinal displacements along x-axis and z-axis directions, i.e.,the beam is considered to be in a state of plane stress, and the elements of structure stiffness and mass matrices can be given explicitly. The geometrical properties of mode shapes are investigated, and the simply supported beam is taken as an example to discuss the accuracy and efficiency of semi-analytical method and two-direction expansion method of comparing the results of the two methods and that of the analytical method.