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-dimensional beam with arbitrary boundary conditions. In these two methods there are no any assumptions on the transverse displacement and the longitudinal displacement 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 matrix 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 the efficiency of the semi-analytic method and the two-direction expansion method through comparing the results of the two methods with that of the analytical method.