Abstract :
Based on the solution of the differential equations governing the dynamic equilibrium of a Timoshenko beam, the dynamic transport matrix equations and load functions are developed. The resulting matrix equations are then used to obtain analytical expressions for the components of dynamic stiffness matrix and load functions assuming that effects of damping and cross-section warping are negligible. The resulting dynamic stiffness matrix procedure is then used to obtain the vector of dynamic stiffness load functions for beam elements subjected to concentrated and distributed loads. In terms of a characteristic ratio Cr (including shear deformations and rotary inertia), the procedure is presented in a unified form by which the dynamic (or static) analysis of an integrated system of Timoshenko beams can be easily automated. Numerical implementation of the resulting dynamic stiffness matrix is verified by studying the effects of shear deformations and/or rotary inertia on values of natural frequencies for several beam cases, and one case of a rigid frame. The results obtained through application of the method of this paper are verified by comparison to results obtained by a finite element code.
