Dynamic stiffness matrix and load functions of Timoshenko beam using the transport matrix
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 characteristicratioCr (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.
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Article: Beam length and dynamic stiffness[show abstract] [hide abstract]
ABSTRACT: The dynamic stiffness matrix is probably the simplest and the most convenient way to deal with the dynamic behavior of a distributed-parameter beam or beam system described in the continuous-coordinate system. The numerical computation of the stiffness coefficients and the determinant of the dynamic stiffness matrix has difficulty at some frequencies. This computational difficulty could be avoided if each beam component of a beam system is divided into the appropriate number of beam elements. Some simple beam examples are included in this paper for demonstration and discussion.Computer Methods in Applied Mechanics and Engineering - COMPUT METHOD APPL MECH ENG. 01/1996; 129(3):311-318.