Dynamic stiffness matrix of a beam-column using power series expansion techniques.

Abstract

The purpose of this thesis is to obtain a power series expansion of the general stiffness matrix for the beam-column element. The general stiffness matrix for a beam-colum element is derived from the Bernoulli-Euler differential equation with the inclusion of the axial force. The terms of the general stiffness matrix containing hyperbolic and harmonic function are expanded in power series form. The resulting matrix series allows for an efficient procedure for computer operations. The matrix series expansion produces an elastic stiffness matrix, a consistent mass matrix, and a geometric matrix associated with axial force. Higher terms in the series are retained to the order of the fourth power in natural frequency and axial force. All coupling terms of lower order between these parameter are retained. The numerical problem is included as an explanation of the derived equations.