Coupled bending-torsional dynamic stiffness matrix for timoshenko beam elements

Abstract

Analytical expressions for the coupled bending-torsional dynamic stiffness matrix elements of a uniform Timoshenko beam element are derived in an exact sense by solving the governing differential equations of motion of the element. Application of the developed theory in the context of wings, blades and grillages is discussed with particular reference to an established algorithm. Programming the derived stiffness expressions on a VAX computer indicates about 87% savings in computer time when compared with the matrix inversion method normally adopted in the absence of such expressions. The correctness of the stiffness expressions is numerically checked up to machine accuracy against the corresponding stiffnesses from the inversion method. The stiffnesses are also checked up to nine figure accuracy against those obtained from a comparable approximate method.