Dynamic stiffness vibration analysis using a high-order beam model

This work presents the derivation of the exact dynamic sti ness matrix for a high-order beam element. The terms are found directly from the solutions of the di erential equations that describe the deformations of the cross-section according to the high-order theory, which include cubic variation of the axial displacements over the cross-section of the beam. The model has six degrees of freedom at the two ends, one transverse displacement and two rotations, and the end forces are a shear force and two end moments. Using the dynamic sti ness matrix exact vibration frequencies for beams with various combinations of boundary conditions are tabulated and compared with results from the Bernoulli–Euler and Timoshenko beam models