DYNAMIC STIFFNESS AND FLEXIBILITY FUNCTIONS FOR AXIALLY STRAINED TIMOSHENKO BEAMS

This paper provides a new formulation for the dynamic stiffness and flexibility functions of axially loaded Timoshenko beams, including the effects of static axial deformations. The equation of motion of a Timoshenko beam, including the effects of static forces and deformations, is first derived. The general solution of the equation of motion is then presented, and the dynamic stiffness and flexibility functions are derived by applying suitable boundary conditions. The effect of the inclusion of the static axial deformations on the frequencies of vibration of axially loaded simply supported beams is demonstrated. The existence of a second frequency spectrum not predicted by the Euler-Bernoulli theory is clearly and amply illustrated. It is also shown how some of these additional frequencies may occur amongst the first few frequencies of the structural system. Finally, the use of the dynamic stiffness and flexibility functions is briefly outlined. © 1992.