Dynamic stability of elastically constrained beams: an exact approach

In this paper a simple and exact procedure that allows the exact solution of the equation of boundary frequencies to be found, i.e. to integrate in an exact form the equation of the motion of beams subject to dynamic loads, is shown. With this procedure the regions of instability of beams generically restrained at the end cross-sections are found. Analysing the results obtained, it can be clearly observed that if the stiffness of the springs increases, the regions of instability shift to higher frequencies of vibration, in accordance with the results obtained previously. The method is a valuable tool for knowing in advance or for verifying the regions of instability of complex structures analysed by a finite element method, reduced to simple beams with springs at the end cross-sections.