Vibration of Beams on Intermediate Elastic Supports

摘要

The problem of free vibration of a beam on intermediate elastic supports is studied. The beam represents an idealized model of a launch vehicle whose dynamic characteristics are to be studied when mounted on an elastic support system. The support system consists of a pair of translational springs, a pair of rotational springs and a cantilevered beam. This configuration of the support system is normally used for mounting the aeroelastic buffet models inside the wind tunnel. Numerical results are obtained for the frequencies and mode shapes of this elastically coupled system, for a range of values of the spring constants and cantilevered beam stiffness and inertia values. The study shows that when the springs are supported at the nodal points corresponding to the first free-free beam mode, the linear spring stiffness has no effect on the first model mode and marginal effect on subsequent model modes. However, the rotational stiffness has a significant effect on all the model modes. The study also shows that though the variations in the stiffness or the inertia values of the cantilever beam affect only the predominantly cantilever modes, these variations become important because of the fact that the cantilever frequencies may come close to or even cross over, the model frequencies.