This paper deals with the nonlinear vibration of a simply supported beam subjected to a sinusoidally distributed impulsive load, and then of the beam with simply supported or clamped ends under a uniform impulsive load, using the Galerkin method. The resulting equations for the mid-span deflection f(t) are solved in closed forms, using Jacobis' elliptic function. The solutions show that the effects of the axial force are large, comparing with solutions of the linear vibrations. Furthermore, the problem of the transverse impact of a mass on a beam with simply supported or clamped ends is treated by using the difference method. These results show the similar tendency to the transverse vibration and the impulsive time becomes shorter as the impulsive velocity becomes large. Although the axialinertia effects are taken into account in this case, they are shown to be negligibly small.
In this paper, dynamical loads of fin-stabilized, uncontrolled, non-spinning, flexible rocket vehicle with some misalignment such as initial deformation of body are analyzed. As the lateral load due to misalignment can be considered to be quasi-steady, the loads are derived from the solution of steady state analyses. The equations are quite similar to those for divergence analysis except the terms of disturbance forces. Therefore, the divergence phenomenon is considered to be a special case of quasi-steady load problems. Then the design limit on the bending rigidity of the vehicle body can be determined by this theory. The analysis has proved that there exists some tendency that the load on single staged high performance vehicle is quite sensitive to the misalignment. And simple formulas for estimating the load by use of the body parameters have been derived.