Dynamic stability of cantilevered timoshenko columns subjected to a rocket thrust

Abstract

The dynamic stability of cantilevered Timoshenko columns subjected to a rocket thrust is described. It is assumed that the thrust force is produced by the installation of a solid rocket motor to the tip end of the cantilevered columns. The rocket motor is assumed to be a rigid body having finite sizes, but not a mass point as it has been assumed so far. A finite element model of the columns is formulated through the extended Hamilton's principle. The dynamic stability of the columns is investigated with respect to (i) the magnitude, rotary inertia and size of the rocket motor and (ii) the shear deformation and rotary inertia parameter of the columns. The theoretical analysis predicts a proper combination of the magnitude and the position of the rocket motor to stabilize the columns. It is shown that the size and rotary inertia of the rocket motor have a great effect on the critical follower force, on the other hand the rotary inertia parameter of the column hardly affects the critical follower force as long as the rotary inertia parameter of the column is small. It is found that when shear deformation parameter is large enough, the shear deformation parameter has a slight effect on the critical follower force.