Vibration of Missiles: Matric Formulation of the Problem Involving Free and Harmonically Forced Flexural Vibrations

The free and harmonically forced flexural vibrations of missiles resting on fixed or mobile launch platforms are considered. A general matric formulation is given for the problem in which the effects of variable boundary conditions at the base support, variable axial loads along the missile length, variable stiffness and material properties, variable mass, variable mass moment of inertia, variable shear stiffness, and variably distributed forcing functions are treated. The problem is matrically formulated in standard eigenvalue form, and no special coding should be required for organizations that are currently solving eigenvalue problems on electronic digital computers. For a particular problem only fundamental data are needed for filling in the element locations of the matrices involved, and almost all calculations are performed within the computer. The matric formulation presented herein is also valid for partially and completely restrained cantilever beams.