Transfer Matrix Method for the Determination of the Natural Vibration Characteristics of Realistic Thrusting Launch Vehicle—Part I

The feasibility of using the transfer matrix method (TMM) to compute the natural vibration characteristics of a flexible rocket/satellite launch vehicle is explored theoretically. In the approach to the problem, a nonuniform free-free Timoshenko and Euler-Bernoulli beamlike structure is modeled. A provision is made to take into consideration the effects of shear deformation and rotary inertia. Large thrust-to-weight ratio leads to large axial accelerations that result in an axial inertia load distribution from nose to tail which causes the development of significant compressive forces along the length of the launch vehicle. Therefore, it is important to take into account this effect in the transverse vibration model. Once the transfer matrix of a single component has been obtained, the product of all component matrices composes the matrix of the entire structure. The frequency equation and mode shape are formulated in terms of the elements of the structural matrices. Flight test and analytical results validate the present TMM formulas.