Hamiltonian dynamic analysis of an axially translating beam featuring time-variant velocity

A dynamic analysis is presented for an axially translating cantilever beam simulating the spacecraft antenna featuring time-variant velocity. The extended Hamilton's principle is employed to formulate the governing partial differential equations of motion for an axially translating Bernoulli-Euler beam. Further, the assumed modes method and the separation of variables are utilized to solve the resulting equation of motion. Attention is focused on assessing the coupling effects between the axial translation motion and the flexural deformation during the beam extension or retraction operations upon the vibratory motion of a beam with an arbitrarily varying length under a prescribed time-variant velocity field. A number of numerical simulations are also presented to illustrate the qualitative features of the underlying mechanical vibration of an axially extending or contracting flexible beam. In general, the transverse beam vibration is stabilized during extension and unstabilized during retraction. The axial acceleration of a translating beam does not affect the transverse vibratory system stabilization.