Abstract
AbstractThis article presents an efficient digital computer procedure, along with the complete listing of the associated computer program, which may be conveniently utilized for the accurate solution of a wide range of practical eigenvalue problems. Important applications of the present work are envisaged in the natural frequency analysis of spinning structures discretized by the finite element technique, and in the determination of transfer function associated with the dynamic blocks of control systems of spacecraft utilizing gas jets or reaction wheels for attitude control, as well as of spin‐stabilized and dual‐spin‐stabilized satellites.The validity of the Sturm sequence property is first established for the related matrix formulation involving Hermitian and real symmetric, positive‐definite matrices, both being usually of highly banded configuration. A numerically stable algorithm based on the Sturm sequence method is then developed which fully exploits the banded form of the associated matrices. The related computer program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be extremely fast and economical in comparison to other existing methods of such analysis. Numerical results are presented for spinning bent cantilever beam and the solar arrays of SKYLAB, the earth‐orbiting space station proposed by NASA.
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