On the solution of S(ω)x=0 by a Newtonian procedure

The method 1] developed for the solution of (E ? λ A)x=0, where E and A are real symmetric matrices, and A is positive definite, is extended to deal with S(ω)x=0, where S is a real symmetric structural dynamic stiffness matrix whose elements are trancendental functions of ω, the radian natural frequency. The method enables all natural frequencies (latent roots 2]) and mode shapes (latent vectors, x) across a prescribed frequency range to be determined infallibly and in ascending frequency order at a speed approaching twice that associated with bisection and sign counting methods 3]. It is ideally suited for use on micro- and minicomputers where single precision working is the norm, and on the Commodore 4032 computer can cope with matrices, S, of order n and bandwidth p provided that np < 4200. Much larger problems, of course, may be dealt with on mainframe machines.