定常振動問題の解と安定判別のための数値解法とプログラム

概要

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A steady-state periodic solution is essential in the study of the vibration theory. A new computer-aided scheme to determine the periodic solution and its stability is discussed, which is a remarkably precise, speedy and powerful method pursuing some classical schemes with the same aim, e.g., the famous harmonic balance method. Since the algorithm consists of a purely numerical procedure, the scheme is very effective for cases in which it is difficult to find steady solutions when employing conventional analytical methods. The scheme is based on a particular conception to determine the specific initial conditions which generate only steady-state solutions without transients. The specific initial conditions are computed by iteration applying a certain improving strategy using the Newton-Raphson method and numerical integration, e. g. , the RKG scheme for the relevant differential equations. Illustrated examples are provided, which demonstrate the convergence of successive trajectories in a phase plane. A full listing of the program is accompanied by its instruction manual.
一般社団法人日本機械学会の論文
1994-01-25