和形係数励振振動の非線形安定性解析 : 数式処理援用による中心多様体理輪とグレブナ基底の応用

概要

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In this paper, the analyses of the averaged equations by using the Grobner basis and Center manifold theory are proposed, and the nonlinear stability of the summed-type combination resonance is practically examined by these analyses. The bifurcation equations are algebraically solved by Grobner basis, so that the steady state amplitude is expressed by the parameters in the equation of motion. Furthermore by introduction the center manifold theory into the analysis of the averaged equation in the vicinity of the bifurcation point, the four dimensional averaged equations are reduced to two dimensional equations on the center manifold, and it is found that in the post-stable region the limit cycle occurs on the center manifold. The state plane is shown and for that limit cycle a more grobally stable analysis than one by using the Routh-Hurwitz criterion is carried out. The above analyses are performed by the use of computer algebra.
一般社団法人日本機械学会の論文
1994-04-25