電磁力を受けるはりに生じるカタストロフィ : Liapunov-Schmidt法と中心多様体理論を用いた非線形解析

概要

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In a beam subjcted to electromagnetic force, that is, the three-current carrying-beam system, the catastrophe of the lateral deflection due to the increase of such force is theoretically investigated by taking account of the nonlinearity of the electromagnetic and elastic forces with respect to the lateral deflection of the beam. Not neglecting the imperfection of the bifurcation, the reduction of the equation with respect to the lateral deflection, to a low-dimensional bifurcation system, is achieved by means of the Liapunov-Schmidt reduction and the center manifold theory. Through the above nonlinear analysis, the bifurcation equation is derived, and the correction of the mode in the higher-order analysis is discussed. Furthermore, by analyzing the bifurcation equation, the bifurcation diagram, equilibrium space and bifurcation set are theoretically obtained, and the characteristics of the catastrophe are qualitatively clarified.
一般社団法人日本機械学会の論文
1994-01-25