固定-単純支持はりのカオス振動に及ぼす軸圧縮荷重の影響

摘要

近年の輸送機械の高速化，効率化に伴い，はりやアーrnチなどの薄肉軽量構造が用いられる．一般に，薄肉構rn造は，他の構造要素と部分的に接合して弾性拘束されrnる場合が多い．弾性拘束となる接合部品に変位を加えrnると，薄肉要素に荷重が作用する．はりに軸圧縮荷重rnが作用すると曲率構造となり，たわみ方向に対する高rn剛性が得られる．しかし，たわみ方向に周期横荷重がrn作用すると大振幅振動が生じやすく，特定の条件でカrnオス振動が発生する．カオス応答は初期たわみや座屈rn変形に敏感であり，著者らは実験と理論解析から詳細rnな研究を行っている．%Experimental results and analytical results are presented on the effects of axial compressive load on chaotic vibrations of a clamped-supported beam subjected to periodic lateral acceleration. The beam is elastically compressed by an axial spring at the simply supported end. In the experiment, nonlinear and chaotic responses are detected under various compressions. In the analysis, the governing equation is reduced to nonlinear differential equations of a multiple-degree-of-freedom system by the Galerkin procedure. The nonlinear periodic responses are calculated by the harmonic balance method. The chaotic responses are numerically integrated by the Runge-Kutta-Gill method. The chaotic responses of the beam under axial compression are examined with the Fourier spectra, the Poincare projections, the maximum Lyapunov exponents and the principal components by the Karhunen-Loeve transformation. Both results of the experiment and the analysis coincide fairly well in detail. The frequency region of the chaos spread with the increment of the axial compressive force. The chaotic responses are generated within the axial compression range of the same ratio to the each buckling load. Distinct fractal pattern can be observed in the attractors of Poincare projections. The number of modes generated in the chaos is counted as three by the maximum Lyapunov exponent and the Lyapunov dimension.