非線形ばねで連結された両端単純支持ばりの定常強制振動解析 : 安定判別解析法と数値計算例(機械力学,計測,自動制御)

概要

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In the previous paper, a nonlinear vibration in a continuous system excited by periodic displacement with arbitrary function was analyzed by the authors. A system of the steady state forced vibration was treated as a simply-supported-beam connected with a nonlinear spring at midpoint of the span. In order to analyze an exact solution of the resulting vibration, the Fourier series method was applied to the system. And some resonance curves were constructed by numerical calculation. This paper deals with the method of stability analysis for the resulting vibration obtained in the former paper. Stability criterion for the periodic solutions is analyzed utilizing variational equation of motion given from modal equation. Next, the stability charts for the resulting vibrations are constructed by numerical calculation. The stability criterion for the periodic solutions on the steady state vibration is discussed utilizing their charts. By using these charts, the stable branches for the resonance curves obtained in the former paper are distinguished from the unstable ones. Furthermore, in order to clarify the influence of nonlinearity for the stability, the stability chart is also constructed taking the nonlinearity as parameter.
社団法人日本機械学会の論文
2009-08-25