F-1213 弾性送水管の力学的不安定現象 : 管内脈動流による係数励振(J28-1 機械システムに発生する複雑現象の解析)(J28 機械・メカトロシステムにおける複雑系の発現機構の解析・制御・応用)

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  • F-1213 Nonlilear Dynamics of an Elastically Constrained Flexible Pipe : Parametric Resonance Due to a Pulsating Flow

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In this paper, we examine the nonlinear lateral vibration of a flexible pipe with a spring supported end, which is parametrically excited due to a pulsating flow. Using Liapnov-schmidt reduction, two first-order ordinary differential equations, which express the amplitude and phase of the lateral pipe vibration, is derived from the nonlinear nonself-adjoint partial differential equation governing the lateral pipe vibration. A first order ordinary differential equation, which govern the dynamics on the center manifold around the pitchfork bifurcation is derived from the amplitude equations of the lateral pipe vibration, with use of the center manifold reduction method. As a result, we clarify the nonlinear effect of the spring supported end on the stability and the lateral displacement of the pipe, from the view point of qualitative nonlinear analysis.

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