Investigation on Static and Dynamic Stability for Simply Supported Flexible Beam with Axial Flow

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Journal of Vibration and Shock ›› 2011, Vol. 30 ›› Issue (7) : 59-62.

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Investigation on Static and Dynamic Stability for Simply Supported Flexible Beam with Axial Flow

WANG Jian-wei; XU Hui; MA Ning

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Abstract

The liquid-solid coupling dynamic equation was established for a simply supported flexible beam with an axial flow on certain assumptions, and the dimensionless state-space equation with finite degrees-of-freedom was derived by introducing dimensionless variables, assuming modes and truncating higher order modes. On the basis of the static bifurcation theory, the Jacobi matrix of the perturbation equation for the system was analyzed, and the static bifurcation critical flow velocity was obtained theoretically. Numerical calculations show that if the flow velocity exceeds the critical velocity, the system is destabilized, and the flexible beam bends upward or downward at random under the external minimal disturbance. Utilizing the dynamic Hopf bifurcation theory and relative algebraic criterion for roots of real-coefficient polynomials, it is proved that the flutter destabilization can’t take place in this system.

Key words

simply supported flexible beam / state-space equations / static bifurcation / critical flow velocity / Hopf bifurcation / flutter destabilization

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WANG Jian-wei; XU Hui;MA Ning. Investigation on Static and Dynamic Stability for Simply Supported Flexible Beam with Axial Flow [J]. Journal of Vibration and Shock, 2011, 30(7): 59-62