横向有限应变对部分浸入水中平面运动柔性梁的非线性振动响应的影响

NON-LINEAR COUPLED VIBRATION OF A PLANNAR MOTION FLEXIBLE BEAM IMMERGED PARTIALLY INTO WATER BY CONSIDERING TRANSVERSE FINITE STRAIN

  • 摘要: 基于Hamilton原理,根据克希霍夫假设以及拉格朗日函数,得到部分浸入水中柔性梁的大挠度条件下的运动方程和边界条件。在运动方程和边界条件的推导过程中,考虑了横向有限变形,并运用格林应变张量表示非零的应变张量分量。然后,应用中心差分法对方程进行数值处理,研究不同涡旋脱落荷载作用下,横向有限应变对结构振动响应的影响。结果表明,涡旋脱落荷载超过一定幅值后,横向有限应变的影响比较明显,不应忽略。

     

    Abstract: Based on Hamilton’s principle and Kirchhoff’s hypothesis, the motion equations and boundary conditions of the flexible beam with large deflection and immerged partially in water are derived by means of Lagrange functions. The beam strain tensor is expressed in Green’s strain tensor and the transverse finite strain is taken into account. By the central difference method, the equations of motions are solved numerically. The vibrational responses of the beam due to the different vortex-shedding loads are obtained, and the influence on vibrational responses due to the transverse finite strain of the beam is studied. The computing results show that, the transverse finite strain should not be neglected for the transverse vibration responses, transverse velocity and longitudinal velocity of the beam. Especially, the transverse finite strain will play more important role when the vortex-shedding load exceeds some given larger amplitude.

     

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