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