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研究浸入流体中自由端具有集中质量块的等截面弹性支承悬臂梁的横向自由振动。考虑由集中质量块引起的轴向力作用,建立了支承处弹性水平位移约束和转动约束耦合情形下悬臂梁横向自由振动数学模型。由于集中质量块的惯性力和惯性距,此模型的边界条件与固有频率相关。推导了梁自由振动的频率方程和振动模态的广义正交性条件。数值研究了水深、集中质量块质量、转动惯量、质心距以及弹簧耦合刚度等参数对悬臂梁固有频率和正则模态的影响。
The transverse free vibration of isosceles elastic support cantilever beam with concentrated mass at the free end in immersed fluid is studied. Taking into account the axial force caused by the concentrated mass, a mathematical model of lateral free vibration of cantilever beam with elastic horizontal displacement constraint and rotational constraint coupling is established. Due to the mass and inertia of the mass, the boundary conditions of this model are related to the natural frequency. The frequency equation of free vibration and the generalized orthogonality condition of vibration mode are deduced. The effects of water depth, mass of concentrated mass, moment of inertia, mass center distance and spring coupling stiffness on the natural frequency and regular mode of cantilever are studied numerically.