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Structural Engineering and Mechanics
  Volume 35, Number 6, August20 2010 , pages 717-733

Dynamic stiffness matrix of an axially loaded slender double-beam element
Li Jun, Hua Hongxing and Li Xiaobin

    The dynamic stiffness matrix is formulated for an axially loaded slender double-beam element in which both beams are homogeneous, prismatic and of the same length by directly solving the governing differential equations of motion of the double-beam element. The Bernoulli-Euler beam theory is used to define the dynamic behaviors of the beams and the effects of the mass of springs and axial force are taken into account in the formulation. The dynamic stiffness method is used for calculation of the exact natural frequencies and mode shapes of the double-beam systems. Numerical results are given for a particular example of axially loaded double-beam system under a variety of boundary conditions, and the exact numerical solutions are shown for the natural frequencies and normal mode shapes. The effects of the axial force and boundary conditions are extensively discussed.
Key Words
    double-beam system; Bernoulli-Euler beam; axial force; free vibration; dynamic stiffness matrix.
Li Jun: Vibration, Shock & Noise Institute, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, People

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