Transverse Bending and Vibration Characteristics of a Simply Supported Discontinuous Beam under Axial Loads

An abrupt change of stiffness may occur at the interface of discontinuous beams, and the transverse stiffness and vibration characteristics of this part of the beam can be significantly different from those of the remaining beam. In this paper, the relationship between the internal force and the displacement of discontinuous beams is analyzed based on the Timoshenko beam theory, and the equations for the deflection curve and free vibration of a simply supported beam under axial load are analytically derived. The normal function of the transverse vibration equation is obtained by separating variables, while the endpoint displacement is derived using the method of transfer matrix. The deflection and free vibration frequency of the discontinuous beam under different axial loads and connection stiffness were calculated. The results show that with an increase of stiffness, the deflection and free vibration frequency decreases and increases exponentially respectively. Moreover, the free vibration frequency of each order decreases with an increase of axial load, and the lower order frequency is more dependent on the axial load. (paper)