STUDY ON VERTICAL FREE VIBRATION OF PRESTRESSED BEAMS SUBJECTED TO AXIAL AND FLEXURAL LOADINGS

Based on the generalized potential energy variational principle with large deflection, the incomplete generalized potential energy functional for free vibration of prestressed beams is established by considering coupling of axial and flexural actions, shearing strain energy and moment of inertia. By variation of vertical displacement, the vertical free vibrational differential equation is formulated .With the consideration of boundary conditions the accurate solutions for free vibration frequencies of pin-ended beam and cantilever beam are obtained. Compared with the Bernoulli-Eular and Timoshenko beams, the effects on natural frequency due to axial loading, shearing behavior and rotation inertia are discussed in detail. It is found that the free vibration frequencies decreased due to compressive axial load, the effects caused by shearing deformation is about three times as large as that caused by rotation inertia, and with the increase in the orders of vibration modals, the effects due to axial load, shearing deformation and rotation inertia become remarkable. Therefore, if , or , such effects must be considered in natural frequencies solution for prestressed concrete beams. By comparison with Bernoulli-Eular and Timoshenko beams, the solution in this paper is proved to be correct.