Free vibrations of cracked prestressed concrete beams

The paper deals with the effects of cracks and the nonlinear material behavior of concrete and prestress reinforcement on the natural frequencies of cracked bonded prestressed beams. The natural frequencies are determined at different levels of crack damage, which are a result of an external static load. The governing dynamic equations of the prestressed beam and their associated boundary and continuity conditions are derived using the variational principle of virtual work. The nonlinear material behavior of the concrete and prestress reinforcement, and the effects of cracking are modeled using the nonlinear constitutive relations of the various materials, which are implemented into an incremental formulation. The formulation yields a set of implicit nonlinear differential equations, which are solved using a linearization procedure and the Multiple Shooting method. Numerical examples are studied to investigate the effects of cracks and the nonlinear behavior of the concrete and prestress reinforcement on the natural frequencies of cracked prestressed beams. It appears that large cracking damage yields drastic reduction in the natural frequencies.