Non-linear Vibration Study Of Reinforced Concrete Beams

Nonlinearity vastly exists in practice, such as material nonlinearity, geometrical nonlinearity and so on. So most vibration systems are nonlinear. Reinforced conctete beams are important structure components in civil engineering. It bears some nonlinear character during vibration just for the material itself being in possess of obvious nonlinearity. So the investigation of its nonlinear dynamic characteristics using nonlinear vibration theory is necessary. .For a long time, researchers have done lots of work in the research of dynamic behavior of nonlinear systems ,either in theory or in numerical calculation, yet haven't found an efficient tool just like the mode analysis of linear system. People are trying their best all the time. Among these efforts, nonlinear normal mode theory is doubtless the most efficient. So here, it is used in the nonlinear vibration analysis of RC beam.In this paper, First, the piecewise linear vibration model of crack RC beams was constructed considering stiffness variety due to the breathing crack. Two parameters associated with crack were introduced. For the model with different parameters, analysis based on nonlinear normal modes of its free and forced vibration told that: the higher mode movement seems to be affected by crack more, while the lower mode relatively be stable. Multiple frequencies are included in higher mode movement. The greater it crazes, the more frequencies it includes.Then, the vibration formulations of RC beams were established in consider of material nonlinearity of concrete. Free and forced vibration analysis based on nonlinear normal modes was done, results showed that: system is similar to a soft spring, whose mode frequency reduced linearly along with the augment of amplitude. Jumping phenomenon occurs with frequency increase or reduction in forced vibration close to resonant. Besides these, thrice superharmonic and third subharmonic resonant may be present in the system.Finally, chaos analysis was done to the single degree material nonlinear model. Melnikov forecast and numerical identification indicated that: chaos may occur through double period bifurcation in the system.