Bilinear elasto-dynamical response of SDOF system under sinusoidal loading

When subjected to time-dependent dynamic loading, concrete structures possess tension cracks. Such existing internal cracks have a breathing action (opening-closing-reopening), rendering such structures nonlinear elastic. For a single load and/or under proportional load variations, these structures have a bilinear mechanical response at the neutral axis in the form of discontinuity. The bilinearity ratio (β) is the aspect that co-relates the two values of flexural rigidity. Typically the value of bilinearity ratio is usually worth up to 10. In this research article, the bilinear dynamic response of a fully cracked concrete fixed beam under the action of sinusoidal loading has been studied by modelling it as a damped bilinear single degree of freedom system. In addition, the comparison of unilinear and bilinear models was explored. The simulations were performed using the software MATLAB. It has been found that such a class of homogeneous dynamical system exhibits linear behavior for a specific sense of applied loads. Moreover, in the case of fundamental resonance, the waveforms for displacement and acceleration exhibit jump phenomena in the form of a sudden change in the sense of the applied load. The shortcomings of current dynamic analysis practice have been addressed, and the practical importance of the work has been examined.