Estimation of Plastic Deformation of Vibrational Systems Using the High-Order Time Derivative of Absolute Acceleration Response

Abstract eng:
Much research has been conducted in the area of structural health monitoring and damage detection, in order to develop methods which are capable of detecting aging deterioration and damage due to earthquakes as well as estimating the maintenance time. When a steel structure experiences a strong earthquake, damage such as yielding, fracture, recontact, and bolt slip in beams and columns, as well as anchor bolt extension and uplift at the column base may occur. These phenomena appear as nonlinearity in the load-displacement relationship. Detection of these changes can result in significant and valuable information regarding the evaluation of damage and residual performance. This study presents a method which is capable of detecting nonlinearity and damage from the absolute acceleration response time history. In a previous paper, we have presented criteria to detect nonlinearity in the restoring force using the second time derivative of the absolute acceleration, which is often referred to as snap. In order to investigate the capability of snap in detecting changes in the stiffness of the system, earthquake response analysis of a single degree of freedom system was conducted. The analysis results show that discontinuous jumps, which coincide with the yielding locations, can be observed in the snap time histories. It is possible to detect the yielding point by comparing a predefined threshold value with the snap time history calculated from the second order central difference approximation of the second time derivative of the absolute acceleration response time history. A limitation of the method is the inability to quantitatively estimate the damage of the system. The method presented in this paper overcomes the previous limitation by enabling the estimation of the plastic deformation using snap. In order to validate the estimation accuracy from the proposed method, plastic deformation computed from earthquake response analysis were obtained and compared to those estimated from the proposed method. The model is a single degree of freedom vibrational system with a bilinear elasto-plastic hysteretic restoring force. The results show that it is possible to estimate the plastic deformation with good accuracy without noise. On the other hand, in the presence of noise, the estimated value has larger error than the case without noise. In particular, it is observed that the error seems larger in the range of smaller plastic deformation. But it is possible to estimate the plastic deformation with approximately 20% error if the value of the plastic deformation becomes larger than 20% of the yield deformation.

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