Dynamic response of asymmetric bodies assuming a rocking behaviour

Abstract

The proposed work aims to clarify the dynamic behaviour of asymmetric bodies in the case of rocking behaviour. The proposed algorithm is based on Housner theory and the integration of the equations of motion is evaluated with Runge-Kutta-Fehlberg (RKF45) method. Significant numerical errors accumulation is evaluated during the integration between two consecutive acceleration points where the rotation sign changes due to wrong adopted equation. An iterative calculation is developed to reduce numerical error depending on a specific tolerance and therefore, the algorithm accuracy is investigated. In addition, the reduction of energy due to the impact at the point of change of sign of rotation is analysed by the means of the restitution coefficient. It is important to note that it is highly dependent on the rigid block properties and experimental programs are required to calibrate properly the restitution coefficient. Sensitivity analyses are performed in order to clarify the effects of convergence parameters and tolerances on the results, due to high numerical instabilities. Furthermore, fragility curves are retrieved based on far field and near field sets of accelerograms proposed by ATC 63 (Applied Technology Council 2008) and a critical discussion is debated about the most efficient intensity measure parameters.