A State Space Formulation for the Evaluation of the Pounding Forces During Earthquake

In recent years, the pounding effect during earthquake is a subject of high significance for structural engineers. In this paper, a state space formulation of the equation of motion is used in a MATLAB code. The pounding forces are calculated using nonlinear viscoelastic impact element. The numerical study is performed on SDOF structures subjected by 1940 EL-Centro and 1977 Vrancea N-S recording. While most of the studies available in the literature are related to Newmark implicit time integration method, in this study the equations of motion in state space form are direct integrated. The time domain is chosen instead of the complex one in order to catch the nonlinear behavior of the structures. The physical nonlinear behavior of the structures is modeled according to the Force Analogy Method. The coupling of the Force Analogy Method with the state space approach conducts to an explicit time integration method. Consequently, the collision is easily checked and the pounding forces are taken into account into the equation of motion in an easier manner than in an implicit integration method. A comparison with available data in the literature is presented.