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

Abstract

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.

Optimization of Two Soil–Structure Interaction Parameters Using Dynamic Centrifuge Tests and an Analytical Approach

“…A time-domain analysis by the State Space Equation (SSE) has been used for the estimation of the dynamic structural response or system identification [11,25,26], and the analytical approach in this study was implemented using MATLAB R2014b. Equation ( 1) can be expressed as Equation ( 7) and the equation was converted to continuous-time SSE (Equation ( 8)), wherein Y in {X} consists of u s , u x , and φ.…”

Time history analysis of structures under multi-support excitation by state-space method

“…Due to that, it used in many domains, mentioning the analysis of vibration of car seat using passive and semi active dampers [5]. In [6] the pounding forces applied on SDOF structure during earthquake was calculated using state space approach and considering nonlinear viscoelastic behavior. A finite element model updating Studies in Engineering and Exact Sciences, Curitiba, v.5, n.1, p. 209-222, 2024 method used to determine the dynamic response of Steel Arch Bridge Based on First-Order Mode Test Data.…”