Pounding of structures modelled as non‐linear impacts of two oscillators

Abstract

SUMMARYA new formulation is proposed to model pounding between two adjacent structures, with natural periods T 1 and T 2 and damping ratios 1 and 2 under harmonic earthquake excitation, as non-linear Hertzian impact between two single-degree-of-freedom oscillators. For the case of rigid impacts, a special case of our analytical solution has been given by Davis ('Pounding of buildings modelled by an impact oscillator' Earthquake Engineering and Structural Dynamics, 1992; 21:253-274) for an oscillator pounding on a stationary barrier. Our analytical predictions for rigid impacts agree qualitatively with our numerical simulations for non-rigid impacts. When the di erence in natural periods between the two oscillators increases, the impact velocity also increases drastically. The impact velocity spectrum is, however, relatively insensitive to the stando distance. The maximum relative impact velocity of the coupled system can occur at an excitation period T * n which is either between those of the two oscillators or less than both of them, depending on the ratios T 1 =T 2 and 1 = 2 . Although the pounding force between two oscillators has been primarily modelled by the Hertz contact law, parametric studies show that the maximum relative impact velocity is not very sensitive to changes in the contact parameters.

Comparison of Numerical Models of Impact Force for Simulation of Earthquake-Induced Structural Pounding

“…In order to model the pounding force-deformation relation more realistically, a nonlinear elastic model following the Hertz law of contact has been adopted by a number of researchers [5,6]. The pounding force, ( ) F t , for this model is expressed by the formula:…”

“…A time-stepping integration procedure with constant time step 6 1 10 s t − Δ = × has been applied to solve the Equation (8) numerically. The values of the impact stiffness parameters: k , β and β , defining the models used in the numerical analysis, have been determined using the method of the least squares.…”

“…Jankowski et al [4] used the same model to study pounding of superstructure segments in bridges. In order to simulate the force-deformation relation more realistically, a non-linear elastic model following the Hertz law of contact has been adopted by a number of researchers (see, for example, [5,6]). For the purposes of a more precise simulation of a physical phenomenon, a non-linear viscoelastic model has also been considered [7][8][9].…”

Key issues regarding interaction of adjacent RC structures

“…Formulation and results are based on elastic dynamic analysis. Chau and Wei [8] have proposed a formulation to model pounding of two adjacent structures under harmonic earthquake excitation as non-linear Hertzian impact between two single-degreeof-freedom oscillators.…”

Utilization of object-oriented programming, design patterns and java for simulating earthquake-induced poundings of base-isolated buildings

“…Pounding incidences between fi xed-supported (FS) buildings during earthquakes had motivated relevant research [1][2][3][4][5]. Yet, very limited research work has been carried out for poundings of multi-storey base-isolated buildings [6][7][8][9][10][11], which exhibit very different dynamic characteristics from FS buildings.…”