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

A new formulation is proposed to model pounding between two adjacent structures, with natural periods T-1 and T-2 and damping ratios zeta (1) and zeta (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 mid 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 difference in natural periods between the two oscillators increases, the impact velocity also increases drastically. The impact velocity spectrum is, however, relatively insensitive to the standoff 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 zeta (1)/zeta (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. Copyright (C) 2001 John Wiley & Sons, Ltd.