Dimensional Analysis of Pounding Response of an Oscillator Based on Modified Kelvin Pounding Model

Abstract

The pounding response between a single oscillator and a rigid barrier was investigated with dimensional analysis in which the modified Kelvin pounding analytical model was used to simulate the contact force. The dimensionless equation of motion of the single pounding oscillator was deduced. In particular, the structural response parameters of the pounding oscillator were characterized by a set of dimensionless terms which were denoted by the Buckingham notation. Therefore, the key parameters governing the impact reaction were reduced so that they could effectively express the pounding response law of the structures subjected to the earthquake excitation. Numerical analysis proved the superiority of the modified Kelvin model compared with the Kelvin model. The effect of pounding on the response of the single oscillator was illustrated in three well-separated spectral regions which were described by the dimensionless system frequency parameters. Parametric analysis showed that the contact stiffness mainly affects the penetration displacements. In addition, the pounding response is insensitive to the initial spacing, but is affected obviously by the coefficient of restitution in the first spectral region.