Dimensional Analysis of the Pounding Response of an Oscillator Considering Contact Duration

Abstract

AbstractThe dynamic response of an elastic pounding oscillator subjected to harmonic excitation is investigated with dimensional analysis. To model the pounding process, a linear viscoelastic model is used to simulate the contact force. Through dimensional analysis, the peak structural response parameters of the pounding oscillator, including structural displacement, velocity, and penetration displacement, are characterized by a set of dimensionless terms (denoted by the Buckingham notation Π). The reduced Π-set explicitly describes the interaction between the oscillator and the rigid barrier. Analytical solutions to dimensionless contact time, displacement, and velocity response are derived in this study and are further verified against the numerical simulation. The effect of pounding on the oscillator’s response is illustrated using three well-divided spectral regions (i.e., amplified, deamplified, and unaffected regions), which are defined based on the dimensionless system frequency parameter Πω. Param...