A time-domain non-linear viscoelastic damper model

A viscoelastic solid model, comprising of a combination of linear and non-linear springs and dashpots, is developed to represent an elastomeric damper. A non-linear constitutive differential equation is derived to characterize the damper behaviour in the time domain. A system identification method is presented to determine the spring - dashpot parameters (coefficients of the constitutive equation) from experimental data. The model is able to predict the non-linear amplitude-dependent behaviour of elastomeric dampers under single as well as dual-frequency excitations. A `two-level implicit - implicit' scheme is developed for the integration of the non-linear damper model into a structural dynamic analysis. With increase in amplitude of excitation, softening behaviour of the lead spring results in lesser motion in the Kelvin chain, lower damping levels, and slower decay of initial perturbations. The baseline model is augmented with additional series and parallel non-linear springs to represent the reduction in damping (G'') at very small amplitudes, and the occurrence of limit cycle oscillations.