Dynamic system with high damping rubber: non-linear behaviour and linear approximation

High Damping Rubber is widely used in seismic engineering and, more generally, in the passive control of vibrations. Its constitutive behaviour is quite complex and is not simply non-linear with respect to strain but also shows a transient response during which material properties change (Mullins effect). A number of recent works were dedicated to analyzing and modelling material behaviour. The present work intends to study the consequences of such non-linear behaviour in the dynamic response of a system where the restoring force is provided by dissipative devices based on HDR (structural system with dissipative bracings and isolated systems). Analyses under harmonic forces and impulsive excitations were carried out in order to characterize the stable and transient responses separately. Two different linear equivalent systems are deduced from the nonlinear analyses in order to estimate the upper and lower bounds for the dynamic response. The responses provided by linear and nonlinear models are then used to study the response of the system under seismic excitation in order to compare solutions and evaluate the ability of linear models in furnishing upper and lower bound of maximum displacements and forces.