An experimental study on a generalized Maxwell model for nonlinear viscoelastic dampers used in seismic isolation

Long-stroke fluid dampers may be installed under seismic isolation systems to provide supplementary damping. Due to the larger vibration amplitude and velocity, highly nonlinear viscoelastic behavior may exist in a long-stroke fluid damper. In order to accurately simulate the hysteretic behavior of such a damper, this paper presents and experimentally verifies a mathematical model called the generalized Maxwell model (GMM). Similar to the classic Maxwell model, the GMM is composed of a stiffness and a viscous elements connected in series. However, nonlinearity is incorporated into both elements of the GMM by assuming that their resistant forces are exponential functions of the relative velocity and deformation of the damper. By adjusting the two exponential coefficients, the GMM is able to simulate the more complicated viscoelastic behavior of fluid dampers. The GMM is reduced to the Maxwell model when both exponential coefficients are set to one. To verify the GMM, both an element test with harmonic excitations and a shaking table test with seismic excitations were conducted for a long-stroke fluid damper with highly nonlinear viscoelastic behavior. The result of the element test confirms that the GMM model is very accurate in simulating the hysteretic property of the fluid damper under a wide range of excitation frequencies, while the classic Maxwell and the viscous models may only be accurate under a certain excitation frequency. Moreover, the shaking table test, in which the fluid damper is used to provide supplementary damping for a sliding isolation system, demonstrates that the GMM is able to more accurately predict the amount of energy dissipation by the damper and also the peak isolator drift of the isolation system, especially for an earthquake with a long-period pulse.