Theoretical and experimental investigation of viscous dampers in applications of seismic and vibration isolation

A fractional derivative Maxwell model is proposed for viscous dampers which are used for vibration isolation of piping systems, forging hammers and other industrial equipment, as well as for vibration and seismic isolation of building structures. The development and calibration of the model is based on experimentally observed dynamic characteristics. The proposed model is validated by dynamic testing and very good agreement between predicted and experimental results is obtained. The steady-state response of a single-degree-of-freedom viscodamper oscillator is shown to exist and it is derived. An equivalent viscous oscillator is defined whose response is essentially the same as that of the viscodamper isolator. The proposed model is employed in the analysis of a base-isolated structure which has been tested on a shaking table.; The coupled lateral-vertical-rocking dynamic response of a spring-viscous damper isolated structure is considered. The fractional derivative differential equations of motion are derived and reduced to a form for direct solution by the Discrete Fourier Transform method. The validity and accuracy of the derived solution is demonstrated by comparison to shake table test results. A simplified method of analysis, which uses a simple numerical formulation in terms of real-valued quantities, is presented. The simplified and rigorous methods of analysis are compared in the seismic analysis of a recently constructed isolated structure. It is shown that the simplified method predicts well the peak response of the isolated structure. The analytical and experimental results demonstrate that spring-viscous damper isolation systems are capable of providing both effective seismic and vibration isolation.; The parameters of the fractional derivative Maxwell model are analytically derived from the viscous fluid properties and the damper geometry. The derivation is based on an approximate solution of the equations of motion, continuity and constitutive relation. The results of the analytical solution are in very good agreement with experimental data and with numerical solutions based on boundary integral equation analysis.; Finally, it is shown that the order of the time derivative in viscoelastic models can be generalized to complex quantities. The condition for existence of complex order time derivatives are examined, and the transformation of these derivatives in the frequency domain is presented. A complex order generalized derivative model is used in modeling the complicated behavior of a spring-viscous damper unit.