Analytic Study on Nonlinear Rolling Isolation System with Viscous or Friction Damper
Date Issued
2010
Date
2010
Author(s)
Hsieh, Cheng-Hsin
Abstract
Abstract
The vibration period of many linear isolation systems are 2 to 3 seconds which is close to the predominant period of near-fault earthquake, and resonance may occur. For this reason, nonlinear isolation systems are developed to avoid resonance. The frequency of nonlinear isolation system is not fixed, so it can keep the structure from resonance. Numerical simulation is conducted for nonlinear isolation system and the corresponding linear system under free vibration, sine wave, far-field and near-fault earthquake. The linear and nonlinear isolations performance of the system due to harmonic and seismic excitations will also be demonstrated and investigated in this study.
In the proposed system, a mass block is pin connected to a set of circular rolling disk. If the pin is connected eccentrically to the center of the disk, the restoring force becomes nonlinear. In addition, energy is dissipated by adding viscous damper or friction damper. The nonlinear governing equation of motion for the eccentric rolling isolation system is derived based on Lagrange’s equation. The isolation frequency as a function of the eccentricity and initial angle will be investigated through free vibration analysis. By the numerical simulation of free vibration, the results show that if the eccentricity or initial angle is small, the dynamic behavior of the system is almost the same as the linear rolling behavior.
When the ground excitation input is sine wave and its frequency equal to the linearized frequency, the numerical simulation results show that if no dissipation mechanism, the linear system will be divergent, but nonlinear systems will be stable because of its nonlinear behavior. When the viscous damper dissipation mechanism is adopted, under resonant frequency of the sine wave, linear isolation system is no longer divergent, but the maximan response of the nonlinear system is only about 50% of the linear system. When the PGA of El Centro and Chi-Chi earthquakes varies from 0.05 to 1 (g), the result shows that the superior of the nonlinear system over the linear system becomes more obvious as PGA increases. Therefore, with viscous damping, the nonlinear isolation system performs better than the linear one in both acceleration ratio and maximum displacement under sine wave, far field under or near fault earthquakes excitation.
When isolation install friction damper, under far field and near-fault earthquake excitation, the best design of friction parameters are very close. Under resonant frequency of sine wave, the response of linear system will be divergent if the friction parameter is not big enough, while nonlinear system is stable and no resonance occurs at same dutam. Then change the PGA of two earthquakes, the range from 0.05 to 1 (g), the result shows that the displacement of the linear isolation system is closer to that of the nonlinear one.With the increases of PGA, nonlinear isolation display the better isolation effect, but linear system don’t have this advantage. Summarized above, with friction damper, the response of nonlinear systems and linear systems are similar, but if the PGA of near-field and far-field earthquakes becomes larger, nonlinear isolation system shows more and more effect than linear system. Thus, by appropriate design, the nonlinear rolling isolation system is feasible in this research.
Subjects
isolation
nonlinear
eccentricity
viscous damper
friction damper
rolling
structural dynamic
Type
thesis
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