- مبلغ: ۸۶,۰۰۰ تومان
- مبلغ: ۹۱,۰۰۰ تومان
The stochastic linearization technique (SLT), in its conventional force-based Gaussian version (FB-G-SLT), is widely adopted in the literature to handle the nonlinear power-law constitutive behavior of fluid viscous dampers (FVDs), either for evaluating the system response, or within optimal design strategies. In this note, the authors prove that, for the kind of nonlinearity induced by FVDs, this version of FB-G-SLT is not the best choice, especially if the velocity-related response is of major importance in an optimal design process. As an example, the energy dissipated by the devices depends upon the square of the velocity at the ends of the dampers. Among six different formulations of SLT examined in this note, an equal-energy non-Gaussian SLT (EE-NG-SLT) is found to be superior to the FB-G-SLT since it more satisfactorily captures the nonlinear response of the structure as predicted by Monte Carlo simulations. This alternative EE-NG-SLT, without requiring higher computational effort than the FB-G-SLT, is therefore recommended, especially when energy-based (or, in general, velocityrelated) objective functions are used in the optimization problem of nonlinear viscous dampers.
Response evaluation of structures equipped with FVDs can be complex due to their nonlinear power-law constitutive behavior. In the framework of SLT, the nonlinear FVDs can be replaced by equivalent linear FVDs, so that linear methods of analysis (e.g., the response spectrum method), or linear random vibration theory are still applicable.
Based on the outcome of this study, it is recommended that the equivalent damping coefficients of nonlinear FVDs be calculated through a developed equal-energy non-Gaussian stochastic linearization technique. The proposed method offers improved accuracy and significant advantages over the force-based Gaussian stochastic linearization technique, widely adopted in the literature. It has been demonstrated that it is better able to capture the nonlinear response of the system in terms of displacement, velocity, and dissipated energy of FVDs, especially for more severe nonlinearities of the FVDs. Furthermore, the proposed expression does not entail any additional computational effort in comparison with the conventional formula, which is important for design purposes.
Two major assumptions are made in this note and should be acknowledged here. The first one is the stationarity of both the input and output processes. The results reported in this note refer strictly to a stationary response analysis. In reality, earthquake ground motions are non-stationary in nature: strictly speaking, the variances of the response process entering the SLT expressions would be functions of the time. However, it is meant that ground motion records are sufficiently long so that there exists a central part of the response, usually the strong motion phase that is of higher importance for design purposes, in which the stationary assumption could be at least acceptable. The second assumption is that the analysis has been restricted to SDOF systems. However, in multi-degree-of-freedom systems with multiple dampers, one-to-one relationships between equivalent damping coefficients and relative velocity variances are involved. Consequently, the developed expressions for SDOF systems are still applicable by substituting σu̇ with σΔu̇ j , where Δu̇ j is the relative velocity at the ends of the j th device.