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Stochastic Response of Nonlinear Base Isolation Systems
Abstract and Figures
A hybrid base isolation system was used to retrofit two residential buildings in Solarino, Sicily. Subsequently, five free vibration tests were carried out in one of these buildings to assess its functionality. The hybrid base isolation system combined high damping rubber bearings with low friction sliders. In terms of numerical modeling, a single-degree-of-freedom system is used here with a new five-parameter trilinear hysteretic model for the simulation of the high damping rubber bearing, coupled with a Coulomb friction model for the simulation of the low friction sliders. Next, experimentally obtained data from the five free vibration tests were used for the calibration of this six parameter model. Following up on the model development , the present study employs Monte-Carlo simulations in order to investigate the effect of the unavoidable variation in the values of the six-parameter model on the response of the base isolation system. The calibrated parameters values from all the experiments are used as mean values, while the standard deviation for each parameter is deduced from the identification tests employing best-fit optimization for each experiment separately. The results show that variation in the material parameters of the base isolation system produce a nonstationary effect in the response. In addition, there is a magnification effect, since the coefficient of variation of the response, for most of the parameters, is larger than the coefficient of variation in the parameter values.
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The best known model for numerically simulating the hysteretic behavior of
various structural components is the bilinear hysteretic system. There are two possible
mechanical formulations that correspond to the same bilinear model from a mathematical
viewpoint. The first one consists of a linear elastic spring connected in series with a parallel
system comprising a plastic slider and a linear elastic spring, while the second one comprises a linear elastic spring connected in parallel with an elastic-perfectly plastic system.
However, the bilinear hysteretic model is unable to describe either softening or hardening
effects in these components. In order to account for this, the bilinear model is extended to a
trilinear one. Thus, two trilinear hysteretic models are developed and numerically tested,
and the analysis shows that both exhibit three plastic phases. More specifically, the first
system exhibits one elastic phase, while the second one exhibits two elastic phases
according to the level of strain amplitude. Next, the change of slope between the plastic
phases in unloading does not occur at the same displacement level in the two models.
Furthermore, the dissipated energy per cycle in the first trilinear model, as proven mathematically and explained physically, decreases in the case of hardening and increases in the
case of softening, while in the second trilinear model the dissipated energy per cycle
remains unchanged, as is the case with the bilinear model. Numerical examples are presented to quantify the aforementioned observations made in reference to the mechanical
behavior of the two trilinear hysteretic models. Finally, a set of cyclic shear tests over a
wide range of strain amplitudes on a high damping rubber bearing is used in the parameter
identification of the two different systems, namely (a) trilinear hysteretic models of the first
type connected in parallel, and (b) trilinear hysteretic models of the second type also
connected in parallel. The results show that the complex nonlinear shear behavior of high damping rubber bearings can be correctly simulated by a parallel system which consists of
only one component, namely the trilinear hysteretic system of the first type. The second
parallel system was not able to describe the enlargement of the dissipated hysteresis area
for large strain amplitudes.
Base isolator devices are widely used for mitigation of vibrations induced in structures by seismic actions. In order to achieve high performances in the mitigation of seismic effects, base isolator mechanical properties should be designed by an optimum criterion. In common approaches, the nature of dynamic loads is assumed as the only source of uncertainty.
In the present paper a robust optimization criterion for base isolator devices design is proposed, considering the unavoidable effects of uncertainty in structural properties and seismic action. Uncertain parameters are modeled as random variables and are represented by bounded independent probability density function, with uniform law. The structure is described by a single-degree-of-freedom model and is protected by a linear base isolator in order to reduce vibration levels induced by base acceleration, here modeled by the stationary Kanai-Tajimi stochastic process. The optimal design is formulated as a constrained minimization problem, assuming as an objective function a suitable measure of the isolator efficiency and imposing a constraint on the maximum isolator displacement. A sensitivity analysis is carried out on the robust solution in order to assess characteristics and differences with respect to the conventional deterministic solution
A physical model composed of a tri-linear spring, a friction slider and a viscous damper is proposed for the
simulation of the dynamic behaviour of hybrid base isolation systems (HBIS) composed of high damping rubber bearings (HDRB) and low friction sliding bearings (LFSB). After the introduction of the constitutive equations for each device composing the overall system, it is shown that the motion of the system consists of alternating linear phases. An analytical solution is provided in compact form for all possible phases of motion. The end conditions for one phase provide the initial conditions for the next one. The solution is applied to the dynamic identification of the HBIS of the Solarino buildings. A well established evolution strategy (CMA-ES) is used as the dynamic identification algorithm. The estimated values of the physical parameters, together with simulated test responses, contribute to a better understanding of the behaviour of HBIS.
The development of a general framework for reliability-based design of base-isolated structural systems under uncertain conditions is presented. The uncertainties about the structural parameters as well as the variability of future excitations are characterized in a probabilistic manner. Nonlinear elements composed by hysteretic devices are used for the isolation system. The optimal design problem is formulated as a constrained minimization problem which is solved by a sequential approximate optimization scheme. First excursion probabilities that account for the uncertainties in the system parameters as well as in the excitation are used to characterize the system reliability. The approach explicitly takes into account all non-linear characteristics of the combined structural system (superstructure-isolation system) during the design process. Numerical results highlight the beneficial effects of isolation systems in reducing the superstructure response.
In the present work, we investigate the response of a hybrid base isolation system under earthquake excitation. The physical parameters of the hybrid base isolation system are identified from dynamic tests performed during a parallel project involving two residential buildings in the town of Solarino, Sicily, using the well-established optimization procedure 'covariance matrix adaptation-evolution strategy' as dynamic identification algorithm in the time domain. The base isolation system consists of high damping rubber bearings and low friction sliding bearings. Two separate models are employed for the numerical simulation of the high damping rubber bearing component, namely a bilinear system and a trilinear system, both in parallel with a linear viscous damper. In addition, a linear Coulomb friction model is used to describe the behavior of the low friction sliding bearing system. Analytical solutions are provided, in compact form, for all possible phases of motion of the hybrid base isolation system under earthquake excitation. A series of numerical simulations are carried out to highlight the behavior of the considered hybrid base isolation system under different excitation and site conditions.
The optimum design of base isolation system to control seismic vibration considering uncertain system parameters are usually performed by minimizing the unconditional expected value of mean square response of a structure without any consideration to the variance of such responses due to system parameter uncertainty. However, the unconditional mean square response based designed may have larger variance of responses due to uncertainty in system parameters and the overall system performance may be sensitive. But, it is desirable that the optimum design should reduce both the mean and variance of dynamic performance measure under system parameter uncertainty. The present study deals with robust design optimization (RDO) of base isolation system considering random system parameters characterizing the structure, isolator and ground motion model. The RDO is performed by minimizing the weighted sum of the expected value of the maximum root mean square acceleration of the structure as well its standard deviation. A numerical study elucidates the importance of the RDO procedure for design of base isolation system by comparing the proposed RDO results with the results obtained by the conventional stochastic structural optimization procedure and the unconditional response based optimization.
In this work, the stochastic response of secondary systems attached to a base-isolated structure undergoing random ground motions is examined. It is assumed that the properties of this combined structural system are deterministic, while the ground motions are described by a filtered white noise model. The only nonlinear component of this structural system is its base isolation mechanism, which is linearized by using equivalent linearization. Also, a substructuring algorithm is developed which requires the dynamic properties of the individual, fixed-base components of the structural system. Both stationary as well as nonstationary cases are considered and comparisons are made with the results of Monte-Carlo simulations to ascertain the validity of this methodology. The example studied herein is a six-storey steel building frame with a base isolation system consisting of sliding bearings and restoring force springs. For this example, spectra are constructed that account for primary-secondary system interaction and depict the effect of variations in the base isolator's structural parameters and in the mass and location of the secondary system on the latter's root-mean-square (RMS) accelerations.