Abstract
In the performance-based design of earthquake-resistant structures, researchers have recently proposed protection systems where base isolation devices are supplemented by active control mechanisms. Established approaches to understanding this problem domain rely on numerical and experimental analyses, which have the disadvantage of obscuring potential insight into cause-and-effect relationships existing between parameters of sub-optimal control and their affect on linear and nonlinear system response. As a first step toward mitigating this limitation, this paper explores the role of symbolic analysis in understanding how sub-optimal bang-bang control mechanisms depend on design objectives and their impact on performance of base isolated structures. New results are obtained through three avenues of investigation: (1) Single- and two-degree-of-freedom systems, (2) Restricted classes of multi-degree-of-freedom systems, and (3) Sensitivity of parameters in modified bang-bang control to localized nonlinear deformations in the base isolation devices. The principle outcome is matrices of symbolic expressions for bang-bang control expressed in terms of the structural system parameters and state. We identify modeling constraints and limits (e.g., perfect isolation) where lengthy symbolic expressions simplify to the point where relationships between the inner workings of the bang-bang control strategy and specific design objectives become evident.
Highlights
In the performance-based design of earthquake-resistant structures, researchers have recently proposed protection systems where base isolation devices are supplemented by active control mechanisms
As a case in point, the emerging interest in base isolation systems supplemented by active control is motivated by the observation that levels of structural response in both moderate and severe earthquakes can be significantly reduced by: (1) introducing mechanisms to separate the natural periods of vibration for the main structural system from the details of ground motions, and (2) complementing the isolated system behavior with active control
This paper explores the role of symbolic analysis in understanding how sub-optimal bang-bang control mechanisms depend on design objectives and their impact on performance of base isolated structures
Summary
The design of structures to resist earthquake loading is complicated by the large uncertainty in predicting the spatial and temporal nature of future seismic events. As a case in point, the emerging interest in base isolation systems supplemented by active control is motivated by the observation that levels of structural response in both moderate and severe earthquakes can be significantly reduced by: (1) introducing mechanisms to separate the natural periods of vibration for the main structural system from the details of ground motions, and (2) complementing the isolated system behavior with active control. Simplified methods of design for base isolated structures have been proposed by Turkington et al [26,27], Ghobarah and Ali [9], among others While these performance-based code provisions and simplified design procedures give high-level guidance regarding acceptable and unacceptable levels of performance (and how to achieve it), there is a mounting body of evidence that base isolation may not always provide adequate protection [10,11,31]. The hypothesis of our work is that formulation of the appropriate methodologies will be facilitated if cause-and-effect relationships existing between design objectives, properties of the control, and their effect on the system response are known
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