Efficient optimal design and design‐under‐uncertainty of passive control devices with application to a cable‐stayed bridge

Summary Structures today may be equipped with passive structural control devices to achieve some performance criteria. The optimal design of these passive control devices, whether via a formal optimization algorithm or a response surface parameter study, requires multiple solutions of the dynamic response of that structure, incurring a significant computational cost for complex structures. These passive control elements are typically point‐located, introducing a local change (possibly nonlinear, possibly uncertain) that affects the global behavior of the rest of the structure. When the structure, other than these localized devices, is linear and deterministic, conventional solvers (e.g., Runge–Kutta, MATLAB's ode45, etc.) ignore the localized nature of the passive control elements. The methodology applied in this paper exploits the locality of the uncertain and/or nonlinear passive control element(s) by exactly converting the form of the dynamics of the high‐order structural model to a low‐dimensional Volterra integral equation. Design optimization for parameters and placement of linear and nonlinear passive dampers, tuned mass dampers, and their combination, as well as their design‐under‐uncertainty for a benchmark cable‐stayed bridge, is performed using this approach. For the examples considered herein, the proposed method achieves a two‐orders‐of‐magnitude gain in computational efficiency compared with a conventional method of comparable accuracy. Copyright © 2016 John Wiley & Sons, Ltd.