Probabilistic characterization of the performance of actively controlled smart structures

摘要

Smart materials and structural systems are increasingly attracting attention from the engineering community because of their importance in current and future high performance structural applications. As these new structural systems emerge, there is an important need to have capabilities that can be employed for assessing their performance with reference to the primary functional requirement of structural integrity and control robustness as well as reliability. Furthermore, it is desirable to establish adequate performance metrics (which account for inherent or environmental uncertainties) that can be used as a quantitative basis for the comparative evaluation of various design options or for assessing the state of such systems that are already in service. In this study, two measures that can be used for probabilistic characterization and assessment of the performance of actively controlled smart structures are developed. The framework is based on the use of the probabilistic finite element strategy for modeling the parent (host) structure as well as the piezoelectric materials that are employed for sensing and actuation in the assembled system. The uncertainties inherent in the parent structure and the piezoelectric materials are propagated through the probabilistic finite element model. This enables rational and realistic characterization of the performance measures. The probabilistic models are based on the use of advanced reliability analysis algorithms which utilize fast probability integration algorithms that are robust and computationally more efficient than Monte Carlo simulation schemes. To facilitate efficient computation, an adaptive response surface methodology is employed for the approximation of the probabilistic finite element response quantities. Example problems are used to illustrate the robustness and usefulness of the proposed methodology.