The exact extreme response and the confidence extreme response analysis of structures subjected to uncertain-but-bounded excitations |
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| Institution: | 1. State Key Laboratory of Robotics, Chinese Academy of Sciences, Shenyang Institute of Automation, Institutes for Robotics and Intelligent Manufacturing, Shenyang 110200, PR China;2. Department of Mechanical Engineering, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;3. Dalian University of Technology, Dalian, PR China;1. Université Paris-Est, Laboratoire Modélisation et Simulation Multi-Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallée, France;1. Key Lab of Science and Technology on Hydrodynamics, China Ship Scientific Research Center, Wuxi, 214082 Jiangsu, People’s Republic of China;2. School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, 201100 Shanghai, People’s Republic of China;1. Department of Mechanics and Engineering Science, Sichuan University, Chengdu 610065, China;2. State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing 400044, China;3. Department of Mechanical Engineering, University of Maryland, Baltimore County, Baltimore, MD 21250, USA;1. Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai 600 036 India;2. Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600 036 India;1. P.N. Lebedev Physical Institute of the RAS, Leninsky prosp. 53, Moscow 119991, Russia;2. Far Eastern Federal University, Sukhanova str. 8, Vladivostok 690090, Russia;3. Department of Energy, CIEMAT, Avda. Complutense 40, Madrid 28040, Spain;4. Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, Moscow 117198, Russia |
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| Abstract: | In this study, the methods for computing the exact bounds and the confidence bounds of the dynamic response of structures subjected to uncertain-but-bounded excitations are discussed. Here the Euclidean norm of the nodal displacement is considered as the measurement of the structural response. The problem of calculating the exact lower bound, the confidence (outer) approximation and the inner approximation of the exact upper bound, and the exact upper bound of the dynamic response are modeled as three convex QB (quadratic programming with box constraints) problems and a problem of quadratic programming with bivalent constraints at each time point, respectively. Accordingly, the DCA (difference of convex functions algorithm) and the vertex method are adopted to solve the above convex QB problems and the quadratic programming problem with bivalent constraints, respectively. Based on the inner approximation and the outer approximation of the exact upper bound, the error between the confidence upper bound and the exact upper bound of dynamic response could be yielded. Specially, we also investigate how to obtain the confidence bound of the dynamic response of structures subjected to harmonic excitations with uncertain-but-bounded excitation frequencies. Four examples are given to show the efficiency and accuracy of the proposed method. |
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