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Structural Engineering and Mechanics   Volume 39, Number 1, July10 2011, pages 47-75
An accurate substructural synthesis approach to random responses
Z.G. Ying, W.Q. Zhu, S.Q. Ye and Y.Q. Ni

Abstract     [Buy Article]
    An accurate substructural synthesis method including random responses synthesis, frequencyresponse functions synthesis and mid-order modes synthesis is developed based on rigorous substructure description, dynamic condensation and coupling. An entire structure can firstly be divided into several substructures according to different functions, geometric and dynamic characteristics. Substructural displacements are expressed exactly by retained mid-order fixed-interfacial normal modes and residual constraint modes. Substructural interfacial degree-of-freedoms are eliminated by interfacial displacements compatibility and forces equilibrium between adjacent substructures. Then substructural mode vibration equations are coupled to form an exact-condensed synthesized structure equation, from which structural mid-order modes are calculated accurately. Furthermore, substructural frequency-response function equations are coupled to yield an exact-condensed synthesized structure vibration equation in frequency domain, from which the generalized structural frequency-response functions are obtained. Substructural frequency-response functions are calculated separately by using the generalized frequency-response functions, which can be assembled into an entire-structural frequency-response function matrix. Substructural power spectral density functions are expressed by the exact-synthesized substructural frequency-response functions, and substructural random responses such as correlation functions and meansquare responses can be calculated separately. The accuracy and capacity of the proposed substructure synthesis method is verified by numerical examples.
Key Words
    substructural synthesis; fixed interface substructure; random response; frequency-response function; mid-order mode
Z.G. Ying and W.Q. Zhu: Department of Mechanics, School of Aeronautics and Astronautics, Zhejiang University,
Hangzhou 310027, P.R. China
S.Q. Ye and Y.Q. Ni: Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong

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