An accurate substructural synthesis approach to random responses

Z. G. Ying, W. Q. Zhu, S. Q. Ye, Yiqing Ni

Research output: Journal article publicationJournal articleAcademic researchpeer-review


An accurate substructural synthesis method including random responses synthesis, frequency-response 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 mean-square responses can be calculated separately. The accuracy and capacity of the proposed substructure synthesis method is verified by numerical examples.
Original languageEnglish
Pages (from-to)47-75
Number of pages29
JournalStructural Engineering and Mechanics
Issue number1
Publication statusPublished - 10 Jul 2011


  • Fixed interface substructure
  • Frequency-response function
  • Mid-order mode
  • Random response
  • Substructural synthesis

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Building and Construction
  • Mechanics of Materials
  • Mechanical Engineering

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