Exact Fixed-Interfacial Substructure Synthesis Using Medium-Order Normal Modes

With the purpose of engineering application, this paper systematically studies exact dynamic substructuring technique based on the use of the medium-order normal mode of each substructure with fixed interface.Firstly a theoretical component mode synthesis for calculation of eigenvalues in medium frequency range is proposed. By utilizing vibration equations of substructures, exact residual constraint modes are formulated, together with medium-order normal modes, to describe dynamic behavior of components. In addition, geometrical compatibility and force equilibrium along substructure boundaries are employed in obtaining reduction transformation for all interfacial degrees of freedom. Thus eigenfunction of the assembled structure in medium frequency range is formed through a Rayleigh-Ritz procedure, thereby obtaining corresponding eigenvalues.Secondly, an accurate dynamic substructuring method for frequency response analysis of a proportional damped structure is presented. Through applying modal superposition to frequency response analysis of substructures, modal response of lower- and higher-order normal mode is formulated, and residual flexibility is introduced to correct the errors generated by cutting off the lower- and higher-order normal modes from substructures in synthesis process. By means of dual compatibility conditions along substructure boundaries, generalized frequency response function based on mid-order normal modes is established, whereby geometrical frequency response function of each substructure can be calculated subsequently through transformations relating geometrical coordinates and generalized coordinates.Finally, based on the use of geometrical frequency response function above, an exact synthesis method for random vibration analysis of substructures is investigated. Partition of coupling frequency response function leads to groups of local frequency response functions. Then random response analysis could be performed on each component independently, through random vibration theory, for calculating the statistical characteristics of substructure response, including substructure deformation and acceleration, such as power spectral density, auto- and cross-correlation, mean value. After that, numerical examples of multi-degree-of-freedom systems, beam and plane structures are presented respectively. Corresponding analysis data would demonstrate the effectiveness and high accuracy of the proposed methods.