Dynamic Substructuring by the Craig–Bampton Method Applied to Frames

Purpose The Craig–Bampton method is a substructuring technique that reduces the number of internal degrees of freedom of substructures by approximations, using a set of truncated vibration modes. It is useful for structural designs with many degrees of freedom. This work aims to develop substructuring through the Craig–Bampton method for free vibration analysis on planar frames according to the frequency range of interest. Methods The finite-element models of different substructures were assembled. Thus, the degrees of physical freedom were reduced according to the frequency range of interest. The reduced-order models were coupled. Thus, the physical response was obtained. Detailed calculation and the algorithm flowchart are provided. Conclusions The study of frame dynamics using the present method in different frequency ranges of interest was presented and validated with the results of a commercial software. It was possible to clarify the coupling formulations of the component mode synthesis, as well as the amount of reduction of the number of equations provided by the method, reaching less than 4% of the complete model, for the considered cases.

[1]  S.W.B. Klaassen,et al.  Experimental twelve degree of freedom rubber isolator models for use in substructuring assemblies , 2020 .

[2]  A. A. Sani,et al.  Free vibration analysis of a steel T-Shape frame including semi-rigid Khorjini connection with continuous beam , 2016 .

[3]  Augusto Pippi,et al.  Dynamic Response to Different Models of Adjacent Coupled Buildings , 2020, Journal of Vibration Engineering & Technologies.

[4]  Matthew S. Allen,et al.  Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction , 2017 .

[5]  Wei Tian,et al.  A review on dynamic substructuring methods for model updating and damage detection of large-scale structures , 2020, Advances in Structural Engineering.

[6]  Phill-Seung Lee,et al.  A dynamic condensation method with free interface substructuring , 2019, Mechanical Systems and Signal Processing.

[7]  Gang S. Chen,et al.  Characterization of Nonlinear Dynamics for a Highway Bridge in Alaska , 2018, Journal of Vibration Engineering & Technologies.

[8]  P. Sahoo,et al.  Free Vibration Analysis of Stiffened Plates , 2020 .

[9]  Daniel J. Rixen,et al.  Comparison of Different Approaches to Include Connection Elements into Frequency-Based Substructuring , 2020, Experimental Techniques.

[10]  Hangxin Liu,et al.  Accurate and fast three-dimensional free vibration analysis of large complex structures using the finite element method , 2019, Computers & Structures.

[11]  Daniel Rixen,et al.  A family of substructure decoupling techniques based on a dual assembly approach , 2012 .

[12]  Chandramouli Padmanabhan,et al.  A fixed–free interface component mode synthesis method for rotordynamic analysis , 2006 .

[13]  Daniel J. Rixen,et al.  A practical handling of measurement uncertainties in frequency based substructuring , 2020 .

[14]  Hongguang Li,et al.  An Improved Method for Parametric Model Order Reduction by Matrix Interpolation , 2019, Journal of Vibration Engineering & Technologies.

[15]  Ki-Tae Kim,et al.  The Bathe subspace iteration method enriched by turning vectors , 2017 .

[16]  Li-xin Lu,et al.  Step-by-step decoupling method for inverse substructuring analysis of a three-component coupled packaging system , 2015 .

[17]  D. Cao,et al.  Free Vibration of Variable Width Beam: Asymptotic Analysis with FEM Simulation and Experiment Confirmation , 2019, Journal of Vibration Engineering & Technologies.

[18]  M. Bampton,et al.  Coupling of substructures for dynamic analyses. , 1968 .

[19]  Ramin Ghiasi,et al.  A three-stage damage detection method for large-scale space structures using forward substructuring approach and enhanced bat optimization algorithm , 2018, Engineering with Computers.

[20]  Thomas Abrahamsson,et al.  Multifidelity component interface reduction and modal truncation augmentation , 2019, International Journal for Numerical Methods in Engineering.

[21]  K. Bathe,et al.  Component mode synthesis with subspace iterations for controlled accuracy of frequency and mode shape solutions , 2014 .

[22]  Xing Wang,et al.  An eigenvector‐based iterative procedure for the free‐interface component modal synthesis method , 2018, International Journal for Numerical Methods in Engineering.

[23]  Hendrik Rentzsch,et al.  Predicting mobile machine tool dynamics by experimental dynamic substructuring , 2016 .