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A Rosenbrock‐W method for real‐time dynamic substructuring and pseudo‐dynamic testing
Author(s) -
Lamarche C. P.,
Bonelli A.,
Bursi O. S.,
Tremblay R.
Publication year - 2009
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.884
Subject(s) - jacobian matrix and determinant , nonlinear system , dynamic testing , eigenvalues and eigenvectors , modal , control theory (sociology) , mathematics , damping matrix , dissipation , stability (learning theory) , dynamic equation , matrix (chemical analysis) , algorithm , stiffness matrix , stiffness , structural engineering , computer science , engineering , materials science , control (management) , quantum mechanics , artificial intelligence , machine learning , polymer chemistry , composite material , thermodynamics , chemistry , physics
A variant of the Rosenbrock‐W integration method is proposed for real‐time dynamic substructuring and pseudo‐dynamic testing. In this variant, an approximation of the Jacobian matrix that accounts for the properties of both the physical and numerical substructures is used throughout the analysis process. Only an initial estimate of the stiffness and damping properties of the physical components is required. It is demonstrated that the method is unconditionally stable provided that specific conditions are fulfilled and that the order accuracy can be maintained in the nonlinear regime without involving any matrix inversion while testing. The method also features controllable numerical energy dissipation characteristics and explicit expression of the target displacement and velocity vectors. The stability and accuracy of the proposed integration scheme are examined in the paper. The method has also been verified through hybrid testing performed of SDOF and MDOF structures with linear and highly nonlinear physical substructures. The results are compared with those obtained from the operator splitting method. An approach based on the modal decomposition principle is presented to predict the potential effect of experimental errors on the overall response during testing. Copyright © 2009 John Wiley & Sons, Ltd.