INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2007; 72:1261–1313 Published online 23 March 2007 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/nme.2038 Numerical aspects of a real-time sub-structuring technique in structural dynamics R. Sajeeb § , D. Roy ¶ and C. S. Manohar ∗, †, ‡ Structures Lab, Department of Civil Engineering, Indian Institute of Science, Bangalore 560012, India SUMMARY A time domain coupling technique, involving combined computational and experimental modelling, for vibration analysis of structures built-up of linear/non-linear substructures is developed. The study permits, in principle, one or more of the substructures to be modelled experimentally with measurements being made only on the interfacial degrees of freedom. The numerical and experimental substructures are allowed to communicate in real time within the present framework. The proposed strategy involves a two-stage scheme: the first is iterative in nature and is implemented at the initial stages of the solution in a non-real-time format; the second is non-iterative, employs an extrapolation scheme and proceeds in real time. Issues on time delays during communications between different substructures are discussed. An explicit integration procedure is shown to lead to solutions with high accuracy while retaining path sensitivity to initial conditions. The stability of the integration scheme is also discussed and a method for numerically dissipating the temporal growth of high-frequency errors is presented. For systems with non- linear substructures, the integration procedure is based on a multi-step transversal linearization method; and, to account for time delays, we employ a multi-step extrapolation scheme based on the reproducing kernel particle method. Numerical illustrations on a few low-dimensional vibrating structures are presented and these examples are fashioned after problems of seismic qualification testing of engineering structures using real-time substructure testing techniques. Copyright 2007 John Wiley & Sons, Ltd. Received 14 June 2006; Revised 28 January 2007; Accepted 10 February 2007 KEY WORDS: real-time sub-structuring; numerical and experimental sub-structures; extrapolations; reproducing kernel particle method; explicit and implicit time-stepping schemes ∗ Correspondence to: C. S. Manohar, Structures Lab, Department of Civil Engineering, Indian Institute of Science, Bangalore 560012, India. † E-mail: manohar@civil.iisc.ernet.in ‡ Professor. § Research Student. ¶ Associate Professor. Contract/grant sponsor: Indian Institute of Science Copyright 2007 John Wiley & Sons, Ltd.