Real-time dynamic substructuring in a coupled oscillator-pendulum system

Real-time dynamic substructuring is a powerful testing method which brings together analytical, numerical and experimental tools for the study of complex structures. It consists of replacing one part of the structure with a numerical model, which is connected to the remainder of the physical structure (the substructure) by a transfer system. In order to provide reliable results, this hybrid system has to remain stable during the whole test. One of the problems with the method is the presence of delay (due to several technical factors) which can lead to destabilization and failure. In this paper we apply the dynamic substructuring technique to a simple nonlinear system, consisting of a pendulum attached to a mass-spring-damper. The latter is replaced by a numerical model and the transfer system is an actuator. The system dynamics is governed by two coupled second order neutral delay differential equations. We carry out a stability analysis of the system and identify possible regions of instability and the number of stability switches depending on parameters and the size of the delay. Using the parameters from a real experiment, we perform numerical simulations which confirm our analytical findings, and show regions of periodic and quasi-periodic behaviour. We also confirm our stability results by comparison with an experiment. The agreement is excellent.