A. Culla, W. D’Ambrogio, A. Fregolent and A. Schiavone 1 Introduction In experimental dynamic substructuring two main problems can be defined: addition of substructures (coupling) and subtraction of substructures (decoupling). Coupling is important to find out the dynamic behaviour of complex structures from a dynamic description of their components. Decoupling can be important in built-up structures where some components (critical subsystems or joints) cannot be removed or accessed easily. Decoupling involves the identification of the dynamic behaviour of a structural subsystem, starting from information about the remaining part of the structural system (residual subsystem) and from the known dynamic behaviour of the complete system. Addition of substructures (coupling) can be seen as a structural modification problem [6]. Similarly, the decoupling problem can be seen as a structural modification problem with negative modification. Due to modal truncation problems, in experimental dynamic substructuring, the use of FRFs (Frequency Based Substructuring) is preferred with respect to the use of modal parameters. The main algorithm for frequency based substructuring is the improved impedance coupling [8] that involves just one matrix inversion with respect to the classical impedance coupling technique that requires three inversions. A general framework for dynamic substructuring is provided in [12, 10]: an interesting formulation is the so called dual domain decomposition that allows to retain the full set of global DoFs by ensuring equilibrium at the interface between substructures. Whatever be the used approach, the dynamic behaviour at all the coupling DoFs must be determined. Therefore, if coupling involves transmission of moments, rotational measurements are required. Lack of or bad information about rotational DoFs is always a problem. Several techniques have been devised to circumvent this problem, such as equivalent multi point connection [1, 10] or transmission simulator method [13]. Furthermore, when using experimental data, several issues can be considered [14]. Whilst addition of substructures often leads to satisfactory results even in relatively complex cases, subtraction of substructures is a source of problems, mainly due to ill-conditioning, even in apparently trivial applications. There are several different reasons leading to ill-conditioning: inertia ratios at interface [9], different stiffnesses at interface [7], internal resonances of the residual subsystem with fixed interface [2, 15]. Some critical issues of decoupling (such as ill-conditioning around a discrete number of frequencies) have been highlighted and verified by using simulated data corrupted by random noise. In this paper, experimental data acquired on a lumped parameter benchmark system with translating masses are used to check previously highlighted problems both in coupling and decoupling, and to look for additional issues (systematic errors, inconsistencies, etc.) that can not be observed from simulated data. The use of a lumped parameter benchmark allows to avoid two series of problems: problems due to rotational DoFs and modal truncation problems which may appear even using an FRF based approach because of curve fitting. 90
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