64 Furkan K. C¸ elik et al. various theoretical and experimental cases. Among these techniques, the application of RCT on nonlinear structures results in quasi-linear FRFs, which opens the way for using linear substructuring methods with nonlinear systems. The theory of the method discussed in this paper is quite straightforward [16] and built on quasi-linear FRFs, which can be obtained by employing RCT. The method makes it possible to apply the decoupling techniques for linear structures to nonlinear structures exhibiting nonlinearities in any or all substructures. In that respect, it extends FDM-NS [10] to nonlinear systems regardless of the location, type, or severity of the nonlinear elements. The application of the method on a real structure with weak and local nonlinearity [17] gave promising results. However, the applications and limitations of the method are not studied extensively. This paper aims to provide an investigation on the applicability, accuracy and limitations of the method. Firstly, the underlying theory of RCT and linear decoupling will be presented, and then examples of decoupling from a single and multiple connection degree of freedoms (DoFs) will be presented to reach conclusions about the accuracy and limitations of the method. Theory The method suggested in [7,10] was restricted to cases where the nonlinearity is localized at the excitation DoF, or the nonlinearity is between two DoFs where the relative displacement of these DoFs is kept constant with closed loop control. This restriction can be bypassed by the application of RCT, which is used to identify various other real system nonlinearities, such as a piezo-actuator shown in Fig. 1 [18] , a control fin actuation mechanism with high friction [19] and a bolted lap-jointed structure [20] . Fig. 1 Quasi-linear constant-response FRFs of Nonlinear Piezoelectric Actuators measured by RCT The equation of motion of a nonlinear system with structural damping can be written in the frequency domain as follows, −ω2MX+iHX+KX+∆(X)X=F (1) Herein, M, K, andHare the underlying linear system’s mass, stiffness, and structural damping matrices, respectively. ∆denotes the response level dependent nonlinearity matrix [21] . Xis the response amplitude vector, F is the harmonic excitation amplitude vector, andωis the excitation frequency. Eq. (1) assumes that the system is under harmonic excitation and that the effect of sub- and super-harmonics is negligible. By keeping any DoF of the system under a constant harmonic displacement amplitude, the displacement amplitudes of all DoFs remain nearly constant around the resonance region due to nonlinear normal mode theory [22] . This approach ensures that the nonlinearity matrix [21] behaves as an equivalent stiffness or damping matrix, making the system quasilinear. Subsequently, classical modal identification techniques like peak-picking are applied to the resulting response-leveldependent quasi-linear FRFs, yielding a response-level-dependent modal model of the system. The constant-force frequency
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