In Fig.3 there is a snapshot of CONCERTO’s output to the analysis of simulated transmissibility of a system with combined nonlinearities (quadratic damping + cubic stiffness) excited by a harmonic base oscillation with amplitude 0.5mm Y = . In the top-left corner, there are the measured points, displayed as response (displacement) spectrum. The transmissibility is also displayed as a Nyquist plot (top-right). The information on the nonlinearities of the system are contained in the two plots in the lower-left corner: one depicts the extracted natural frequency, Eqn.(3), and the other the loss factor, Eqn.(4), (displayed as damping ratio using and the approximation 2 η ζ ≈ ) as function of the amplitude of vibration displacement response of the mass. Fig.3: Example of CONCERTO output for the analysis of a nonlinear system with combined cubic stiffness and quadratic damping From the frequency and damping plots (against the displacement), it is possible to identify rather clearly the stiffening effects and the linear increase of damping with displacement (an indication of a quadratic function of the velocity). In order to assess the quality of the results obtained with CONCERTO when applied to transmissibility data, these are compared with those obtained using the identification method on FRF data and which have been published in reference [7]. The results obtained with the identification algorithm CONCERTO are shown in Fig.4-6. Fig. 4 (a) shows the results obtained by analysing a system with cubic hardening spring: it can be seen that by increasing the level of excitation, and thus the amplitude of response, there is a 9 10 11 2 4 6 8 x 10 -3 Frequency [Hz] Displacement [m] Real Imag 0 0.005 0.01 10 10.5 Frequency [Hz] 0 0.005 0.01 0 2 4 Displacement [m] Damping Ratio [%] 485
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