b'Engineer Innovation | AerospaceFigure 2: experimental and numerical results for unstable control casea) Experimental results: unstable control caseb) Numerical results: unstable control caseapproach is able to validate andnumerical parameters used in the reproduce all cases with both stable andmechanical model are defined. unstable control. As a reference, we can report here the instability of the controlEven in this case, we were able to at the notching sensor (2nd DOF forreproduce almost all the experimental numerical model) obtained with a veryresults as shown in Figures 1 and 2 strong reactivity control around theusing only the linear mechanical model. resonance frequency of the structureIn some cases, the experimental results (Figure 2).in Figure 2 show that a non-linear mechanical model is necessary to Now we repeat the same approach forreproduce the experimental behavior. an industrial test: the Galileo satellite.Using the example of a transversal The approach is the same. We considerconfiguration for a sweep sine of the transversal and longitudinal0.5 oct/min and without notching, we configurations. The numerical approachare able to control in experimental tests is similar to the previous one becausethe vibration at the base of shaker, we focus our attention only on the firstwhich is not true in the numerical mode shape of the satellite. In Figure 3,approach as shown in Figure 4. we show the experimental set-up forMoreover, the experimental signal the transversal configuration and theshows multi-harmonics of the mechanical model. In Table 1, thefundamental excitation frequency. This behavior is typical of a non-linear behavior of the structure and this is the main reason why the simulation model cannot reproduce the experimental results. For this reason the next step was to show the approach that can be used in case of non-linear structures. Non-linear approachAriane Group has detected the presence of multiple odd and even harmonics in the measured time responses of the notching and control channels both for Figure 3: Tested coupled structure the longitudinal and transversal testing (a) Experimental set-up (b) Mechanical modelling in Simcenterconfigurations. During longitudinal integrated environment tests, the dispenser is connected to the expander head of the shaker by a Mass (KG)Stiffness (N/m)Damping (N m/s) Nat frequency (Hz)fixation system comprising a series of fasteners. These fasteners are assumed Shaker1,500 236.87 x103 1,88 x103 (5%) 2 to suffer from a loss of stiffness when Galileo2,500 22,2 x106 3,78 x103 (0.8%) 15 subjected to a tensile load. To represent this behavior, a non-linear restoring Table 1: Physical properties of the 2-DOF linear model force law is added as a parallel spring 58'