42 S. B. Cooper et al. attached with two stores used to illustrate the behavior of a wing and an engine suspended by a means of nonlinear pylon also displayed the presence of weak nonlinearities during a vibration test, the results obtained illustrated some hardening characteristics as show in [6]. Similar study was also carried out on a large helicopter with the identification of weak nonlinear softening behavior on one of the vibration modes as shown in [7]. Other examples of case studies where nonlinearity have been noticed in aerospace structures can be found in [8] where nonlinearity was also detected at the elastomeric mounts supporting the four turboprop engines of the aircraft during the Ground Vibration Test (GVT) of the Airbus A400M aircraft designed for military purpose. The F-16 fighter aircraft also showed a nonlinear behavior at wing-to-payload mounting interface of the aircraft when a similar GVT was conducted [9]. Nonlinearities were also detected on the Cassini spacecraft due to the presence of gaps in the support of the Huygens probe [10]. More case studies on the presences of nonlinearities in engineering structures can be found in the literature, it is therefore possible to conclude that the development of identification techniques which are capable of producing satisfactory results when linear identification techniques fail is an active area of study in today’s structural dynamics society. In the real-world application nonlinearity is ever-present and as engineers push to design lighter, more flexible and more efficient structures, the design are shifting towards non-linear regime which also shows that there is a need for developing strategies for understanding the nonlinear response of these structures. Hence this paper addresses the nonlinear experimental identification, and the force controlled experimental test conducted on a demo aircraft model. This involves the use of established and robust identification techniques to identify the type of nonlinearity present in the assembled missile, the complete identification process i.e. (Detection, Characterization and initial Parameter estimation) was achieved based on experimental data. Measured time series and frequency data driven by sine-sweep test and random excitation were exploited to gain an initial insight to the dynamic behavior and properties of the assembly. The structure of the paper is as follows: Sect. 5.3 describes the first case experimental study conducted on the demo aircraft followed by the linear identification based on measured data from low level random excitation and a correlation and model updating step. Section 5.4 includes the pylon elements in the physical and numerical model, and correlate the former using again a low level random excitation. In Sect. 5.5, the nonlinear identification is initiated based on measured data and the use of the first two stages of the white-box identification process. (Detection, Characterization and Parameter Estimation), where random multisines, sine sweeps and force-controlled stepped sine data were used for most of the analyses. The conclusion of the study, an outline on future works and the collective use of different analysis techniques in this research are finally summarized in Sect. 5.6. 5.2 Description of the Test Item The baseline test item analyzed in this paper is a demo aircraft model, used extensively for demonstration and training purposes in the context of modal analysis and GVT. The plane, entirely built in aluminum, consists of a beam with square cross-section (the fuselage), connected to a bigger (wings) and smaller (horizontal stabilizer or tail plane)-plates. An additional vertical plate, representing the fin or vertical stabilizer, is connected to the tail plane by means of L-shaped beam. All components are connected by mean of bolts. At the front and rear of the fuselage, two eye bolts easily allow suspending the demo aircraft and obtain the desired boundary conditions for modal testing. A CAD representation of the whole aircraft model is shown in Fig. 5.1. To introduce a local nonlinearity, the pylon models previously analyzed in [6, 11] are also here used: in these elements, the geometric nonlinearity of the thin plates supporting the lumped masses is combined with the cubic profiles of the blocks which connect the “engine” to the wing. As the engine deflection increases, a bigger portion of the pylon comes into contact with the blocks’ surface, thus introducing a stiffening effect. The position of the pylons on the wings and the length and thickness of it were designed and optimized to observe modal interactions when the nonlinearity is excited. By connecting the pylon to the slender wings, it is expected that some nonlinearities on the aircraft might also be triggered. First of all, the connection between the pylon and the wings relies on two M3 bolts, which might cause the connection to open when the system is excited at resonance. Secondly, all plates are connected with bolts which, at high response levels, might induce a local softening behaviour. Finally, as the wings are relatively slender, it might be expected that, similarly to the pylon, they might also experience a geometric nonlinear response for high wing tip displacements. It will be also an objective of this paper to detect and quantify the nonlinear response at these locations, but the identification will mostly focus on the pylon behavior.
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