Using Video Processing for the Full-Field Identification of Backbone Curves in Case of Large Vibrations

Abstract

Nonlinear modal analysis is a demanding yet imperative task to rigorously address real-life situations where the dynamics involved clearly exceed the limits of linear approximation. The specific case of geometric nonlinearities, where the effects induced by the second and higher-order terms in the strain–displacement relationship cannot be neglected, is of great significance for structural engineering in most of its fields of application—aerospace, civil construction, mechanical systems, and so on. However, this nonlinear behaviour is strongly affected by even small changes in stiffness or mass, e.g., by applying physically-attached sensors to the structure of interest. Indeed, the sensors placement introduces a certain amount of geometric hardening and mass variation, which becomes relevant for very flexible structures. The effects of mass loading, while highly recognised to be much larger in the nonlinear domain than in its linear counterpart, have seldom been explored experimentally. In this context, the aim of this paper is to perform a noncontact, full-field nonlinear investigation of the very light and very flexible XB-1 air wing prototype aluminum spar, applying the well-known resonance decay method. Video processing in general, and a high-speed, optical target tracking technique in particular, are proposed for this purpose; the methodology can be easily extended to any slender beam-like or plate-like element. Obtained results have been used to describe the first nonlinear normal mode of the spar in both unloaded and sensors-loaded conditions by means of their respective backbone curves. Noticeable changes were encountered between the two conditions when the structure undergoes large-amplitude flexural vibrations.

The Teager-Kaiser Energy Cepstral Coefficients as an Effective Structural Health Monitoring Tool

“…The second case study concerns the spar of a prototype wing, the linear and nonlinear dynamics of which have been investigated in recent studies [61,62]. Importantly, the prototype skin is supposed to completely transfer the aerodynamic loads to the spar, making the structural behaviour of the latter a good approximation of the dynamical response of the whole spar-skin ensemble.…”

“…Therefore, this value has been set as the new cut-off frequency. The centre frequencies for MO-MMFCCs were defined from the modal analysis of the wing spar and benchmarked and validated against experimental data obtained in [61,62]; they correspond, in order of increasing natural frequency, to the 1st, 2nd, 3rd, and 4th flapwise bending mode; the 1st torsional mode; the 5th flapwise flexural; the 1st chordwise bending mode; the 2nd torsional; and, the 6th flexing modes. The tenth mode (the 7th flapwise) fell over the maximum investigable frequency at 333.88 Hz and was therefore replaced by adding '1 to the begin of the array, thus resulting in To conclude, the low frequency range of LO-MMFCCs was not changed and it remains defined between 0 and f s /2, which here becomes 128 Hz.…”

The Extreme Function Theory for Damage Detection: An Application to Civil and Aerospace Structures

“…The spar-portrayed in Figure 4a-can be seen as a thin, plate-like structural element with a peculiar shape. Due to its large flexibility, the spar may undergo large flap-wise oscillations [34,35] and it is therefore highly subject to the insurgence of fatigue damage, especially close to its clamped end and in its mid-length at the section where the width taper angle change. The simple Finite Elements (FE) model utilised here was realised in Ansys ® Mechanical APDL; 400 8-noded, 6-degrees-of-freedom-per-node quadratic shell elements were utilised.…”

Experimental modal analysis of structural systems by using the fast relaxed vector fitting method

“…Noteworthy, all tests were performed on the spar alone rather than on the actual skin‐spar ensemble, as the innovative external skin (modelled in the framework of the BEARD project 27 ) is supposed to transfer all the aerodynamical loads to the spar itself. Major details can be found in the inherent works 28,29,30 . The structure was considered when loaded with four inertial measurement units (IMUs) as depicted in Figure 5.…”