Focussing elastic waves in wing leading edge structures

Raffaele, Davide (2022) Focussing elastic waves in wing leading edge structures. University of Southampton, Doctoral Thesis, 137pp.

Record type: Thesis (Doctoral)

Abstract

Wings and other aircraft lifting surfaces must be kept free from ice during flight to maintain aerodynamic performance and avoid loss of control. In recent years, as an alternative to traditional thermal methods, several low-energy approaches that use high amplitude shock or vibration have been explored. Amongst them, ultrasonic vibration methods have been successfully validated, but the need to drive the piezoelectric actuators at resonance can cause them to debond from the structure, heat up or crack. To circumvent this problem, a method that achieves amplification through wave focussing instead of resonance has been recently proposed. This approach has been successfully validated for a beam and shown capable of delaminating an ice substitute. However, extension
of this method to realistic wing structures requires prior knowledge of dispersion characteristics. This thesis originates from research questions regarding the assessment of the feasibility of such a method and other wave focussing techniques present in the literature to wing structures, concentrating in particular on the wing slat leading edge where ice accumulates.

The thesis starts by introducing an analytical model of an infinite Euler-Bernoulli beam characterised by a single wave mode. Three wave focussing techniques (i.e. the Precompensation, Inverse filter, and Time reversal techniques) are then presented and successfully applied to the same beam model, highlighting the important aspects from the viewpoint of the application. Successively, the formulation of the Semi-Analytical Finite Element (SAFE) method is briefly introduced, followed by a pre-existing SAFE implementation for free wave propagation in the commercial Comsol Multiphysics software. Thanks to a powerful tool of this software that allows one to set up and solve Comsol models directly from the Matlab environment, a procedure to extract the SAFE global mass and stiffness matrices is proposed. A pre-existing SAFE formulation to compute the forced response is also implemented, leading to a customised software that allows conducting the SAFE modelling of an arbitrary waveguide, solving both free and forced wave propagation entirely in the Matlab environment. Through the use of the proposed SAFE implementation, a simply supported plate strip is then modelled and the obtained results are validated with analytical solutions.

A SAFE model of an idealised wing slat leading edge is developed to predict the dispersion characteristics and structural response to a concentrated load for the application of wave focussing techniques. To account for energy loss within the material, some structural damping in a small percentage is then introduced through the hysteretic model. Three experimental techniques of wavenumber estimation are presented and applied to an Euler-Bernoulli beam with emulated anechoic terminations. For each technique, the estimated and predicted results are compared, evidencing their capabilities and limitations. Amongst them, the correlation method has been revealed to be the most accurate and is then used to validate the SAFE model of the idealised wing slat leading edge through experimental measurements on a laboratory structure.

In the last part of the thesis, the three wave focussing techniques implemented to the Euler-Bernoulli beam model are extended to the SAFE model of the idealised wing slat leading edge, highlighting their strengths and limitations. From the obtained results, the Pre-compensation technique has shown not to be able to provide wave focussing due to the high interference amongst waves. Conversely, the time reversal technique was able to generate a high shock response at the target position. The inverse filter technique, instead, showed ability to reconstruct the original excitation waveform and focusing waves at the target position; however, the enhanced quality of the focal signal came at the expense of lower focal amplitude. The one-bit method, a technique used in time-reversal experiments to increase the amplitude of the focal signal, is also implemented. The results showed that with the one-bit time reversal, the response at the focal point was three times bigger than the conventional time reversal technique, suggesting its use for de-icing applications.

The SAFE model is also used to conduct a parametric study on the time reversal technique to investigate the effects of the excitation bandwidth, propagation distance and structural damping on wave focussing. To evaluate how much greater the response obtained using time reversal focussing is compared to another excitation signal used as a reference, an amplification factor in terms of power and peak amplitude is also defined. The results showed that, although different in values, both amplification factors follow a similar trend. In particular, the amplification factor related to peak amplitude increases as the excitation bandwidth and focal distance increase. However, at higher focal distances
and levels of damping, attenuation is responsible for reducing the amplification.
Finally, through measured FRFs from a laboratory structure consistent with the SAFE model of the idealised wing slat leading edge, a simpler approach to the conventional time reversal technique is successfully implemented.