Simulación y ensayos de vibraciones en placas de material compuesto de fibra de carbono y detección de daño mediante la respuesta en frecuencia y la transformada wavelet

Resum

There is no doubt that damage detection in materials and structures is a topic of great industrial interest, since it allows one to reduce maintenance costs as well as technological, economic and social risks related to the structure. This is a key issue in engineering, particularly in design and industrial production, that has been addressed by a number of research efforts. To date, researchers have put forth multiple methods and techniques under what is generically referred to as Non-Destructive Tests (NDT), including ultrasonic, acoustic emission, eddy current, thermography, electromagnetic methods, and penetrant liquid tests. All of them are based on inspection of the structure at time intervals and fixed positions; that is, at the time and place of performance by technicians. They are therefore known as local methods. In contrast, a more recent trend is to inspect the health of the entire structure continuously over time, extracting features that allow it to be permanently monitored in terms of its state, providing conclusions that underline its life-time and the need for any repairs (global methods). This idea gives rise to self-disciplinary R+D work, named Structural Health Monitoring (SHM). The pioneer work by Chang indicates various scientific and economic aspects, along with an array of applications of SHM. Composite materials are required for many industrial sectors, given their low density and high strength and stiffness. Outstanding among these is Carbon Fiber Reinforced Polymer (CFRP). However, it is well known that its mechanical properties may be significantly degraded in the presence of damage. Given its multilayer construction, the most common damage is an internal delamination, which also often occurs after the impact of some external object. It is the main material used in this Thesis, but one plate used was aluminium, a material widely studied and widely used in aeronautics. This PhD Thesis uses Kirchoff plate theory, Ritz method and Finite Element Method (FEM) as the pillars of the theoretical calculations. The experimental work performed in this Thesis consists of vibration tests on rectangular plates, making them vibrate with a known excitation, using piezoelectric (PZT) actuators and sensors. Three plates were studied: one of aluminium (isotropic material), and two of CFRP (CFRP1 and CFRP2), the first one made of an orthotropic material and the second one made of a quasi-orthotropic material. Plate CFRP2 plate had two zones with different thicknesses. The plates were excited through a signal by means of one of the piezoelectric actuators (one on the center of the plate, the other one on the lower left quarter). The response signal of the plate was measured by four piezoelectric sensors positioned symmetrically with respect to the center. The plate was fully clamped (with a rigid steel frame) in most experiments, and quasi-free (resting on a sponge) in some of them. Piezoelectric sensors were connected with STP cables to the Brüel & Kjaer PULSE equipment input channels. The excitation signal was also generated with the PULSE output port. The Piezosystem EPA-104 amplifier boosted, with x20 gain, the PULSE output signal to the actuator. To reduce the influence of external vibrations, the frame was fixed to an anti-vibration table and the measurements were carried out at night with minimal environmental noise. To minimize the electromagnetic interference and electrical noise, the measurements were made in a differential way, and all equipment, including connection boxes, cable shields, frame, plates and support table, was connected to an independent ground system. A characterization of the PZT used demonstrated that they have a flat response from 200 to 1600 Hz. To characterize the vibration response of the undamaged plates used throughout this work we applied two approaches: modal analysis, which consists of studying the vibration modes and main frequencies of the plate, and transient analysis, studying the response of the plate in the time domain to a given excitation. For the modal analysis, three tools were used: FEM, Ritz method, and frequency analysis of experimental signals. The transient analysis involved the use of two tools: analysis of experimental signals and FEM signal. For modal analysis, the first step was to use frequency analysis of experimental signals to identify the initial main frequencies of the plate. Then, because it is very difficult to experimentally measure the thickness of the plate with accurate precision, an adjustment was made in order to find the optimal thickness. Having the optimal value of thickness, FEM simulations and Ritz method calculations were performed, obtaining similar results with the two, and differences with experimental frequencies were less than 3% in most cases. The mode shapes obtained with FEM and the Ritz method were very similar. For transient analysis, the first step was to experimentally measure the Rayleigh damping coefficients for all the plates, using these values for the FEM simulations. The excitations used were of two types: a random white-noise vibration signal with frequencies from 0 to 1600, and sines of different frequencies. The tests using white-noise as the excitation signal gave very similar results in the experimental and simulation tests. On the other hand, the tests using sines as the excitation signal gave different results for each test, despite the fact that the plate was always the same. This is because the obtained Frequency Response is dominated by the first harmonics of the excitation frequency, and the values of this peak are not always in the same proportions. It was proven that the cause of this behaviour was a misalignment between the PZT used and the plate, or possibly an internal misalignment of the PZT themselves. Damage studies were carried out using both modal and transient analysis. For modal analysis, the damage performed computationally (FEM and Ritz method) was holes, density increase and decrease, and Young's modulus reduction, all of them in three positions. In this case, the techniques used to detect the damage were the Modal Assurance Criterion (MAC), the Wavelet Transform using information of the undamaged plate, and an hybrid technique presented in this Thesis, using Wavelet Transform and the Ritz method, which allows for damage detection without having information about the undamaged plate. Regarding the transient analysis, the types of damage performed with the FEM simulations were the same as in modal analysis, but in only one position. The damage performed in the experimental tests consisted of added mass in different positions, boundary condition changes, and temperature increase. The technique used to detect the damage was a damage index presented in this Thesis, that computes the differences between the Frequency Responses of the damaged and undamaged plates. The results of the damage detection using modal analysis show that MAC is a valid technique to detect all but the smallest damage. In general, the results of applying the MAC to FEM and Ritz modes is similar, except for the holes, where the Ritz method provides much higher values, suggesting that the damage is overestimated in this case. The disadvantages of MAC would be that it needs a large number of modes to make the results reliable, it does not provide information about the location of the damage, and it requires information about the undamaged plate. On the other hand, with the Wavelet Transform technique it is possible to detect and locate the damage, even the smallest, and especially holes and Young's modulus reduction damage, with both the FEM and Ritz modes. For increases and decreases in density, the damage is barely located using FEM modes, and only for the greatest values. However, using Ritz modes the damage is clearly located in almost all cases, suggesting again that the damage is overestimated when the damage modes are computed by means of the Ritz method. This technique is also hampered by the fact that it requires information about the undamaged plate, which is not always possible from a practical standpoint. The third technique used to detect damage with modal analysis is an hybrid technique presented in this Thesis, using the Ritz method and Wavelet Transform. Despite its being less effective than the other Wavelet-based technique, it has the great advantage of not requiring information about the undamaged plate. Finally, the results of the damage detection using transient analysis show that the computational simulated damage, being too small, is barely or not detected (though it is relatively easy to detect with modal analysis). The experimental damage was detected in all cases. For the added mass damage, it is shown that different positions cause large changes in different frequency ranges. The change of temperature when the plate is clamped causes a change in the Frequency Response of the plate, visible even for a few Celsius degrees of change. This is due to thermal stresses caused by the difference between linear expansion coefficients of the rigid frame material (steel) and plate materials (aluminium, CFRP). When the coefficient of linear expansion of the plate material is greater than the frame, the plate loses stiffness under increased temperature, and when it is lower, it gains rigidity when the temperature increases. When the plate is quasi-free, no shifts in the peaks of the frequency response are observed. The final study carried out for this Thesis was about the tolerance of one of the defined damage index to noise. To do this, artificial noise was added to the signals, and the results were compared between three types of distances (spearman, citiblock and euclidean), showing that spearman distance is more tolerant to noise. This distance has the added advantage of being independent of the applied normalization.