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Oftentimes, researchers in the area of vibration-based structural health monitoring (SHM) and damage detection focused their attention on the global properties of structures, which are modal frequencies and modal damping factors. However, the effect on the local properties for SHM, that is, modal constants, has not been extremely explored. In this paper, the elliptical plane modal identification method is proposed to be used as a damage identification method itself. It is observed that when the receptance is plotted in the elliptical plane, the area of the ellipse formed close to the resonant frequencies (which depends on the modal constants) can be used to detect damage, namely, composite carbon fibre reinforced polymer (CFRP) rectangular plates. Although a mathematical correlation has not been established yet, results show that the method is sensitive to the presence of damage in the test plates, as the area of the ellipse changes with damage.

The ever-developing world as continuously demanded an advancement in every field of endeavour to meet up with the increasing desire for a better society yet does not have a damaging effect on the environment. In the field of engineering, a composite carbon fibre reinforced polymer (CFRP) is one of such materials that has shaped and challenged several industries such as marine, aerospace, civil infrastructural, and automotive and sports equipment, owing to their rare mechanical properties, namely, strength and stiffness to weight ratios [

Several nondestructive techniques (NDTs), such as acoustic emission, ultrasound, visual inspection, X-ray, or eddy currents, among others [

The method is hinged upon knowing the state of the healthy characteristics of the structure and using it as a baseline to compare with the vibration characteristics of the structure at a planned period or at its damaged state. The comparison would highlight any noticeable deviation in the case of the presence of damage and might even reveal the damage location and its severity.

An extensive review on SHM and techniques for damage detection has been presented in [

It is difficult to analyse the interactions between all the features of mechanical systems. However, the dynamic properties of the mechanical system can be represented if the basic properties are assumed to be a single-degree-of-freedom (SDOF) system and considered separately [

Over the years, researchers have always been focusing on the global properties of structures for SHM, with little interest in the local properties—the modal constants. This work explores the plausibility of damage identification with the modal constants. This study focuses on understanding the possible relationships between the deviation in the ellipse area and damage. The modal constants of the CFRP material determine the area and shape of the ellipse.

In this investigation, laminates with dimensions as shown in Table

Types of specimens and designations.

Quantity | Designation | Material | Stacking sequence | Laminate type | Dimensions (mm) | Aspect ratio (a/b) |
---|---|---|---|---|---|---|

2 | Plate A1–A3 | FibreDUX 6268C-HTA 12K | [90/±45/0]_{s} |
Quasi-isotropic | 310 × 240 × 2 | 1.29 |

2 | Plate B1-B2 | FibreDUX 6268C-HTA 12K | [90/0/±45]_{s} |
Quasi-isotropic | 310 × 240 × 2 | 1.29 |

2 | Plate C1–C3 | FibreDUX 6268C-HTA 12K | [90/0]_{2s} |
Cross-ply | 310 × 240 × 2 | 1.29 |

2 | Plate D1 | FibreDUX 6268C-HTA 12K | [90_{2}/0_{3}]_{s} |
Cross-ply | 310 × 240 × 2 | 1.29 |

1 | Plate E1 | FibreDUX 6268C-HTA 12K | [90_{3}/0_{3}]_{s} |
Cross-ply | 300 × 241 × 3 | 1.24 |

It is a unidirectional (UD) prepreg FIBREDUX 6268-HTA (12K) carbon/epoxy material. HexPly® 6268 provides good adhesion to honeycomb core and suitable for aircraft structures. All the test samples were manufactured using the hand layup, and a bagging film (Nylon 66) that can withstand high temperatures and pressures was used during the curing process. The bagging process can be seen in Figure

Vacuum bagging process.

To avoid sticking of the prepreg laminates to the aluminium plate (forming tool), the prepreg laminates were sandwiched between two release films. The vacuum bag was sealed with an inner yellow sealant tape; the pressure gauge and vacuum pipes were connected to the vacuum bagging through valves. For the autoclave curing cycle, start-up heat was 20°C and heat up rate was 1°C/min until it reached 121°C. The laminates were cured at 106 kPa for 2 hours and then naturally cooled.

The composite plates were suspended vertically under a free-free simulated configuration with 2 nylon strings as shown in Figure

Experimental setup for vibration testing [

The response of the samples due to the generation of a multisine [

A number of experiments were conducted by assembling/disassembling, and results were generally consistent although a statistical analysis was not formally conducted.

In order to introduce damage in the specimen, static testing (ST) was performed using a 25 kN Tinius-Olsen universal testing machine. This technique has been followed by other authors in the absence of impact testing machines, such as [

Static testing.

An indenter made from carbon steel with a hemispheric tip of 24.5 mm in diameter was used. The setup consists of a 350 mm^{2} rectangular fixture base plate with a cutout of 250 × 150 mm. A total of six vertical toggle clamps hold the specimen to the fixture base, three spaced equally on each side of the length of the fixture base. The specimen is clamped to the base plate to avoid movement during loading. The ST was conducted at a loading speed of 10 mm/min, with the application of varying force. After each round of loading, the energy dissipated on the test plates was within the range of 0.41 kJ to 18 kJ. The study considered five different stacking sequences, and they are labelled in alphanumeric style, that is, plates A1, A2, B1, B2, C1, C2, D1, and D2, as shown from Figures

Variation in the area of the ellipse for plates (a) A1, (b) A2, (c) A3, and (d) B1.

Variation in the area of the ellipse for plates (a) B2, (b) C1, (c) C2, and (d) C3.

Variation in the area of the ellipse for plates (a) D1 and (b) E1.

Since the area and the shape of the ellipse depend on the real and imaginary modal constants, a possible deviation in the area of the ellipse due to damage would suggest a correlation. The area of the ellipse from the test specimens was identified using the elliptical method [

The theoretical development of the elliptical method and its properties are presented in [

Ellipse area for plate A1: (a) healthy; (b) damaged.

Ellipse area for plate B1: (a) healthy; (b) damaged.

The amplitudes of the healthy and damaged ellipse for plate A1 shown in Figure

Again, the ellipse area for the healthy plate B1 is larger than that for the damaged plate as shown in Figure

Obviously, from Figures

It is important to note that the amount of reduction in the ellipse areas as shown from Figures

A novel method for damage identification from FRF, based on the representation of the receptance on the elliptical plane, was presented. It was shown that the area of the ellipse, which is related to the modal constants (local modal properties), is sensitive to damage in a consistent manner. Hence, this paper offers new possibilities for other researchers who are concerned with damage diagnosis in lightly damped structures since the elliptical plane modal identification method provides promising results for damage identification in CFRP rectangular plates. However, more studies are still required in terms of experimental work to find what the mathematical correlation is (if any) between damage and the shape of the ellipse, for example, by taking into account that damage in CFRPs has complex morphologies that may affect the plates and how the modal constants are affected by the presence of damage.

The Frequency Response Functions (FRFs) data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest.

Daerefa-a Mitsheal Amafabia and Diogo Montalvão conceived and designed the experiments. Daerefa-a Mitsheal Amafabia, Diogo Montalvão, and Opukuro David-West conducted the experiments. Daerefa-a Mitsheal Amafabia conducted the formal analysis. Opukuro David-West, Diogo Montalvão, and George Haritos supervised the work.

This research was funded by the Niger Delta Development Commission (NDDC), Nigeria (Grant number NDDC/DEHSS/2015PGFS/RVS/025/30).