# Experimental investigation on the influence of a “soft layer” on the structural performance of a smart composite structure

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## Abstract

The composite structures embedding piezoelectric implants are developed due to their abilities of modifying mechanical properties according to the environment, of keeping their integrity, of interacting with human beings or with other structures. One way to functionalize a mechanical device consists in embedding the transducers inside the final composite structure via a “soft” layer. This layer consists of two plies sandwiching the transducers, impregnated with a resin compatible with the one of the final composite structures. The test structures are laminates made of a glass-fiber reinforced plastic with a polyester resin. In this paper, we propose to experimentally investigate the influence of the through-the-thickness position of the “soft layer” on specific parameters of design such as eigenfrequencies, modal amplitude, damping ratio and Lamb wave propagation properties. Results show that the “soft” layer behavior can not be neglicted to predict the behavior of the final product in particular for the eigenfrequencies and the modal amplitudes. However, the “soft layer” has no impact on the damping ratio and the Time-of-Flight of a wave train.

## Keywords

Experimental investigation Smart composite Soft layer Laminates Piezoelectric transducer## 1 Introduction

Currently, in many industrial fields such as transportation, a research effort is conducted to reduce the structural weight [5, 41]. Composite materials turn to be one of the most interesting solutions because their mass density is low and their stiffness is high. A composite material can be defined as a combination of two or more materials, in general strong fibers embedded in a weaker matrix, that results in better properties than those of the individual components used alone [4, 15]. However, these materials have also some shortcomings such as weakness to delamination, low-velocity impact resistance or low damping ratio [16, 22]. It is then of first importance to monitor the structural health of these composite structures. This can be done by designing and manufacturing composite structures with a distributed set of integrated transducers [2, 14]. These smart composite structures have the abilities of modifying mechanical properties according to the environment (e.g. active vibration control [10]), of keeping their integrity (e.g. structural health monitoring [18]), of interacting with human beings (e.g. Human-Machine Interaction [3]) or with other structures (e.g. mechatronic [46]). This paper is focused on composite structures with embedded bulk piezoelectric transducers [11].

One key point of this technology is the way of embedding the smart materials during the manufacturing process. The easiest method consists in directly placing the transducers between two plies, but resin pockets usually appear at the transducer boundaries, which can create structural weaknesses [32]. Moreover, the transducer location is not accurately guaranteed because the piezoelectric elements can move during the compaction and resin spread. Another method is to use a ply with cut-out, corresponding to the exact geometry of the transducer, but some discontinuities are created in the fiber layer [17]. An analytical study performed by Chow and Graves has proved that the insertion of transducers can affect the integrity of smart structures [8]. The results show that the magnitude of inter-laminar stresses in a graphite/epoxy laminate increases by five times, due to the presence of embedded inert rectangular implant. Hansen and Vizzini [20] have performed static tension and tension-tension fatigue tests on carbon/epoxy composites with inserted glass slices. Their results show that embedding techniques have significant influence on the static and fatigue strengths of the composites. Particularly, compared with interlacing technique, cut-out method can significantly degrade the fatigue life of embedded composites. Moreover, for complex structures, the geometry of the cut-out and the accurate positioning of the transducers can be difficult to obtain. Specific manufacturing methods have been developed to place the transducers system at the heart of the composite material. Stanford Multi-Actuator-Receiver Transduction Layer (“SMART Layer”) has been developed by Lin and Chang [27], which is used to integrate a network of distributed piezoceramic transducers into the heart of graphite/epoxy composite laminates in their manufacturing process. For this, a semi-finished product based on a polyimide encapsulation for the transducers, is created during a supplementary manufacturing step. They have demonstrated that the embedded transducers can be used without degrading the structural integrity of the host composite structures [36]. But, this solution needs to pay a particular attention to the ratio between the semi-finished product surface and the overall product surface because the encapsulation material and the matrix do not have the same chemical nature. If this ratio is too high, delamination problems could occur. In this work, a glass-fiber reinforced plastic (GFRP) composite with two plies sandwiching the transducers and impregnated with a resin compatible with the one of the final composite structure has been used to create a “soft layer” as a semi-finished product [6, 24, 29, 31, 32, 37].

From an industrial point of view, it is essential to understand the influence of the “soft layer” on the operating performance of the smart composite structures in order to manage it during the design stages of the product lifecycle and to integrate it in the technical requirements [30]. The effect of integrated transducers on the mechanical behaviour of composite structures has been extensively studied and reported from a numerical point of view [23, 34, 38, 39]. From the authors’ knowledge, much less attention has been devoted to experimentally evaluate it [21]. This article is focused on the experimental investigation of the impact of the through-the-thickness location of the “soft layer” on the final performance of the smart composite structure. Furthermore, the results obtained can constitute an experimental benchmark data set that will be useful for validation of computational codes or model developments.

The paper is organized as follows. The description of the samples tested and the composite manufacturing process are introduced in Sect. 2. Section 3 describes the experimental technique used for the samples characterization and the data correction used to compare the experimental data. In Sect. 4, the results are presented, compared and discussed. Finally, concluding remarks are given.

## 2 Samples description and manufacturing process

In order to study the influence of the “soft layer” on the structural performance of the smart composite structures, a set of smart composite beams are manufactured. This section describes the geometry of the beams and their manufacturing process.

The worldwide production of composite structures reached around 10 millions tonnes in 2016. Glass fibers are still by far the most commonly used reinforcing material in fiber reinforced plastics and composites (More than 90% of all composites) [1, 45]. 70% of composite structures are made of thermoset polymer matrix, in particular unsaturated polyester resins [1, 45]. This is the reason why this work is focused on laminates made of a glass-fiber reinforced plastic (GFRP) with a polyester resin.

### 2.1 Samples description

Location of the piezoelectric transducers for each beam reference (the reference surface is the bottom electrode of the transducers)

Beam reference | Specific depth (mm) | Location of the transducers |
---|---|---|

a | 0 | Glued on the top surface of the beam |

b | 0.32 | Embedded between the top surface and Ply 1 |

c | 0.65 | Embedded between Ply 1 and 2 |

d | 0.98 | Embedded between Ply 2 and 3 |

e | 1.32 | Embedded between Ply 3 and 4 |

f | 1.98 | Embedded between Ply 5 and 6 |

### 2.2 Manufacturing process

- 1.
*Preparation of the “soft layer”*The piezo ceramics are positioned at the accurate locations on one light glassfiber ply (surface mass of 30 \(\mathrm{g\,m}^{-2}\)). Another light glassfiber ply is positioned on the transducers. This dry device is reinforced with the same polyester resin used for the whole composite structure in order to guarantee the continuity of the material properties. - 2.
*Laminate preparation*Six layers of glass mat are used (surface mass of 300 \(\mathrm{g\,m}^{-2}\)). The “soft layer” is put between two fiber layers. According to the technical requirements, the transducer location is accurately guaranteed by using the “soft layer” [24]. Then the matrix is reinforced by a polyester resin. - 3.
*Manufacturing process*After organizing the laminates, a draining net as well as a tube are used to ensure the resin can feed every part of the model, as shown in Fig. 2. The draining net and the feeding tube are put on the top surface of the laminates. A vacuum bag is positioned at the end, covering all the composite structure. A pump is used to achieve full vacuum in order to compact the fibers and the resin. After the curing, a large plate is demolded. This plate is finally machined to obtain 6 beams.

## 3 Experimental characterization method

### 3.1 Measurement apparatus and characterization method

In Fig. 3, the experimental setup is presented. The test beams are hanged by two wires in order to approximate free boundary conditions. The deflection shapes of the beams are measured with a scanning vibrometer (Polytec, PSV-500-3D). The frequency range is from 1 to 1200 Hz with a step of 0.3 Hz. The piezo-ceramics are used one after the other as actuators. 105 scan points (21 by 5 grid) are measured on each beam. The eigenfrequencies, the modal damping ratio and the vibration amplitudes from the first five natural bending modes of each beam are extracted and analyzed. In order to extract the damped parameters from the measurements, a method of reconstruction of the damped vibration behavior is used [9, 13, 19] via a modal analysis software package called MODAN [35]. The least-square complex frequency domain (LSCF) method is used for modal identification [33, 44].

### 3.2 Mass and elastic properties

First of all, it is necessary to identify the mass density and the fibre volume ratio for the composite material manufactured. As the fiber volume ratio is an important input data for the composite models, a ThermoGravimetric Analysis (TGA) is achieved. At the end of this analysis, the weight ratio of the glass fibers is measured at 57.8%. The mass density of the glass fibers is \(2600\,{\pm \,3\%}\, {\text{kg}} {\cdot} {\text{m}}^{-3}\) and that of the thermosetting plastic is around \(1100\,{\pm \,3\%}\,{\text{kg}} {\cdot} {\text {m}}^{-3}\). Therefore, the glass fiber volume ratio for the composite material is 37%. The mass density is classically measured at around 1 \(630\,{\pm \,3\%}\, {\text{kg}} {\cdot} {\text{m}}^{-3}\). Concerning the “soft layer”, the mass density is around 1 \(150\,{\pm \,3\%}\,{\text{kg}} {\cdot} {\text{m}}^{-3}\).

The Resonalyser method is applied to extract the material parameters. For the composite material, the Young’s modulus of the composite material is measured at \(14.6\,{\pm \,6.2\%}\) GPa and the Poisson’s ratio \(0.24\,{\pm \,2\%}\). For the “soft layer”, the Young’s modulus is measured at \(7\,{\pm \,6.2\%}\) GPa and the Poisson’s ratio \(0.32\,{\pm \,2\%}\).

### 3.3 Data correction of the experimental results

Due to the geometric uncertainties (length, width and thickness) from the manufacturing process, the geometry of the test beams is not strictly equivalent. In order to preserve the possibility to directly compare the results obtained, it is necessary to correct these deviations by applying a specific computation process. A finite element model is built, which is used as a reference to correct the data from each beam, in order to ensure that all the compared beams have the same length, width and thickness. A 2D model is built according to a cut-plane along the length axis and the thickness axis. Transducers are not modeled. Indeed, in view of the thicknesses involved and the stiffness ratios, the “soft layer” is the main responsible for the variation of the natural frequencies. The material parameters applied are from the identification done in the last subsection with the Resonalyser method. Second-order quadratic rectangular elements are used for the mesh. A mapped quadrilateral mesh with 15 by 9 rectangle grid (15 along the length and 9 along the thickness with 3 per layer) is used, as depicted in Fig. 5. The blue part is the “soft layer” and the grey part is composite. This mesh is optimized with a convergence analysis as shown in Fig. 6. The reference for the error computation is the eigenfrequencies obtained for 40 finite elements along the beam axis.

- 1.
A first finite element model is built with the real dimensions of the beam studied The eigenfrequencies are computed and stored.

- 2.
The dimensions of this finite element model are modified to obtainthe “ideal” ones (\(715\,\times \,50\,\times \,2.5\,\mathrm{mm}^3\)) The computation is launched again and new eigenfrequencies are obtained (called “ideal” eigenfrequencies).

- 3.
For each test beam and for each natural mode, a correction value is calculated from the ratio between the “ideal” eigenfrequency and the initial eigenfrequency

- 4.
These correction values are applied to the measured eigenfrequencies for the specific test beam and for each mode.

Initial (I) and corrected (C) data for each beam reference from a to c

Beam reference | a | b | c | |||
---|---|---|---|---|---|---|

Initial (I) or corrected (C) data | I | C | I | C | I | C |

Length (mm) | 713 | 715 | 715 | 715 | 713 | 715 |

Width (mm) | 50 | 50 | 50 | 50 | 50 | 50 |

Thickness (mm) | 2.03 | 2.5 | 2.48 | 2.5 | 2.4 | 2.5 |

F1 (Hz) | 11.37 | 13.93 | 12.57 | 12.68 | 13.27 | 13.70 |

F2 (Hz) | 31.59 | 38.68 | 34.93 | 35.23 | 36.85 | 38.05 |

F3 (Hz) | 62.66 | 76.70 | 69.28 | 69.87 | 73.08 | 75.46 |

F4 (Hz) | 105.23 | 128.76 | 116.32 | 117.31 | 122.69 | 126.67 |

F5 (Hz) | 160.30 | 196.06 | 177.15 | 178.65 | 186.82 | 192.87 |

Initial (I) and corrected (C) data for each beam reference from d to f

Beam reference | d | e | f | |||
---|---|---|---|---|---|---|

Initial (I) or corrected (C) data | I | C | I | C | I | C |

Length (mm) | 712 | 715 | 714 | 715 | 715 | 715 |

Width (mm) | 50 | 50 | 50 | 50 | 50 | 50 |

Thickness (mm) | 2.39 | 2.5 | 2.53 | 2.5 | 2.51 | 2.5 |

F1 (Hz) | 13.82 | 14.28 | 14.67 | 14.46 | 13.78 | 13.70 |

F2 (Hz) | 38.39 | 39.65 | 40.74 | 40.16 | 38.26 | 38.05 |

F3 (Hz) | 76.12 | 78.61 | 80.77 | 79.63 | 75.87 | 75.46 |

F4 (Hz) | 127.76 | 131.94 | 135.55 | 133.64 | 127.36 | 126.67 |

F5 (Hz) | 194.51 | 200.85 | 206.33 | 203.43 | 193.91 | 192.87 |

### 3.4 Repeatability analysis

In order to confirm the results, an additional rush of beams have been processed, and all the experiments have been repeated. The Repeatability Standard Deviation (RSD) from the results is computed and given for all the investigations. Of course, the changes in the data observed between the reference beams must be much higher than this value in order to be relevant and representative. Moreover, 5 more samples of Beam (c) are manufactured with a position variation with respect to the feeding tube in order to guarantee that the Vacuum Assisted Resin Transfer Molding (VARTM) has no impact on the beams parameters. These 5 beams are tested following the same experimental procedure, in order to validate the repeatability and accuracy of the manufacturing process. No significant variation is obtained.

## 4 Results and discussion

In order to experimentally investigate the influence of the “soft layer” location along the thickness-axis on the performance of the smart composite structures, several design parameters have be investigated such as the eigenfrequencies, the modal effective electromechanical coupling coefficient, the modal damping ratios, the vibration amplitude and the Lamb waves propagation.

### 4.1 Natural bending frequencies

Corrected experimental eigenfrequencies for each beam reference and maximal standard deviation for each natural vibration frequency and all beam references

Beam reference | a | b | c | d | e | f | RSD (%) |
---|---|---|---|---|---|---|---|

F1 (Hz) | 13.59 | 13.77 | 14.71 | 15.13 | 15.60 | 14.63 | 0.12 |

F2 (Hz) | 37.36 | 38.12 | 40.53 | 42.12 | 42.52 | 39.99 | 0.05 |

F3 (Hz) | 73.24 | 74.66 | 79.29 | 81.49 | 82.46 | 78.90 | 0.08 |

F4 (Hz) | 121.72 | 125.07 | 128.33 | 136.15 | 137.57 | 131.08 | 0.04 |

F5 (Hz) | 180.59 | 186.70 | 200.27 | 202.57 | 207.08 | 196.93 | 0.08 |

Figure 8 presents the relative deviation of the eigenfrequencies with respect to the eigenfrequencies obtained for Beam (a) in function of the location of the “soft layer”. For all beams, the tendency for each eigenfrequency is similar. The maximum value of the eigenfrequency is obtained when the “soft layer” is embedded in the middle of the composite structure. The highest variation is above 10% with regards to the standard setup when the transducers are glued on the top surface of the beam. This fact is explained by the modification of the second moment of area due to the through-the-thickness location of the “soft layer”.

### 4.2 Modal effective electromechanical coupling coefficient

Eigenfrequencies when Piezo 1 is short-circuited (SC) or open-circuited (OC) for beam d and f

Beam reference | d | f | RSD (%) | ||
---|---|---|---|---|---|

Short-circuit (SC) or open-circuit (OC) | OC | SC | OC | SC | |

F1 (Hz) | 14.64 | 14.64 | 14.02 | 14.21 | 0.12 |

F2 (Hz) | 41.18 | 41.17 | 39.49 | 39.39 | 0.05 |

F3 (Hz) | 81.47 | 81.47 | 78.08 | 78.05 | 0.08 |

F4 (Hz) | 135.50 | 135.54 | 130.09 | 130.06 | 0.04 |

F5 (Hz) | 202.71 | 202.79 | 196.04 | 195.98 | 0.08 |

When the electric boundary conditions of Piezo 1 is modified, the eigenfrequencies are slightly changed. But by comparing with the Repeatability Standard Deviation, the eigenfrequency deviation is not significant enough. So it is not possible to evaluate the EMCC in this situation. In conclusion, the smart composite structures are considered a weakly coupled.

### 4.3 Modal damping ratio and vibration amplitude

In this section, the maximum amplitudes and the damping ratios for each natural mode and for each beam reference are given respectively in Table 6 and in Table 7.

Maximal amplitudes for each beam reference and for each natural mode

Beam reference | a | b | c | d | e | f | RSD (%) |
---|---|---|---|---|---|---|---|

Mode 1 amplitude (\(\mu \hbox {m}\)) | 32.7 | 14.6 | 6.5 | 7.06 | 0.49 | 3.27 | 3.42 |

Mode 2 amplitude (\(\mu \hbox {m}\)) | 11.9 | 6.03 | 4.83 | 2.21 | 0.16 | 5.46 | 3.44 |

Mode 3 amplitude (\(\mu \hbox {m}\)) | 4.37 | 5.47 | 2.76 | 0.7 | 0.08 | 1.24 | 3.84 |

Mode 4 amplitude (\(\mu \hbox {m}\)) | 2.69 | 1.81 | 0.91 | 0.95 | 0.09 | 1.61 | 0.91 |

Mode 5 amplitude (\(\mu \hbox {m}\)) | 1.95 | 1.36 | 0.67 | 0.5 | 0.04 | 1.11 | 0.43 |

Modal damping ratios for each beam reference

Beam reference | a | b | c | d | e | f | RSD (%) |
---|---|---|---|---|---|---|---|

Mode 1 damping ratio (%) | 0.58 | 0.47 | 0.55 | 0.51 | 0.53 | 0.32 | 4.93 |

Mode 2 damping ratio (%) | 0.51 | 0.51 | 0.5 | 0.65 | 0.41 | 0.5 | 2.02 |

Mode 3 damping ratio (%) | 0.53 | 0.38 | 0.41 | 0.84 | 0.42 | 0.88 | 4.39 |

Mode 4 damping ratio (%) | 0.25 | 0.44 | 0.44 | 0.43 | 0.39 | 0.48 | \(\approx 0.00\) |

Mode 5 damping ratio (%) | 0.47 | 0.61 | 1.2 | 0.4 | 0.37 | 0.44 | 1.21 |

### 4.4 Lamb waves propagation

To generate and capture the wave trains, the piezoelectric transducers embedded in the composite are used. The advantage of this method compared with Resonalyser Method is that T-o-F Method is easier and faster to extract the material properties along the propagation axis. But, it is necessary to evaluate the Poisson’s ratio. The Poisson’s ratio of the glass fiber is around 0.23 and that of the thermosetting plastic around 0.37, so the Poisson’s ratio can be evaluated at 0.32 with the classical rule of mixtures [15].

Time-of-flight values for each beam reference

Beam reference | a | b | c | d | e | f | RSD (%) |
---|---|---|---|---|---|---|---|

Time-of-flight (\(\upmu\)s) | 126 | 125 | 126 | 126 | 128 | 127 | 0.08 |

## 5 Conclusion

The work is focused on smart composite structures and, in particular, composite structures activated by a “soft layer” containing transducers. The test structures are beams made of Glass Fibers Reinforced Polymer (GFRP) laminates. The influence of the through-the-thickness position of the “soft layer” on the structural performance of the beams was experimentally investigated. The eigenfrequencies, the modal amplitudes, the damping ratios and the Time of flight of the Lamb waves are analyzed. Five different beam setups were tested and compared to the standard setup when the transducers are glued on the top surface of the beam. Repeatability tests to calculate the Repeatability Standard Deviation (RSD) for each result were done as well as repeatability tests in order to evaluate the stability of the manufacturing process. A numerical method based on a finite element model has been developed to take into account the geometry variation.

The results demonstrated that the “soft layer” can not be neglicted to model the behavior of the final product. In particular, the through-the-thickness position has an influence of the eigenfrequencies and the modal amplitudes. The maximal frequencies is obtained when the “soft layer” is located at the middle of the beam. The maximal modal amplitude is obtained when the “soft layer” is at the top surface of the beam. However, the “soft layer” does not increase the overall damping ratio of the final structures and the through-the-thickness position of the “soft layer” has no influence on the damping ratios. The Lamb wave propagation inside the composite material is not impacted the “soft layer”. This data is important in particular to design Stuctural Health Monitoring (SHM) strategies based on Lamb waves. The results obtained can constitute an experimental benchmark data that will be useful for validation of computational codes or model developments.

## Notes

### Acknowledgements

This project has been performed in cooperation with the EUR EIPHI program (Contract ANR 17-EURE-0002). This work was partly supported by a financial support from the UTBM, France and is part of the collaborative project named SyRaCuSE (SmaRt Composite StructurE). The authors are grateful to Mr Romain Viala from the FEMTO-ST Institute for his help and his fruitful assistance on modal analysis. The first author thanks the China Scholarship Council for financial support gratefully (Contract No. 201504490012).

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

## References

- 1.Agarwal BD, Broutman LJ, Chandrashekhara K (2017) Analysis and performance of fiber composites. Wiley, New YorkGoogle Scholar
- 2.Akhras G (2000) Smart materials and smart systems for the future. Can Mil J 1(3):25–31Google Scholar
- 3.Calvary G, Delot T, Sedes F, Tigli JY (2013) Computer science and ambient intelligence. Wiley, New YorkGoogle Scholar
- 4.Campbell FC (2010) Structural composite materials. ASM International, Materials ParkGoogle Scholar
- 5.Cheah LW (2010) Cars on a diet: the material and energy impacts of passenger vehicle weight reduction in the us. PhD thesis, Massachusetts Institute of TechnologyGoogle Scholar
- 6.Chen X, Lachat R, Salmon S, Ouisse M, Meyer Y (2017a) Complex composite structures with integrated piezoelectric transducers. Int J Comput Methods Exp Meas 5(2):125–134Google Scholar
- 7.Chen X, Meyer Y, Lachat R, Ouisse M (2017b) Laminates with integrated piezoelectric transducers:influence of the transducers location along the thickness-axis on the structural performance. In: International center for numerical methods in engineering (CIMNE), VIII ECCOMAS thematic conference on smart structures and materials (SMART 2017), pp 594–605Google Scholar
- 8.Chow W, Graves M (1992) Stress analysis of a rectangular implant in laminated composites using 2-d and 3-d finite elements. In: 33rd structures, structural dynamics and materials conference, p 2477Google Scholar
- 9.Chu M, Golub G, Golub GH (2005) Inverse eigenvalue problems: theory, algorithms, and applications, vol 13. Oxford University Press, oxfordCrossRefGoogle Scholar
- 10.Collet M, Ouisse M, Tateo F (2014) Adaptive metacomposites for vibroacoustic control applications. IEEE Sens J 14(7):2145–2152CrossRefGoogle Scholar
- 11.Crawley E, Luis DE (1987) Use of piezoelectric actuators as elements of intelligent structures. AIAA J 25(10):1373–1385CrossRefGoogle Scholar
- 12.De Visscher J, Sol H, De Wilde W, Vantomme J (1997) Identification of the damping properties of orthotropic composite materials using a mixed numerical experimental method. Appl Compos Mater 4(1):13–33Google Scholar
- 13.Foltete E, Gladwell G, Lallement G (2001) On the reconstruction of a damped vibrating system from two complex spectra, part 2: experiment. J Sound Vib 240(2):219–240CrossRefGoogle Scholar
- 14.Gandhi MV, Thompson B (1992) Smart materials and structures. Springer Science & Business Media, BerlinGoogle Scholar
- 15.Gay D (2014) Composite materials: design and applications. CRC Press, Boca RatonCrossRefGoogle Scholar
- 16.George HS (1999) Laminate analysis. Laminar composites, BostonGoogle Scholar
- 17.Ghezzo F, Huang Y, Nemat-Nasser S (2009) Onset of resin micro-cracks in unidirectional glass fiber laminates with integrated shm sensors: experimental results. Struct Health Monit 8(6):477–491CrossRefGoogle Scholar
- 18.Giurgiutiu V, Zagrai A, Jing Bao J (2002) Piezoelectric wafer embedded active sensors for aging aircraft structural health monitoring. Struct Health Monit 1(1):41–61CrossRefGoogle Scholar
- 19.Gladwell G (2001) On the reconstruction of a damped vibrating system from two complex spectra, part 1: theory. J Sound Vib 240(2):203–217CrossRefGoogle Scholar
- 20.Hansen J, Vizzini A, Hansen J, Vizzini A (1997) Fatigue response of a host structure with interlaced embedded devices. In: 38th structures, structural dynamics, and materials conferenceGoogle Scholar
- 21.Hufenbach W, Böhm R, Thieme M, Tyczynski T (2011) Damage monitoring in pressure vessels and pipelines based on wireless sensor networks. Proced Eng 10:340–345CrossRefGoogle Scholar
- 22.Hull D, Clyne T (1996) An introduction to composite materials. Cambridge University Press, CambridgeCrossRefGoogle Scholar
- 23.Kapuria S (2001) An efficient coupled theory for multilayered beams with embedded piezoelectric sensory and active layers. Int J Solids Struct 38(50–51):9179–9199CrossRefGoogle Scholar
- 24.Lachat R, Meyer Y (2017) Method for producing a part made of a composite material, incorporating components and marking means. WO Patent WO/2017/013346Google Scholar
- 25.Lachat R CW Borza D (2004) Manufacture of smart composite panels for the industry and verification of teir structural properties with holographic methods. In: ICEM12–12th international conference on experimental mechanics, Bari, Italy, p 8Google Scholar
- 26.Lauwagie T (2005) Vibration-based methods for the identification of the elastic properties of layered materials (trillingsgebaseerde methodes voor de identificatie van de elastische eigenschappen van gelaagde materialen). PhD thesis, Katholieke Universiteit LeuvenGoogle Scholar
- 27.Lin M, Chang FK (2002) The manufacture of composite structures with a built-in network of piezoceramics. Compos Sci Technol 62(7–8):919–939CrossRefGoogle Scholar
- 28.Meyer Y, Lachat R (2015) Vibration characterization procedure of piezoelectric ceramic parameters-application to low-cost thin disks made of piezoceramics. In: MATEC web of conferences, EDP Sciences, vol 20, p 01003Google Scholar
- 29.Meyer Y, Lachat R (2016) Smart composite structures: benefits, technical issues and potential applications. JEC Compos Mag 105Google Scholar
- 30.Meyer Y, Lachat R, Chen X, Salmon S, Ouisse M (2017) Smart composite structure (project syracuse) towards mastering challenges concerning the product lifecycle. In: 20th international conference on composite structures (ICCS20), ParisGoogle Scholar
- 31.Paradies R (1997) Statische verformungskontrolle hochgenauer faserverbundreflektorschalen mit hilfe aktiver elemente. PhD thesis, ETH Zurrich, SwitzerlandGoogle Scholar
- 32.Paradies R, Ruge M (2000) In situ fabrication of active fibre reinforced structures with integrated piezoelectric actuators. Smart Mater Struct 9(2):220CrossRefGoogle Scholar
- 33.Peeters B, Van der Auweraer H, Guillaume P, Leuridan J (2004) The polymax frequency-domain method: a new standard for modal parameter estimation? Shock Vib 11(3,4):395–409CrossRefGoogle Scholar
- 34.Phung-Van P, De Lorenzis L, Thai CH, Abdel-Wahab M, Nguyen-Xuan H (2015) Analysis of laminated composite plates integrated with piezoelectric sensors and actuators using higher-order shear deformation theory and isogeometric finite elements. Comput Mater Sci 96:495–505CrossRefGoogle Scholar
- 35.Piranda J (2001) Analyse modale expérimentale. Techniques de l’ingénieur Bruit et vibrations 6180:1776–0143Google Scholar
- 36.Qing XP, Beard SJ, Kumar A, Ooi TK, Chang FK (2007) Built-in sensor network for structural health monitoring of composite structure. J Intell Mater Syst Struct 18(1):39–49CrossRefGoogle Scholar
- 37.Sala G, Olivier M, Bettini P, Sciacovelli D (2004) Embedded piezoelectric sensors and actuators for control of active composite structures. Mechanical and Thermal Engineering Department, Carlo Gavazzi Space ESTEC, European Space AgencyGoogle Scholar
- 38.Saravanos DA, Heyliger PR (1995) Coupled layerwise analysis of composite beams with embedded piezoelectric sensors and actuators. J Intell Mater Syst Struct 6(3):350–363CrossRefGoogle Scholar
- 39.Saravanos DA, Heyliger PR, Hopkins DA (1997) Layerwise mechanics and finite element for the dynamic analysis of piezoelectric composite plates. Int J Solids Struct 34(3):359–378CrossRefGoogle Scholar
- 40.Song X (2003) Vacuum assisted resin transfer molding (vartm): model development and verification. PhD thesis, Virginia TechGoogle Scholar
- 41.Taminger K (2012) Technical challenges to reducing subsonic transport weight. In: AIAA aerospace sciences meetingGoogle Scholar
- 42.Trindade MA, Benjeddou A (2009) Effective electromechanical coupling coefficients of piezoelectric adaptive structures: critical evaluation and optimization. Mech Adv Mater Struct 16(3):210–223CrossRefGoogle Scholar
- 43.Tucker B (2001) Ultrasonic plate waves in wood-based composite panels. PhD thesis, Washington State University, USAGoogle Scholar
- 44.Van Der Auweraer H, Guillaume P, Verboven P, Vanlanduit S (2001) Application of a fast-stabilizing frequency domain parameter estimation method. J Dyn Syst Meas Control 123(4):651–658CrossRefGoogle Scholar
- 45.Witten E, Kraus T, Kühnel M (2016) Composites market report 2016. Federation of Reinforced Plastics, GermanyGoogle Scholar
- 46.Wlezien R, Horner G, McGowan A, Padula S, Scott M, Silcox R, Simpson J (1998) The aircraft morphing program. In: 39th AIAA/ASME/ASCE/AHS/asc structures, structural dynamics, and materials conference and exhibit, p 1927Google Scholar