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This article was submitted to Structural Materials, a section of the journal Frontiers in Materials

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For the high strength, corrosion resistance, and good stability, carbon fiber–reinforced polymer (CFRP) composites have been made into pipes to transfer gasses and oils in subsea environment. Structural performance of CFRP composite pipes is particularly important to sustain the regular operation of the delivery system. To obtain the in-field behavior of the CFRP composite pipes, quasi-distributed optical fiber sensing techniques are developed based on the multiple configuration of fiber Bragg grating (FBG) sensing elements. Theoretical investigation on the dynamic response of the pipes is performed. Experiments on cantilever CFRP pipes with surface-attached FBGs in series and packaged FBG sensors have been conducted to check the feasibility and effectiveness of the proposed sensing technique. Results validate the good measurement performance of the proposed sensors and the accuracy of the vibration analysis. The study can be adopted to instruct the establishment of the structural health monitoring system of CFRP composite pipes and assess the safety operation state of the pipe systems.

Pipe transportation has become the main channel for oil and gas, due to the advantages of high efficiency, low energy consumption, and reasonable cost. Submarine pipes with extremely high fabrication cost are prone to local buckling, cracking, perforation, and fatigue fracture damages induced by seawater corrosion, sea sand erosion, waves, and other multimedia cycle coupling action during the long-term operation process (

Submarine pipelines have always been under the action of waves and currents. When the fluid flows bypass both sides of the suspended pipe, the change of pressure difference makes the boundary layers separate, and then the wake vortex falls off, leading to vibration of the pipe with certain frequency. When the excitation frequency that makes the vortex fall off is equal to or approaches the inherent frequency of the submarine pipe, the vibration locking phenomenon (resonance) occurs, and the amplitude of the pipe increases dramatically, which can induce fatigue failure of the pipe. Therefore, it is particularly important to explore the dynamic characteristics, dynamic failure mode, and dynamic damage monitoring methods of submarine pipelines, so as to develop preventive control measures for preventing the fatigue fracture damage inspired by vortex-induced vibration (

Currently, considerable attempts have contributed to analyzing the dynamic characteristics of pipe structures. Kershenbaum et al. (

The mentioned analysis on pipes under various vibration actions based on the simplified theoretical solutions, finite element simulation (

Some scholars used piezoceramic transducers to detect the defect of pipelines (

In view of this, the vibration characteristics of the CFRP composite pipe structures have been analyzed, and the displacements and strain responses of the pipe under bending vibration have been described from the perspective of continuum vibration differential equations. Experimental investigations on the vibration response characteristics of the CFRP composite pipes have been performed based on quasi-distributed optical fiber sensing technology. Furthermore, the effectiveness and applicability of the testing method have been demonstrated by the comparative analysis on calculated and measured dynamic strain responses.

The aspect ratio of the CFRP pipe is larger than 50, which has the characteristics of the beam. Therefore, the infinite degree of freedom beam vibration model with uniform mass distribution is used to study the vibration of the CFRP pipe. The research objective is referred to submarine pipelines for transporting oil/gas, which belongs to slender beam and is dominated by low-order natural vibration. Therefore, the Bernoulli–Euler beam model can be used for analysis. The coordinates of the CFRP pipe follow

Bernoulli–Euler beam model:

The dynamic equilibrium condition in

Ignoring the second-order small quantity, the balance condition of the rotation of the infinitesimal element around the centroid can be obtained.

According to the mechanics of materials,

Substituting

For free vibration, the external excitation force

Substituting

The above formula can be rewritten as

The premise that

Considering the cantilever constraints, at the fixed end (

At the free end (

If both

To solve

Using the mode superposition method to calculate the vibration of the beam, the vibration response of the beam can be expressed as

Substituting it into

Introducing the boundary condition

Substituting

According to the bending theory of beams, the axial strain response caused by bending can be obtained

Given the theoretical analysis above, a related numerical calculation program has been compiled to calculate the displacement and strain response of the cantilever CFRP pipe under the action of a unit harmonic force with an excitation frequency of 10 Hz.

Space–time distribution of displacements and strains of pipe2.

Space–time distribution of displacements and strains of pipe3.

To verify the feasibility and effectiveness of the installed FBGs in series to measure the vibration response of the pipe structures, experiments on vibration testing of the CFRP tube have been carried out. Surface-attached FBGs in series have been designed to measure the distributed strains in the axial direction of the pipe. The Optical system 200 has been used to demodulate FBG signal information, and the sampling frequency is 100 Hz.

Two kinds of CFRP pipes have been used in the cantilever vibration experiments, as shown in

Setup of pipe2:

Setup of pipe3:

In the vibration experiment, the effect of the frequency change on the response information of the CFRP pipes and the effectiveness of the FBG measurement has been checked by changing the excitation frequency. The excitation frequencies acting on pipe2 include 10, 20, 30, and 50 Hz. Three bare FBGs in series attached on pipe2 are separately connected to channel 4, channel 5, and channel 6 of the demodulation device, and the E-packaged FBG is connected to channel 8. A simple harmonic force with a frequency of 50 Hz has been applied to the end of pipe2, and the loading time lasts about 2,000 s. After the completion of the first load, the excitation frequency is adjusted to 30 Hz, and the loading time of pipe2 lasts about 4,000 s. After that, the third load has been carried out, and the excitation frequency is 20 Hz with the load time about 8,000 s. Finally, the fourth load with an excitation frequency of 10 Hz has been conducted, and the load time lasts about 2,000 s. An FBG from each channel has been taken out for analysis. The changes of FBG central wavelength increments with excitation frequencies are shown in

Relationship of central wavelength increment with loading time at 10 Hz:

Relationship of central wavelength increment with loading time at 20 Hz:

Relationship of central wavelength increment with loading time at 30 Hz:

Relationship of central wavelength increment with loading time at 50 Hz:

In the vibration test, the excitation frequencies of pipe3 were 20, 30, and 50 Hz. The two bare FBGs in series attached on pipe3 have been connected to channel 2 and channel 3 of the demodulation device, and the S-packaged FBG has been connected to channel 8. A simple harmonic force with frequency 50 Hz has first been applied to the end of pipe3, and the loading time lasts about 8,000 s. Second, adjusting the excitation frequency to 30 Hz, the load time on pipe3 lasts about 2,000 s. After that, the excitation frequency has changed to 20 Hz, and the loading time lasts about 1,000 s. An FBG from each channel was taken out for analysis. The FBG wavelength increment changes corresponding to the three excitation frequencies of 20, 30, and 50 Hz are shown in

Relationship of central wavelength increment with loading time at 20 Hz:

Relationship of central wavelength increment with loading time at 30 Hz:

Relationship of central wavelength increment with loading time at 50 Hz:

According to the aforementioned analysis on forced vibration of the cantilever beam, when a simple harmonic excitation is applied at the end of the beam, the strain response of the beam section at any point ^{3}. The simple harmonic excitation force

Comparison of calculated strain and measured strain in 10 Hz:

Comparison of theoretical strain and measured strain in 20 Hz:

Statistical analysis on the data presented in

Statistical analysis on the measured data.

Iterm | Bare-FBG6-pipe2 | Bare-FBG5-pipe3 | ||
---|---|---|---|---|

Testing value | Theoretical value | Testing value | Theoretical value | |

Mean value | 74.55 | 74.64 | −89.96 | −89.98 |

Standard error | 0.07 | 0.06 | 0.17 | 0.14 |

Median | 74.76 | 74.64 | −90.08 | −89.92 |

Standard deviation | 1.16 | 1.05 | 2.39 | 1.96 |

Variance | 1.35 | 1.11 | 5.73 | 3.86 |

Kurtosis | −1.34 | −1.37 | −1.23 | −1.20 |

Min value | 72.12 | 72.85 | −94.15 | −93.42 |

Max value | 76.38 | 76.36 | −85.71 | −86.54 |

Sum | 22,067.73 | 22,093.54 | −17902.42 | −17905.58 |

Number | 296 | 296 | 199 | 199 |

Through comparison analysis, it can be seen that the error between the peak values of the theoretical vibration strain time–history curve and the FBG-measured curve is very small. That is, the peak value of the measured curve can much accurately reflect the vibration deformation response of the submarine pipes, and it is effective for adopting the proposed FBG sensors to measure the vibration strain. Based on the study, further work will be conducted to consider the random vibration-induced dynamic response of CFRP pipes based on the proposed FBGs in series and packaged FBG senosrs. Furthermore, it is feasible to describe the dynamic deformation state of submarine pipelines under complex working conditions according to the information measured by FBGs.

Based on the fundamental study, the proposed sensing techniques can be further used to characterize the dynamic response of CFRP pipes under unknown excitation. It can be a challenging issue to configure the load spectrum and assess the structural performance of the pipes based on the effective data measured by FBG sensors.

CFRP composite pipes have been considered as the replacement of steel pipes in the transportation of oil and gas under deep submarine environment. Thus, the vibration characteristics of the CFRP pipes have been investigated by theoretical analysis and experimental testing. Measurement on vibration responses of the CFRP pipes have been performed based on proposed quasi-distributed optical fiber sensing technology. The following conclusions can be drawn from the study:

1) The dynamic response of the pipe beam model is derived from the continuum vibration differential equations, and the comparison analysis validates the accuracy of this simplified theoretical model to describe the bending vibration-induced response.

2) The designed FBGs in series attached on the CFRP pipes have measured the dynamic strain responses with much high sensitivity and accuracy, which indicates the feasibility of the proposed monitoring technique for detecting the dynamic performance of composite pipes under arbitrary excitation.

3) The sensing performance of two packaged FBG sensors has also been checked, and the reasonable outputs indicate the effectiveness of the measurement. The results also indicate that the epoxy resin packaged FBG sensor installed on the CFRP composite pipes provides good measurement stability, which can be considered for the detection of submarine pipes under large dynamic deformation.

The original contributions presented in the study are included in the article/Supplementary Material; further inquiries can be directed to the corresponding authors.

H-PW and S-YF contributed to the main part of the manuscript. X-SG, Y-XG, and YF contributed to the experimental study. PX checked the manuscript.

This study was supported by the National Natural Science Foundation of China (Grant Nos. 51908263 and 11932008). The authors would also like to appreciate the funding support by the Fundamental Research Funds for the Central Universities (Grant No. lzujbky-2020-56), Provincial Projects (2020-0624-RCC-0013 and JK 2021-18), and Key Lab of Structures Dynamic Behavior and Control (Harbin Institute of Technology) of Ministry of Education (HITCE201901).

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Special thanks are due to Prof. Jinping Ou and Prof. Zhi Zhou of Dalian University of Technology, and Prof. Youhe Zhou and Prof. Ning Huang of Lanzhou University. The findings and opinions expressed in this article are only those of the authors and do not necessarily reflect the views of the sponsors.