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Analysis of vibration reduction characteristics of composite fiber curved laminated panels
Journal Pre-proofs Analysis of Vibration Reduction Characteristics of Composite Fiber Curved Laminated Panels Wang Xianfeng, Wang Huaqiao, Ma cheng, Xiao Jun, Li Liang PII: DOI: Reference:
S0263-8223(19)31748-9 https://doi.org/10.1016/j.compstruct.2019.111396 COST 111396
To appear in:
Composite Structures
Received Date: Revised Date: Accepted Date:
10 May 2019 3 August 2019 9 September 2019
Please cite this article as: Xianfeng, W., Huaqiao, W., cheng, M., Jun, X., Liang, L., Analysis of Vibration Reduction Characteristics of Composite Fiber Curved Laminated Panels, Composite Structures (2019), doi: https://doi.org/ 10.1016/j.compstruct.2019.111396
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2019 Published by Elsevier Ltd.
Analysis of Vibration Reduction Characteristics of Composite Fiber Curved Laminated Panels Wang Xianfeng1, Wang Huaqiao2, Ma cheng1, Xiao Jun1,Li Liang1 1, College of Material Science & Technology, Nanjing University of Aeronautics and Astronautics. 2, School of Mechanical Science & Engineering, Huazhong University of Science and Technology. Abstract: Firstly, based on modal experiment, this paper analyses composite fiber curve laminates, which includes [<0|15>]8, [<15|30>]8, [<30|45>]8, [<45|60>]8, [<60|75>]8, [<75|90>]8, and then gets damping ratio of each laminated plate. After analysis, the results showed that the curve of fiber layer for <30|45> composite laminated plate damping ratio is the maximum, however, the curve of fiber layer for <60|75> composite laminated plate damping ratio is the maximum. Secondly, the simple harmonic test of laminated plates with curved layers was carried out. Those plates includes [0/45/<0|15>/-45]s, [0/45/<15|30>/-45]s, [0/45/<30|45>/-45]s, [0/45/<45|60>/-45]s, [0/45/<60|75>/-45]s, [0/45/<75|90>/-45]s. It is easy to get the acceleration response maps of each laminated plate. The above simple harmonic test results showed that larger the damping ratio, the better the damping effect and the smaller the amplitude of acceleration. The amplitude of acceleration changes inversely with the change of damping ratio. Finally, the conclusion is that the laminated plate with the best vibration damping effect is [<30|45>]8, and the laminated plate with the worst vibration damping effect is [<60|75>]8. Keywords: Fiber curve placement; Modal experiment; Simple harmonic vibration experiment; Damping ratio; Vibration reduction Vibration is ubiquitous in modern aerospace vehicles, vibration not only affects the structural stability of aircraft, but also has a tremendous impact on the safety of pilots. One of many excellent properties of composite materials is superior vibration characteristic. Therefore, this research focuses on how to obtain better effect of vibration reduction. Because of visco elasticity, the damping coefficient of composite material is larger than that of metal material, therefore, in the vibration environment, energy is consumed more in composite components, and the vibration reduction effect is superior to metal materials. The research on the damping of composite materials is an important part of the research on the damping characteristics of composite materials. The damping mechanism of carbon fiber reinforced resin matrix composites is obviously different from that of metal materials, mainly in the following aspects[1]: （1）Damping of fibers and matrix; the damping of carbon fiber reinforced resin matrix composites mainly comes from the matrix and fiber. （2）Damping of the intermediate phase between the fiber and the matrix; the intermediate phase is the transition region between the fiber and the matrix, high shear strain exists in this region, which provides a premise for energy consumption. （3）Microstructure damage of composites; the sliding friction damping of fiber fracture,
matrix crack and degumming in the composite material. （4）Nonlinear visco elastic damping with local stress concentration; In the case of large amplitude and high stress, non-linear damping occurs in the local area between fibers due to the high concentration of stress and strain. （5）Thermo elastic damping generated by periodic thermal flow; Damping due to cyclic thermal flow from tensile stress zone to compressive stress zone in composites. At present, the research on the vibration characteristics of composite materials mainly focuses on the fiber linear lamination. There are few reports on the vibration characteristics of fiber curve placement, Cheng bo[2] found that the damping ratio of composite laminates with different placement order and different placement angle is different. Qi[3]Based on the principle of dissipative energy equivalence, the damping prediction model of composite laminates is established, the accuracy is tested by modal experiments. Li Mingjun et al[4] introduced anisotropic design in composite laminated plate damping, The characteristics and control mechanism of damping anisotropy of composite laminated plates are analyzed. M. anapathi et al. [5] established the vibration equation based on the first-order shear deformation theory and verified the validity of the vibration equation of laminated plates by combining the curvature of different laminates and the ratio of laminates. Shi Junping[6]studied the vibration characteristics and damping of composite sandwich plates, a new displacement correction model is proposed for the dynamic problem of sandwich plates, the accuracy of the method is verified by experiments. Wang Jingsheng et al.[7] analyzed the anisotropic composite sandwich plate damping structure by using the finite element method. The results of damping vibration reduction and noise reduction were summarized and elaborated by Dai Depei [8-9] and Liu Dihua [10].Without changing the satellite structure, constrained damping layer method is used to deal with the original structure by Shen Zhichun[11].It was found that the maximum value decreased by 22.3% in the vibration environment. Li Diansen et al.[12] studied the vibration damping characteristics of 3d woven composite materials by using the method of cantilever beam free attenuation experiment. The vibration characteristics of composite laminated plates were calculated and analyzed by Li Longyun [13], and the general asymptotic expression of natural frequencies of laminates is given. Berthelot[14]studied the damping performance of hybrid epoxy resin matrix composites reinforced with single-phase fiber. Guan et al.[15]proposed a new three-dimensional finite element model that can effectively predict the damping of composite laminated plates. At present, the study of the vibration characteristics of composite laminates is mainly for the straight line laying of laminates. There are few reports on the vibration characteristics of fiber curve laminates. Therefore, it is of great significance to study the vibration characteristics of composite fiber curvilinear ply laminates. In this paper, fiber curve laminate is made, those are [<0|15>]8,[<15|30>]8,[<30|45>]8,[<45|60>]8,[<60|75>]8,[<75|90>]8, laminates for each fiber curve are subjected to modal experimental analysis, obtain the damping ratio of each laminate. Fiber curve laminate is designed as following,[0/45/<0|15>/-45]s,[0/45/<15|30>/-45]s, [0/45/<30|45>/-45]s, [0/45/<45|60>/-45]s, [0/45/<60|75>/-45]s, [0/45/<75|90>/-45]s. Each laminate should be subjected to simple harmonic analysis. The relationship between damping ratio and acceleration amplitude could be obtained by data from modal experiment and harmonic experiment. The relationship between fiber change angle and vibration damping performance of composite laminates could also be obtained after analyses. Based on the above relationships, the
fiber angle change can be obtained during pursing the best vibration damping effect. So, this research must have important application value. 1. Theoretical analysis of laminates vibration 1.1 Stress-strain constitutive relationship of laminates According to classical laminate theory, the stress-strain relationship of the anisotropic composite single-layer plate in the axial direction is as follows:
s1 Q11 Q12 s Q 2 12 Q22 0 s3 0
0 e1 0 e2 Q66 e3
(1-1)
Where
Q11
E11
1 12 21
E 1
Q
12
12
12
E2
Q22
21
Q66 Q12
1 12 21
21
21 E1
12 E2
When the composite fiber placing, there is an angle between the fiber direction and the direction of the layup coordinate system, which is the fiber placement angle , as shown in Figure 1.
Fig.1 Schematic diagram of the layer coordinates According to the coordinate transformation, the stress strain in any direction can be obtained.
x
x
y
y
xy
T
1
2
12
xy
T
1
2
12
T
T
1
1
T
(1-2)
T
Where
cos T sin sin cos
sin
2
2
cos sin cos
2
2
2 sin cos 2 sin cos cos sin 2
(1-3)
2
The stress strain in any direction can be obtained according to formula (1-1) and formula (1-3):
x
y
xy
Q Q Q
12
Q Q
16
Q 26
11
12
22
Q
Q Q
16
x
26
y
66
xy
(1-4)
Where Q11 Q11 cos 4 2Q12 2Q66 sin 2 cos 2 Q22 sin 4 Q12 Q11 Q22 4Q66 sin 2 cos 2 Q12 sin 4 cos 4 Q22 Q11 sin 4 2Q12 2Q66 sin 2 cos 2 Q22 cos 4
(1-5)
Q16 Q11 Q12 2Q66 sin cos 3 Q11 Q22 2Q66 sin 3 cos Q 26 Q11 Q12 2Q66 sin 3 cos Q11 Q22 2Q66 sin cos 3
Q 66 Q11 Q22 2Q12 2Q66 sin 2 cos 2 Q66 sin 4 cos 4
It can be known from Formula (1-5): if the laminate laying angle θ is a certain value,
Q
is
the determined value. When the composite fiber curve is laid, the fiber angle of the layer is gradually changed in the plane, with it, the stiffness of the composite fiber curve is changed with the fiber angle. For materials used in engineering, not only high stiffness but also high damping is required. However, it is hard to have both high damping and high stiffness for the same material [16]. The composite fiber curve placement design can meet the structural requirements of stiffness and damping ratio. Therefore, it is of great engineering significance to explore the damping of composite laminates with variable stiffness. 2. Manufacturing composite fiber curve laying laminate Composite fiber curve placement means that the fiber angle keeps continuous change in the same layer, and is different at different locations, as shown in Figure 2. In same laminate, it contains both straight and curve layers.
Fig.2 Schematic diagram of fiber curve placement To obtain the relationship between the fiber curve angle and the damping effect of composite laminates, 6 pieces of fiber curve laying laminates were prepared by automatic fiber placement, which are all 1mm thick and whose curve angles are [<0|15>]8,[<15|30>]8,[<30|45>]8,[<45|60>]8,[<60|75>]8,[<75|90>]8. Each fiber curve laminate is
subjected to modal test to obtain its damping ratio. For example, [<45|60>]8 laying track is shown in Figure 3:
60
45
Fig.3 Schematic diagram of the change in the trajectory angle of <45|60> Damping ratio of different fiber curve laying laminates can be measured by modal experiment, the greater the damping ratio of the fiber curve laying laminate, the better the damping effect. 6 pieces of composite laminates are made by automatic fiber placement, which are [0/45/<0|15>/-45]s,[0/45/<15|30>/-45]s,[0/45/<30|45>/-45]s,[0/45/<45|60>/-45]s,[0/45/<60|75>/-45]s ,[0/45/<75|90>/-45]s. Each laminate is subjected to simple harmonic analysis. And then the acceleration response of each laminate can be obtained. According to the modal experiment results, when the damping ratio is greater, the damping effect is better. Fiber curve sandwich laminate and fiber curve laminate are shown in Figure 4 below.
(a) Fiber curve sandwich laminate
(b) Fiber curve laminate Fig.4 Composite fiber placement laminate 3 Composite laminate vibration test 3.1 Fiber curve laying laminate modal experiment To obtain the damping ratio of the laminates with different fiber curves, the fiber curve laminates are analyzed experimentally, and damping ratio of each laminated plate is calculated by the frequency response function, then damping ratio trend of composite laminates changing with fiber angle is analyzed. One side of the composite laminate is fixed on the experimental device platform, and free on the other side. Selecting points 1~9 as the excitation force point in the laminate, as shown in Figure 5. Acceleration signal receiver is installed on the reverse side of the laminate at point 5.
Fig.5 Location of the excitation force point Connecting signal amplifier and dynamic analyzer to digital computer, hammering the action points 1~9, the dynamic analyzer analyzes the signal collected by the acceleration sensor at point 5. Frequency response function diagram of composite laminates can be output to digital computer. The frequency response function diagram of the fiber curve laying laminate is shown in Figure 6.
(a)[<0|15>]8
(b)[<15|30>]8
(c) [<30|45>]8
(d) [<45|60>]8
(e) [<60|75>]8
(f) [<75|90>]8 Fig.6 Fiber curve laying layer plate frequency response function diagram Based on the frequency response function obtained by modal experiment, in digital computers, the damping ratio of different composite fiber curve laying laminates is calculated by special software. As shown in Table 1 below: Table 1 Damping ratio of composite fiber curve laminated laminates Fiber angle
<0|15>
<15|30>
<30|45>
<45|60>
<60|75>
<75|90>
Damping ratio 5.38 7.54 12.84 4.45 1.91 4.02 （%） It can be seen from table 1 that the damping ratio of composite laminates is the largest when the fiber angle changes between 30 and 45 degrees. The damping ratio of composite laminates is
Damping ratio（%）
the smallest when the fiber angle is between 60 and 75 degrees. The damping ratio change trend of the laminates with fiber angle can be described in another way. As shown in Fig.7, it is represented as a line graph. Along with the increase of fiber placement angle, the damping ratio of composite fiber curve laminates increases gradually when the angle change is under <30|45>. When the fiber angle changes between 30 and 45, the damping ratio of composite fiber curve laminate reaches the maximum. As the fiber angle increasing, the damping ratio of laminates gradually decreases. When the fiber angle changes between 60 and 75, the damping ratio of laminated plate is the smallest. If the fiber angle increases to 90°, the damping ratio of the laminate increases slightly.
Fiber angle
Fig. 7 Relation between damping ratio and fiber angle
3.2 Analysis of simple harmonic experiment The greater the damping ratio of the composite laminates, the better the vibration damping performance. Fiber curve laying laminates are made in the method of [0/45/<0|15>/-45]s,[0/45/<15|30>/-45]s,[0/45/<30|45>/-45]s,[0/45/<45|60>/-45]s,[0/45/<60|75>/-45]s ,[0/45/<75|90>/-45]s. After simple harmonic vibration analysis of the laminate, the response of the acceleration under the simple harmonic excitation force can be obtained. According to the results of the modal experiment, fiber curve laying laminate [<30|45>]8 has the largest damping ratio and should have the best vibration damping effect. Fiber curve laying laminate [<60|75>]8 has the smallest damping ratio and should have the worst vibration damping effect. Therefore, when the laminate is applied to the same simple harmonic excitation force, composite laminate [0/45/<30|45>/-45]s should have the lowest acceleration amplitude, and composite laminate [0/45/<60|75>/-45]s should have the largest acceleration amplitude. The composite laminate should be fixed on the experimental device platform firstly. And then, the harmonic exciter is installed in the center of the composite laminate. Finally, an acceleration sensor to receive the signal is installed on the free end side. The experiment is shown in Fig.8:
excitation point
acceptance point
Fig.8 Simple harmonic vibration excitation point test point position Applying a simple harmonic force to the composite laminate through a simple harmonic exciter, the magnitude of the force is f ( x ) sin( 10t ) , as shown in Fig. 9: 2. 0 1. 8
1. 00
111: pl : 2: +Z
F
1. 6 1. 4 1. 2
Simple harmonic N
1. 0 0. 8 0. 6 0. 4 Ampl i t ude
Real
0. 2 0. 0 - 0. 2 - 0. 4 - 0. 6 - 0. 8 - 1. 0 - 1. 2 - 1. 4 - 1. 6 - 1. 8 - 2. 0
0. 00
3
0
8
5
10
13
15
18
23
20 s
28
25
30
33
35
38
41
Time/s Fig.9 Simple harmonic excitation By simple harmonic vibration test for each laminate, the harmonic excitation signal can be gotten and transmitted to the dynamic analyzer. Finally, the acceleration curve of each laminate is obtained and is shown in Fig.10: 47e- 3
F F
40e- 3
1. 00
71: pl : 2: +Z 70: pl : 9: +Z
35e- 3
20e- 3 15e- 3 10e- 3 5. 0e- 3 0. 0
Ampl i t ude
Real
2) Acceleration/(m/s g
30e- 3 25e- 3
- 5. 0e- 3 - 10e- 3 - 15e- 3 - 20e- 3 - 25e- 3 - 30e- 3 - 35e- 3 - 40e- 3 - 45e- 3 - 53e- 3
0. 00
0
3
5
8
10
13
15
18
20 s
23
25
Time/s (a) [0/45/<0|15>/-45]s
28
30
33
35
38
41
70e- 3 60e- 3
F F
1. 00
71: pl : 2: +Z 70: pl : 7: +Z
50e- 3
30e- 3 20e- 3 10e- 3 0 - 10e- 3
Ampl i t ude
2) g Acceleration/(m/s Real
40e- 3
- 20e- 3 - 30e- 3 - 40e- 3 - 50e- 3 - 60e- 3 - 70e- 3 - 80e- 3 - 90e- 3 - 100e- 3
0. 00
0
5
10
15
20
25
30 s
35
40
45
50
55
61
Time/s (b) [0/45/<15|30>/-45]s 0. 1 90e- 3
F F
1. 00
71: pl : 2: +Z 70: pl : 8: +Z
80e- 3 70e- 3
50e- 3 40e- 3 30e- 3 20e- 3
Ampl i t ude
2) g Acceleration/(m/s Real
60e- 3
10e- 3 0. 0 - 10e- 3 - 20e- 3 - 30e- 3 - 40e- 3 - 50e- 3 - 60e- 3 - 70e- 3
0. 00
0
3
5
8
10
13
15
18
20 s
23
25
28
30
33
35
38
41
Time/s (c) [0/45/<30|45>/-45]s 0. 2
F F
0. 2
1. 00
71: pl : 2: +Z 70: pl : 9: +Z
0. 2
0. 1 0. 1 0. 1 80e- 3
Ampl i t ude
2) g Acceleration/(m/s Real
0. 2
60e- 3 40e- 3 20e- 3 0. 0 - 20e- 3 - 40e- 3 - 60e- 3 - 90e- 3
0. 00
0
3
5
8
10
13
15
18
20 s
23
25
Time/s (d) [0/45/<45|60>/-45]s
28
30
33
35
38
41
0. 1
F F
1. 00
71: pl : 2: +Z 70: pl : 9: +Z
80e- 3
40e- 3 20e- 3 Ampl i t ude
2) g Acceleration/(m/s Real
60e- 3
0. 0 - 20e- 3 - 40e- 3 - 60e- 3 - 80e- 3 - 0. 1 - 0. 1
0. 00
0
3
5
8
10
13
15
18
20 s
23
25
28
30
33
35
38
41
Time/s (e) [0/45/<60|75>/-45] 0. 2
F F
0. 2
1. 00
71: pl : 2: +Z 70: pl : 9: +Z
0. 2 0. 1 0. 1 0. 1 80e- 3
Ampl i t ude
g 2) Acceleration/(m/s Real
0. 2
60e- 3 40e- 3 20e- 3 0. 0 - 20e- 3 - 40e- 3 - 60e- 3 - 90e- 3
0. 00
0
3
5
8
10
13
15
18
20 s
23
25
28
30
33
35
38
41
Time/s (f) [0/45/<75|90>/-45]s Fig.10 Simple vibration results of fiber curve sandwich laminate It can be seen from Fig.10 that under the same external excitation force, the acceleration magnitude responses composite laminates amplitude. The maximum amplitude of the acceleration response occurs on the composite laminate [0/45/<60|75>/-45]s, while the minimum amplitude of the acceleration response occurs on the laminate [0/45/<30|45>/-45]s. The relationship between the amplitude of the composite laminate and the angle of fiber change is shown in Fig.11. It reflects the consistency of the modal experiment and the harmonic experiment. From the results of the harmonic experiment, it can be seen that with the increase of the fiber angle, acceleration amplitude of composite laminates is decreasing, and reaches to minimize at <30|45>. As the angle increasing goes on, the acceleration amplitude gradually increases, and gets to maximum when the fiber angle is <60|75>. The laminate plate amplitude decreases when the fiber angle continues to increase.
Acceleration/(m/s2)
Damping ratio %
Acceleration Damping ratio
Fiber angle Fig.11 Comparison of modal experiment and simple harmonic experiment In short, the results of the harmonic experiment are in accordance with the results of the modal experiment. The variation of the acceleration amplitude corresponds to the change of the damping ratio of the laminate. 4. Summary (1) Laminates [<0|15>]8, [<15|30>]8, [<30|45>]8, [<45|60>]8, [<60|75>]8, [<75 |90>]8 are subjected to modal experimental analysis. Frequency response function and damping ratios of laminates with different fiber angles can be gotten. It is also found that the damping ratio of fiber curve ply laminates is the greatest when the fiber angle is between 30 and 45, and it is the smallest during 60 and 75. (2) Harmonic experiments are carried out on the laminates of [0/45/<0|15>/-45]s,[0/45/<15|30>/-45]s,[0/45/<30|45>/-45]s,[0/45/<45|60>/-45]s,[0/45/<60|75>/-45]s ,[0/45/<75|90>/-45]s. Under the same simple harmonic excitation force, the acceleration variation diagram can be gotten. It is also found that the laminate [0/45/<30|45>/-45]s has the smallest acceleration amplitude, while [0/45/<60|75>/-45]s has the largest acceleration amplitude. (3) The damping ratio measured by the modal experiment is consistent with the trend of the acceleration amplitude measured by the harmonic experiment. The laminate has the smallest acceleration amplitude of the laminate with the largest damping ratio, while the laminate has the largest amplitude with the smallest damping ratio. (4) The larger the damping ratio of composite laminates, the better the vibration damping effect. When the fiber angle varies between 30 and 45, the composite laminate has the best vibration damping effect. When the fiber angle changes between 60 and 75, the laminate has the worst vibration damping effect. Acknowledgement The work reported here is supported by Youth Innovation Fund from Nanjing University of Aeronautics and Astronautics (NS2015057). Data Availability
The raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations.
Reference： [1] Ren Yongsheng, Liu Lihou. Advances in damping analysis and design of fiber reinforced composite material structures[J]. Mechanics and Practice, 2004, 26(1). [2] Cheng Bo. Research on Analysis method of Damping Prediction and Vibration Response for Composite Components with Laminated Structure[D]. Nanjing university of aeronautics and astronautics, 2014. [3] Qi Wenkai, Cheng Bo. Predictive Analysis and Verification of Damping for composite Laminates[J]. Journal of Vibration, Measurement＆Diagnosis. 2013, 33(6):1049-1053. [4] Li Mingjun, Liu Guiwu, Xu Yongwen et al. Effect of adhesive layer on internal dissipation characteristics of anisotropic laminated damping structures[J]. Journal Of Composite Materials, 2005, 22(4):96-99. [5] Ganapathi M, Kalyani A, Mondal B, et al. Free vibration analysis of simply supported composite laminated panels[J]. Composite Structures, 2009, 90(1):100-103. [6] Shi Junping, Liu Xiehui, Yue Jucai et al. Analysis of vibration and damping of composite plates[J]. Chinese Journal Of Applied Mechanics, 1996(2):132-136. [7] Wang Jingsheng, Wu Yousheng. Vib-Acoustic Analysis of Viscoelastic Composite Sandwich Plates with Transversely Deformable Core[J]. JOURNAL OF VIBRATION AND SHOCK, 2006, 25(5):6-9. [8] Dai Peide. Damping vibration and noise reduction technology[M]. Xi'an: Xi'an Jiaotong University press, 1986. [9] Dai Peide. Engineering application of damping technology[M]. Beijing: Tsinghua University Press, 1991. [10] Liu Lihua. Application technology of viscoelastic damping for vibration and noise reduction[M]. Beijing: aerospace press, 1990. [11] Shen Zhichun, Liang Lu, Zheng Gangtie, et al. Vibration Suppression of a Payload Bracket in a Satellite[J]. Journal of Astronautics,2006, 27(3):503-506. [12] Li Diansen, Lu Zixing, Li Jianlu et al. Experimental Research On The Vibration Damping Properties Of 3D Braided Composites[J]. Journal Of Mechanical Strength, 2009, 31(2):211-214. [13] Li Longyuan. Analysis of dynamic characteristics of composite laminates[J]. Journal Of Computational Mechanics, 1988, 5(3):64-71. [14] Berthelot J M . Damping analysis of laminated beams and plates using the Ritz method[J]. Composite Structures, 2006, 74(2):186-201. [15] Guan Y J , Wei Y T . A new effective 3-D FE formulation of FRP structural modal damping for thick laminate[J]. Composite Structures, 2009, 87(3):225-231. [16] Qi Wenkai, Cheng Bo. Predictive Analysis and Verification of Damping for composite Laminates[J]. Journal of Vibration, Measurement＆Diagnosis. 2013, 33(6):1049-1053.
S0263-8223(19)31748-9 https://doi.org/10.1016/j.compstruct.2019.111396 COST 111396
To appear in:
Composite Structures
Received Date: Revised Date: Accepted Date:
10 May 2019 3 August 2019 9 September 2019
Please cite this article as: Xianfeng, W., Huaqiao, W., cheng, M., Jun, X., Liang, L., Analysis of Vibration Reduction Characteristics of Composite Fiber Curved Laminated Panels, Composite Structures (2019), doi: https://doi.org/ 10.1016/j.compstruct.2019.111396
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2019 Published by Elsevier Ltd.
Analysis of Vibration Reduction Characteristics of Composite Fiber Curved Laminated Panels Wang Xianfeng1, Wang Huaqiao2, Ma cheng1, Xiao Jun1,Li Liang1 1, College of Material Science & Technology, Nanjing University of Aeronautics and Astronautics. 2, School of Mechanical Science & Engineering, Huazhong University of Science and Technology. Abstract: Firstly, based on modal experiment, this paper analyses composite fiber curve laminates, which includes [<0|15>]8, [<15|30>]8, [<30|45>]8, [<45|60>]8, [<60|75>]8, [<75|90>]8, and then gets damping ratio of each laminated plate. After analysis, the results showed that the curve of fiber layer for <30|45> composite laminated plate damping ratio is the maximum, however, the curve of fiber layer for <60|75> composite laminated plate damping ratio is the maximum. Secondly, the simple harmonic test of laminated plates with curved layers was carried out. Those plates includes [0/45/<0|15>/-45]s, [0/45/<15|30>/-45]s, [0/45/<30|45>/-45]s, [0/45/<45|60>/-45]s, [0/45/<60|75>/-45]s, [0/45/<75|90>/-45]s. It is easy to get the acceleration response maps of each laminated plate. The above simple harmonic test results showed that larger the damping ratio, the better the damping effect and the smaller the amplitude of acceleration. The amplitude of acceleration changes inversely with the change of damping ratio. Finally, the conclusion is that the laminated plate with the best vibration damping effect is [<30|45>]8, and the laminated plate with the worst vibration damping effect is [<60|75>]8. Keywords: Fiber curve placement; Modal experiment; Simple harmonic vibration experiment; Damping ratio; Vibration reduction Vibration is ubiquitous in modern aerospace vehicles, vibration not only affects the structural stability of aircraft, but also has a tremendous impact on the safety of pilots. One of many excellent properties of composite materials is superior vibration characteristic. Therefore, this research focuses on how to obtain better effect of vibration reduction. Because of visco elasticity, the damping coefficient of composite material is larger than that of metal material, therefore, in the vibration environment, energy is consumed more in composite components, and the vibration reduction effect is superior to metal materials. The research on the damping of composite materials is an important part of the research on the damping characteristics of composite materials. The damping mechanism of carbon fiber reinforced resin matrix composites is obviously different from that of metal materials, mainly in the following aspects[1]: （1）Damping of fibers and matrix; the damping of carbon fiber reinforced resin matrix composites mainly comes from the matrix and fiber. （2）Damping of the intermediate phase between the fiber and the matrix; the intermediate phase is the transition region between the fiber and the matrix, high shear strain exists in this region, which provides a premise for energy consumption. （3）Microstructure damage of composites; the sliding friction damping of fiber fracture,
matrix crack and degumming in the composite material. （4）Nonlinear visco elastic damping with local stress concentration; In the case of large amplitude and high stress, non-linear damping occurs in the local area between fibers due to the high concentration of stress and strain. （5）Thermo elastic damping generated by periodic thermal flow; Damping due to cyclic thermal flow from tensile stress zone to compressive stress zone in composites. At present, the research on the vibration characteristics of composite materials mainly focuses on the fiber linear lamination. There are few reports on the vibration characteristics of fiber curve placement, Cheng bo[2] found that the damping ratio of composite laminates with different placement order and different placement angle is different. Qi[3]Based on the principle of dissipative energy equivalence, the damping prediction model of composite laminates is established, the accuracy is tested by modal experiments. Li Mingjun et al[4] introduced anisotropic design in composite laminated plate damping, The characteristics and control mechanism of damping anisotropy of composite laminated plates are analyzed. M. anapathi et al. [5] established the vibration equation based on the first-order shear deformation theory and verified the validity of the vibration equation of laminated plates by combining the curvature of different laminates and the ratio of laminates. Shi Junping[6]studied the vibration characteristics and damping of composite sandwich plates, a new displacement correction model is proposed for the dynamic problem of sandwich plates, the accuracy of the method is verified by experiments. Wang Jingsheng et al.[7] analyzed the anisotropic composite sandwich plate damping structure by using the finite element method. The results of damping vibration reduction and noise reduction were summarized and elaborated by Dai Depei [8-9] and Liu Dihua [10].Without changing the satellite structure, constrained damping layer method is used to deal with the original structure by Shen Zhichun[11].It was found that the maximum value decreased by 22.3% in the vibration environment. Li Diansen et al.[12] studied the vibration damping characteristics of 3d woven composite materials by using the method of cantilever beam free attenuation experiment. The vibration characteristics of composite laminated plates were calculated and analyzed by Li Longyun [13], and the general asymptotic expression of natural frequencies of laminates is given. Berthelot[14]studied the damping performance of hybrid epoxy resin matrix composites reinforced with single-phase fiber. Guan et al.[15]proposed a new three-dimensional finite element model that can effectively predict the damping of composite laminated plates. At present, the study of the vibration characteristics of composite laminates is mainly for the straight line laying of laminates. There are few reports on the vibration characteristics of fiber curve laminates. Therefore, it is of great significance to study the vibration characteristics of composite fiber curvilinear ply laminates. In this paper, fiber curve laminate is made, those are [<0|15>]8,[<15|30>]8,[<30|45>]8,[<45|60>]8,[<60|75>]8,[<75|90>]8, laminates for each fiber curve are subjected to modal experimental analysis, obtain the damping ratio of each laminate. Fiber curve laminate is designed as following,[0/45/<0|15>/-45]s,[0/45/<15|30>/-45]s, [0/45/<30|45>/-45]s, [0/45/<45|60>/-45]s, [0/45/<60|75>/-45]s, [0/45/<75|90>/-45]s. Each laminate should be subjected to simple harmonic analysis. The relationship between damping ratio and acceleration amplitude could be obtained by data from modal experiment and harmonic experiment. The relationship between fiber change angle and vibration damping performance of composite laminates could also be obtained after analyses. Based on the above relationships, the
fiber angle change can be obtained during pursing the best vibration damping effect. So, this research must have important application value. 1. Theoretical analysis of laminates vibration 1.1 Stress-strain constitutive relationship of laminates According to classical laminate theory, the stress-strain relationship of the anisotropic composite single-layer plate in the axial direction is as follows:
s1 Q11 Q12 s Q 2 12 Q22 0 s3 0
0 e1 0 e2 Q66 e3
(1-1)
Where
Q11
E11
1 12 21
E 1
Q
12
12
12
E2
Q22
21
Q66 Q12
1 12 21
21
21 E1
12 E2
When the composite fiber placing, there is an angle between the fiber direction and the direction of the layup coordinate system, which is the fiber placement angle , as shown in Figure 1.
Fig.1 Schematic diagram of the layer coordinates According to the coordinate transformation, the stress strain in any direction can be obtained.
x
x
y
y
xy
T
1
2
12
xy
T
1
2
12
T
T
1
1
T
(1-2)
T
Where
cos T sin sin cos
sin
2
2
cos sin cos
2
2
2 sin cos 2 sin cos cos sin 2
(1-3)
2
The stress strain in any direction can be obtained according to formula (1-1) and formula (1-3):
x
y
xy
Q Q Q
12
Q Q
16
Q 26
11
12
22
Q
Q Q
16
x
26
y
66
xy
(1-4)
Where Q11 Q11 cos 4 2Q12 2Q66 sin 2 cos 2 Q22 sin 4 Q12 Q11 Q22 4Q66 sin 2 cos 2 Q12 sin 4 cos 4 Q22 Q11 sin 4 2Q12 2Q66 sin 2 cos 2 Q22 cos 4
(1-5)
Q16 Q11 Q12 2Q66 sin cos 3 Q11 Q22 2Q66 sin 3 cos Q 26 Q11 Q12 2Q66 sin 3 cos Q11 Q22 2Q66 sin cos 3
Q 66 Q11 Q22 2Q12 2Q66 sin 2 cos 2 Q66 sin 4 cos 4
It can be known from Formula (1-5): if the laminate laying angle θ is a certain value,
Q
is
the determined value. When the composite fiber curve is laid, the fiber angle of the layer is gradually changed in the plane, with it, the stiffness of the composite fiber curve is changed with the fiber angle. For materials used in engineering, not only high stiffness but also high damping is required. However, it is hard to have both high damping and high stiffness for the same material [16]. The composite fiber curve placement design can meet the structural requirements of stiffness and damping ratio. Therefore, it is of great engineering significance to explore the damping of composite laminates with variable stiffness. 2. Manufacturing composite fiber curve laying laminate Composite fiber curve placement means that the fiber angle keeps continuous change in the same layer, and is different at different locations, as shown in Figure 2. In same laminate, it contains both straight and curve layers.
Fig.2 Schematic diagram of fiber curve placement To obtain the relationship between the fiber curve angle and the damping effect of composite laminates, 6 pieces of fiber curve laying laminates were prepared by automatic fiber placement, which are all 1mm thick and whose curve angles are [<0|15>]8,[<15|30>]8,[<30|45>]8,[<45|60>]8,[<60|75>]8,[<75|90>]8. Each fiber curve laminate is
subjected to modal test to obtain its damping ratio. For example, [<45|60>]8 laying track is shown in Figure 3:
60
45
Fig.3 Schematic diagram of the change in the trajectory angle of <45|60> Damping ratio of different fiber curve laying laminates can be measured by modal experiment, the greater the damping ratio of the fiber curve laying laminate, the better the damping effect. 6 pieces of composite laminates are made by automatic fiber placement, which are [0/45/<0|15>/-45]s,[0/45/<15|30>/-45]s,[0/45/<30|45>/-45]s,[0/45/<45|60>/-45]s,[0/45/<60|75>/-45]s ,[0/45/<75|90>/-45]s. Each laminate is subjected to simple harmonic analysis. And then the acceleration response of each laminate can be obtained. According to the modal experiment results, when the damping ratio is greater, the damping effect is better. Fiber curve sandwich laminate and fiber curve laminate are shown in Figure 4 below.
(a) Fiber curve sandwich laminate
(b) Fiber curve laminate Fig.4 Composite fiber placement laminate 3 Composite laminate vibration test 3.1 Fiber curve laying laminate modal experiment To obtain the damping ratio of the laminates with different fiber curves, the fiber curve laminates are analyzed experimentally, and damping ratio of each laminated plate is calculated by the frequency response function, then damping ratio trend of composite laminates changing with fiber angle is analyzed. One side of the composite laminate is fixed on the experimental device platform, and free on the other side. Selecting points 1~9 as the excitation force point in the laminate, as shown in Figure 5. Acceleration signal receiver is installed on the reverse side of the laminate at point 5.
Fig.5 Location of the excitation force point Connecting signal amplifier and dynamic analyzer to digital computer, hammering the action points 1~9, the dynamic analyzer analyzes the signal collected by the acceleration sensor at point 5. Frequency response function diagram of composite laminates can be output to digital computer. The frequency response function diagram of the fiber curve laying laminate is shown in Figure 6.
(a)[<0|15>]8
(b)[<15|30>]8
(c) [<30|45>]8
(d) [<45|60>]8
(e) [<60|75>]8
(f) [<75|90>]8 Fig.6 Fiber curve laying layer plate frequency response function diagram Based on the frequency response function obtained by modal experiment, in digital computers, the damping ratio of different composite fiber curve laying laminates is calculated by special software. As shown in Table 1 below: Table 1 Damping ratio of composite fiber curve laminated laminates Fiber angle
<0|15>
<15|30>
<30|45>
<45|60>
<60|75>
<75|90>
Damping ratio 5.38 7.54 12.84 4.45 1.91 4.02 （%） It can be seen from table 1 that the damping ratio of composite laminates is the largest when the fiber angle changes between 30 and 45 degrees. The damping ratio of composite laminates is
Damping ratio（%）
the smallest when the fiber angle is between 60 and 75 degrees. The damping ratio change trend of the laminates with fiber angle can be described in another way. As shown in Fig.7, it is represented as a line graph. Along with the increase of fiber placement angle, the damping ratio of composite fiber curve laminates increases gradually when the angle change is under <30|45>. When the fiber angle changes between 30 and 45, the damping ratio of composite fiber curve laminate reaches the maximum. As the fiber angle increasing, the damping ratio of laminates gradually decreases. When the fiber angle changes between 60 and 75, the damping ratio of laminated plate is the smallest. If the fiber angle increases to 90°, the damping ratio of the laminate increases slightly.
Fiber angle
Fig. 7 Relation between damping ratio and fiber angle
3.2 Analysis of simple harmonic experiment The greater the damping ratio of the composite laminates, the better the vibration damping performance. Fiber curve laying laminates are made in the method of [0/45/<0|15>/-45]s,[0/45/<15|30>/-45]s,[0/45/<30|45>/-45]s,[0/45/<45|60>/-45]s,[0/45/<60|75>/-45]s ,[0/45/<75|90>/-45]s. After simple harmonic vibration analysis of the laminate, the response of the acceleration under the simple harmonic excitation force can be obtained. According to the results of the modal experiment, fiber curve laying laminate [<30|45>]8 has the largest damping ratio and should have the best vibration damping effect. Fiber curve laying laminate [<60|75>]8 has the smallest damping ratio and should have the worst vibration damping effect. Therefore, when the laminate is applied to the same simple harmonic excitation force, composite laminate [0/45/<30|45>/-45]s should have the lowest acceleration amplitude, and composite laminate [0/45/<60|75>/-45]s should have the largest acceleration amplitude. The composite laminate should be fixed on the experimental device platform firstly. And then, the harmonic exciter is installed in the center of the composite laminate. Finally, an acceleration sensor to receive the signal is installed on the free end side. The experiment is shown in Fig.8:
excitation point
acceptance point
Fig.8 Simple harmonic vibration excitation point test point position Applying a simple harmonic force to the composite laminate through a simple harmonic exciter, the magnitude of the force is f ( x ) sin( 10t ) , as shown in Fig. 9: 2. 0 1. 8
1. 00
111: pl : 2: +Z
F
1. 6 1. 4 1. 2
Simple harmonic N
1. 0 0. 8 0. 6 0. 4 Ampl i t ude
Real
0. 2 0. 0 - 0. 2 - 0. 4 - 0. 6 - 0. 8 - 1. 0 - 1. 2 - 1. 4 - 1. 6 - 1. 8 - 2. 0
0. 00
3
0
8
5
10
13
15
18
23
20 s
28
25
30
33
35
38
41
Time/s Fig.9 Simple harmonic excitation By simple harmonic vibration test for each laminate, the harmonic excitation signal can be gotten and transmitted to the dynamic analyzer. Finally, the acceleration curve of each laminate is obtained and is shown in Fig.10: 47e- 3
F F
40e- 3
1. 00
71: pl : 2: +Z 70: pl : 9: +Z
35e- 3
20e- 3 15e- 3 10e- 3 5. 0e- 3 0. 0
Ampl i t ude
Real
2) Acceleration/(m/s g
30e- 3 25e- 3
- 5. 0e- 3 - 10e- 3 - 15e- 3 - 20e- 3 - 25e- 3 - 30e- 3 - 35e- 3 - 40e- 3 - 45e- 3 - 53e- 3
0. 00
0
3
5
8
10
13
15
18
20 s
23
25
Time/s (a) [0/45/<0|15>/-45]s
28
30
33
35
38
41
70e- 3 60e- 3
F F
1. 00
71: pl : 2: +Z 70: pl : 7: +Z
50e- 3
30e- 3 20e- 3 10e- 3 0 - 10e- 3
Ampl i t ude
2) g Acceleration/(m/s Real
40e- 3
- 20e- 3 - 30e- 3 - 40e- 3 - 50e- 3 - 60e- 3 - 70e- 3 - 80e- 3 - 90e- 3 - 100e- 3
0. 00
0
5
10
15
20
25
30 s
35
40
45
50
55
61
Time/s (b) [0/45/<15|30>/-45]s 0. 1 90e- 3
F F
1. 00
71: pl : 2: +Z 70: pl : 8: +Z
80e- 3 70e- 3
50e- 3 40e- 3 30e- 3 20e- 3
Ampl i t ude
2) g Acceleration/(m/s Real
60e- 3
10e- 3 0. 0 - 10e- 3 - 20e- 3 - 30e- 3 - 40e- 3 - 50e- 3 - 60e- 3 - 70e- 3
0. 00
0
3
5
8
10
13
15
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20 s
23
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41
Time/s (c) [0/45/<30|45>/-45]s 0. 2
F F
0. 2
1. 00
71: pl : 2: +Z 70: pl : 9: +Z
0. 2
0. 1 0. 1 0. 1 80e- 3
Ampl i t ude
2) g Acceleration/(m/s Real
0. 2
60e- 3 40e- 3 20e- 3 0. 0 - 20e- 3 - 40e- 3 - 60e- 3 - 90e- 3
0. 00
0
3
5
8
10
13
15
18
20 s
23
25
Time/s (d) [0/45/<45|60>/-45]s
28
30
33
35
38
41
0. 1
F F
1. 00
71: pl : 2: +Z 70: pl : 9: +Z
80e- 3
40e- 3 20e- 3 Ampl i t ude
2) g Acceleration/(m/s Real
60e- 3
0. 0 - 20e- 3 - 40e- 3 - 60e- 3 - 80e- 3 - 0. 1 - 0. 1
0. 00
0
3
5
8
10
13
15
18
20 s
23
25
28
30
33
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41
Time/s (e) [0/45/<60|75>/-45] 0. 2
F F
0. 2
1. 00
71: pl : 2: +Z 70: pl : 9: +Z
0. 2 0. 1 0. 1 0. 1 80e- 3
Ampl i t ude
g 2) Acceleration/(m/s Real
0. 2
60e- 3 40e- 3 20e- 3 0. 0 - 20e- 3 - 40e- 3 - 60e- 3 - 90e- 3
0. 00
0
3
5
8
10
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18
20 s
23
25
28
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41
Time/s (f) [0/45/<75|90>/-45]s Fig.10 Simple vibration results of fiber curve sandwich laminate It can be seen from Fig.10 that under the same external excitation force, the acceleration magnitude responses composite laminates amplitude. The maximum amplitude of the acceleration response occurs on the composite laminate [0/45/<60|75>/-45]s, while the minimum amplitude of the acceleration response occurs on the laminate [0/45/<30|45>/-45]s. The relationship between the amplitude of the composite laminate and the angle of fiber change is shown in Fig.11. It reflects the consistency of the modal experiment and the harmonic experiment. From the results of the harmonic experiment, it can be seen that with the increase of the fiber angle, acceleration amplitude of composite laminates is decreasing, and reaches to minimize at <30|45>. As the angle increasing goes on, the acceleration amplitude gradually increases, and gets to maximum when the fiber angle is <60|75>. The laminate plate amplitude decreases when the fiber angle continues to increase.
Acceleration/(m/s2)
Damping ratio %
Acceleration Damping ratio
Fiber angle Fig.11 Comparison of modal experiment and simple harmonic experiment In short, the results of the harmonic experiment are in accordance with the results of the modal experiment. The variation of the acceleration amplitude corresponds to the change of the damping ratio of the laminate. 4. Summary (1) Laminates [<0|15>]8, [<15|30>]8, [<30|45>]8, [<45|60>]8, [<60|75>]8, [<75 |90>]8 are subjected to modal experimental analysis. Frequency response function and damping ratios of laminates with different fiber angles can be gotten. It is also found that the damping ratio of fiber curve ply laminates is the greatest when the fiber angle is between 30 and 45, and it is the smallest during 60 and 75. (2) Harmonic experiments are carried out on the laminates of [0/45/<0|15>/-45]s,[0/45/<15|30>/-45]s,[0/45/<30|45>/-45]s,[0/45/<45|60>/-45]s,[0/45/<60|75>/-45]s ,[0/45/<75|90>/-45]s. Under the same simple harmonic excitation force, the acceleration variation diagram can be gotten. It is also found that the laminate [0/45/<30|45>/-45]s has the smallest acceleration amplitude, while [0/45/<60|75>/-45]s has the largest acceleration amplitude. (3) The damping ratio measured by the modal experiment is consistent with the trend of the acceleration amplitude measured by the harmonic experiment. The laminate has the smallest acceleration amplitude of the laminate with the largest damping ratio, while the laminate has the largest amplitude with the smallest damping ratio. (4) The larger the damping ratio of composite laminates, the better the vibration damping effect. When the fiber angle varies between 30 and 45, the composite laminate has the best vibration damping effect. When the fiber angle changes between 60 and 75, the laminate has the worst vibration damping effect. Acknowledgement The work reported here is supported by Youth Innovation Fund from Nanjing University of Aeronautics and Astronautics (NS2015057). Data Availability
The raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations.
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