Abstract
This study investigates the vibration transmission and suppression of a laminated composite panel with variable angle tow (VAT) designs and an attached inerter-based passive nonlinear energy sink. Based on analytical and numerical methodologies, the substructure technique is used to obtain a steady-state dynamic response and the results are verified by experimental and analytical methods. It is demonstrated that fiber orientation has a significant impact on the natural frequencies. The dynamic responses and energy transmission path characteristics are determined and evaluated by forced vibration analysis. The main vibration transmission paths inside the structure are displayed using power flow density vectors. It is demonstrated that the dynamic responses of the plate can be changed considerably by using various fiber placement schemes and passive suppression devices. In addition, it is indicated that the vibration transmission paths are significantly influenced by the tailored fiber angles for improved dynamic performance. Our investigation enhances the understanding of enhanced vibration suppression designs of variable-stiffness composite plates with attached passive devices.
摘要
目的
工程复合材料结构经常受到动载荷而发生振动。本文研究通过变刚度纤维铺缝设计和附加惯容型非线性能量汇实现结构减振。
创新点
1. 本文发展子结构分析方法, 系统研究了纤维角度和不同非线性能量汇的设计参数对复合材料板结构受迫振动的位移和能量响应; 2. 从振动功率流角度研究变刚度复合材料层合板的受迫振动响应和减振性能。
方法
1. 通过子结构法, 研究线性和非线性无能量汇的各个参数对于整体结构在受迫振动下的能量传递的影响; 2. 通过仿真模拟, 研究变角度纤维铺层对结构自由振动和受迫振动响应的影响; 3. 通过实验研究, 获得复合材料板结构的自由频率, 并与解析法、仿真法所得结果进行交叉对比, 验证方法的准确性。
结论
1. 变角度纤维铺层设计可以有效地改善结构的自由振动与受迫振动响应; 2. 通过调整纤维的铺层角度, 可以改变主要模态振型和振动功率流的主要传递路径; 3. 非线性能量汇的使用可有效降低结构响应, 从而达到良好减振的效果。
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References
Abdalla MM, Setoodeh S, Gürdal Z, 2007. Design of variable stiffness composite panels for maximum fundamental frequency using lamination parameters. Composite Structures, 81(2):283–291. https://doi.org/10.1016/j.compstruct.2006.08.018
Akbarzadeh AH, Nik MA, Pasini D, 2016. Vibration responses and suppression of variable stiffness laminates with optimally steered fibers and magnetostrictive layers. Composites Part B: Engineering, 91:315–326. https://doi.org/10.1016/j.compositesb.2016.02.003
Blom AW, Setoodeh S, Hol JMAM, et al., 2008. Design of variable-stiffness conical shells for maximum fundamental eigenfrequency. Computers & Structures, 86(9):870–878. https://doi.org/10.1016/j.compstruc.2007.04.020
Chen HY, Mao XY, Ding H, et al., 2020. Elimination of multi-mode resonances of composite plate by inertial nonlinear energy sinks. Mechanical Systems and Signal Processing, 135:106383. https://doi.org/10.1016/j.ymssp.2019.106383
Cho DS, Kim BH, Kim JH, et al., 2015. Forced vibration analysis of arbitrarily constrained rectangular plates and stiffened panels using the assumed mode method. Thin-Walled Structures, 90:182–190. https://doi.org/10.1016/j.tws.2015.01.020
Coburn BH, Wu ZM, Weaver PM, 2014. Buckling analysis of stiffened variable angle tow panels. Composite Structures, 111:259–270. https://doi.org/10.1016/j.compstruct.2013.12.029
Dai W, Yang J, Shi BY, 2020. Vibration transmission and power flow in impact oscillators with linear and nonlinear constraints. International Journal of Mechanical Sciences, 168: 105234. https://doi.org/10.1016/j.ijmecsci.2019.105234
Dai W, Yang J, Wiercigroch M, 2022. Vibration energy flow transmission in systems with Coulomb friction. International Journal of Mechanical Sciences, 214:106932. https://doi.org/10.1016/j.ijmecsci.2021.106932
Gurdal Z, Olmedo R, 1993. In-plane response of laminates with spatially varying fiber orientations-variable stiffness concept. AIAA Journal, 31(4):751–758. https://doi.org/10.2514/3.11613
Honda S, Oonishi Y, Narita Y, et al., 2008. Vibration analysis of composite rectangular plates reinforced along curved lines. Journal of System Design and Dynamics, 2(1):76–86. https://doi.org/10.1299/jsdd.2.76
Houmat A, 2013. Nonlinear free vibration of laminated composite rectangular plates with curvilinear fibers. Composite Structures, 106:211–224. https://doi.org/10.1016/j.compstruct.2013.05.058
Ibrahim RA, 2008. Recent advances in nonlinear passive vibration isolators. Journal of Sound and Vibration, 314(3–5):371–452. https://doi.org/10.1016/j.jsv.2008.01.014
Jahangir I, Barazanchy D, van Zanten FJ, et al., 2022. Tow path planning strategies for fiber steered laminates. Journal of Aircraft, 59(2):502–514. https://doi.org/10.2514/1.C036481
Javidialesaadi A, Wierschem NE, 2019. An inerter-enhanced nonlinear energy sink. Mechanical Systems and Signal Processing, 129:449–454. https://doi.org/10.1016/j.ymssp.2019.04.047
Jiang JZ, Matamoros-Sanchez AZ, Goodall RM, et al., 2012. Passive suspensions incorporating inerters for railway vehicles. Vehicle System Dynamics, 50(Supplement):263–276. https://doi.org/10.1080/00423114.2012.665166
Lazar IF, Neild SA, Wagg DJ, 2014. Using an inerter-based device for structural vibration suppression. Earthquake Engineering & Structural Dynamics, 43(8):1129–1147. https://doi.org/10.1002/eqe.2390
Li Y, Jiang JZ, Neild S, 2017. Inerter-based configurations for main-landing-gear shimmy suppression. Journal of Aircraft, 54(2):684–693. https://doi.org/10.2514/1.C033964
Lopes CS, Camanho PP, Gürdal Z, et al., 2007. Progressive failure analysis of tow-placed, variable-stiffness composite panels. International Journal of Solids and Structures, 44(25–26):8493–8516. https://doi.org/10.1016/j.ijsolstr.2007.06.029
Mace BR, Shorter PJ, 2000. Energy flow models from finite element analysis. Journal of Sound and Vibration, 233(3):369–389. https://doi.org/10.1006/jsvi.1999.2812
Nik MA, Fayazbakhsh K, Pasini D, et al., 2014a. Optimization of variable stiffness composites with embedded defects induced by automated fiber placement. Composite Structures, 107:160–166. https://doi.org/10.1016/j.compstruct.2013.07.059
Nik MA, Fayazbakhsh K, Pasini D, et al., 2014b. A comparative study of metamodeling methods for the design optimization of variable stiffness composites. Composite Structures, 107:494–501. https://doi.org/10.1016/j.compstruct.2013.08.023
Pedersen P, 1991. On thickness and orientational design with orthotropic materials. Structural Optimization, 3(2):69–78. https://doi.org/10.1007/BF01743275
Rahman T, Ijsselmuiden ST, Abdalla MM, et al., 2011. Post-buckling analysis of variable stiffness composite plates using a finite element-based perturbation method. International Journal of Structural Stability and Dynamics, 11(4):735–753. https://doi.org/10.1142/S0219455411004324
Raju G, Wu ZM, Weaver PM, 2015. Buckling and postbuckling of variable angle tow composite plates under in-plane shear loading. International Journal of Solids and Structures, 58: 270–287. https://doi.org/10.1016/j.ijsolstr.2015.01.011
Reddy JN, 1997. Mechanics of Laminated Composite Plates: Theory and Analysis. CRC Press, Boca Raton, USA.
Rivin EI, 2003. Passive Vibration Isolation. ASME Press, New York, USA.
Setoodeh S, Abdalla MM, Gürdal Z, 2005. Combined topology and fiber path design of composite layers using cellular automata. Structural and Multidisciplinary Optimization, 30(6):413–421. https://doi.org/10.1007/s00158-005-0528-y
Shi BY, Yang J, 2020. Quantification of vibration force and power flow transmission between coupled nonlinear oscillators. International Journal of Dynamics and Control, 8(2): 418–435. https://doi.org/10.1007/s40435-019-00560-7
Shi BY, Yang J, Rudd C, 2019. On vibration transmission in oscillating systems incorporating bilinear stiffness and damping elements. International Journal of Mechanical Sciences, 150:458–470. https://doi.org/10.1016/j.ijmecsci.2018.10.031
Smith MC, Wang FC, 2004. Performance benefits in passive vehicle suspensions employing inerters. Vehicle System Dynamics, 42(4):235–257. https://doi.org/10.1080/00423110412331289871
Tan P, Nie GJ, 2016. Free and forced vibration of variable stiffness composite annular thin plates with elastically restrained edges. Composite Structures, 149:398–407. https://doi.org/10.1016/j.compstruct.2016.04.021
Vijayachandran AA, Waas AM, 2022a. Minimizing stress concentrations using steered fiberpaths and incorporating realistic manufacturing signatures. International Journal of Non-Linear Mechanics, 146:104160. https://doi.org/10.1016/j.ijnonlinmec.2022.104160
Vijayachandran AA, Waas AM, 2022b. Steered fiber paths for improved in-plane compressive response of aerostructural panels: experimental studies and numerical modeling. Composite Structures, 289:115426. https://doi.org/10.1016/j.compstruct.2022.115426
Wang FC, Liao MK, Liao BH, et al., 2009. The performance improvements of train suspension systems with mechanical networks employing inerters. Vehicle System Dynamics, 47(7):805–830. https://doi.org/10.1080/00423110802385951
Wang FC, Hong MF, Chen CW, 2010. Building suspensions with inerters. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 224(8):1605–1616. https://doi.org/10.1243/09544062JMES1909
Wang ZH, Xing JT, Price WG, 2002. Power flow analysis of indeterminate rod/beam systems using a substructure method. Journal of Sound and Vibration, 249(1):3–22. https://doi.org/10.1006/jsvi.2001.3645
White SC, Raju G, Weaver PM, 2014. Initial post-buckling of variable-stiffness curved panels. Journal of the Mechanics and Physics of Solids, 71:132–155. https://doi.org/10.1016/j.jmps.2014.07.003
White SC, Weaver PM, Wu KC, 2015. Post-buckling analyses of variable-stiffness composite cylinders in axial compression. Composite Structures, 123:190–203. https://doi.org/10.1016/j.compstruct.2014.12.013
Wu CP, Lee CY, 2001. Differential quadrature solution for the free vibration analysis of laminated conical shells with variable stiffness. International Journal of Mechanical Sciences, 43(8):1853–1869. https://doi.org/10.1016/S0020-7403(01)00010-8
Wu ZM, Weaver PM, Raju G, et al., 2012. Buckling analysis and optimisation of variable angle tow composite plates. Thin-Walled Structures, 60:163–172. https://doi.org/10.1016/j.tws.2012.07.008
Wu ZM, Raju G, Weaver PM, 2013. Postbuckling analysis of variable angle tow composite plates. International Journal of Solids and Structures, 50(10):1770–1780. https://doi.org/10.1016/j.ijsolstr.2013.02.001
Wu ZM, Raju G, Weaver PM, 2018. Optimization of post-buckling behaviour of variable thickness composite panels with variable angle tows: towards “Buckle-Free” design concept. International Journal of Solids and Structures, 132–133:66–79. https://doi.org/10.1016/j.ijsolstr.2017.08.037
Xiong YP, Xing JT, Price WG, 2001. Power flow analysis of complex coupled systems by progressive approaches. Journal of Sound and Vibration, 239(2):275–295. https://doi.org/10.1006/jsvi.2000.3159
Xiong YP, Xing JT, Price WG, 2003. A general linear mathematical model of power flow analysis and control for integrated structure-control systems. Journal of Sound and Vibration, 267(2):301–334. https://doi.org/10.1016/S0022-460X(03)00194-9
Yang J, Xiong YP, Xing JT, 2013. Dynamics and power flow behaviour of a nonlinear vibration isolation system with a negative stiffness mechanism. Journal of Sound and Vibration, 332(1):167–183. https://doi.org/10.1016/j.jsv.2012.08.010
Yang J, Xiong YP, Xing JT, 2014. Nonlinear power flow analysis of the Duffing oscillator. Mechanical Systems and Signal Processing, 45(2):563–578. https://doi.org/10.1016/j.ymssp.2013.11.004
Yang J, Xiong YP, Xing JT, 2015. Power flow behaviour and dynamic performance of a nonlinear vibration absorber coupled to a nonlinear oscillator. Nonlinear Dynamics, 80(3):1063–1079. https://doi.org/10.1007/s11071-014-1556-1
Yang J, Xiong YP, Xing JT, 2016. Vibration power flow and force transmission behaviour of a nonlinear isolator mounted on a nonlinear base. International Journal of Mechanical Sciences, 115–116:238–252. https://doi.org/10.1016/j.ijmecsci.2016.06.023
Zhang SY, Jiang JZ, Neild S, 2017. Optimal configurations for a linear vibration suppression device in a multi-storey building. Structural Control and Health Monitoring, 24(3):e1887. https://doi.org/10.1002/stc.1887
Zhu CD, Yang J, 2019. Free and forced vibration analysis of composite laminated plates. Proceedings of the 26th International Congress on Sound and Vibration.
Zhu CD, Yang J, 2022. Vibration transmission and energy flow analysis of variable stiffness laminated composite plates. Thin-Walled Structures, 180:109927. https://doi.org/10.1016/j.tws.2022.109927
Zhu CD, Yang J, Rudd C, 2021a. Vibration transmission and energy flow analysis of L-shaped laminated composite structure based on a substructure method. Thin-Walled Structures, 169:108375. https://doi.org/10.1016/j.tws.2021.108375
Zhu CD, Yang J, Rudd C, 2021b. Vibration transmission and power flow of laminated composite plates with inerter-based suppression configurations. International Journal of Mechanical Sciences, 190:106012. https://doi.org/10.1016/j.ijmecsci.2020.106012
Zuo H, Yang ZB, Chen XF, et al., 2015. Analysis of laminated composite plates using wavelet finite element method and higher-order plate theory. Composite Structures, 131: 248–258. https://doi.org/10.1016/j.compstruct.2015.04.064
Acknowledgments
This work is supported by the National Natural Science Foundation of China (Nos. 12172185, U1809218, and U1864211), the Zhejiang Provincial Natural Science Foundation of China (Nos. LY22A020006, LD22E050011, and LQ23A020003), the Ningbo Municipal Natural Science Foundation of China (No. 2022J174), and the Ningbo Key Projects of Science and Technology Innovation 2025 Plan (No. 2021Z124).
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Jian YANG designed the research. Chen ZHOU processed the corresponding data. Chen ZHOU wrote the first draft of the manuscript. Jian YANG and Chendi ZHU helped to organize the manuscript. Jian YANG and Yingdan ZHU revised and edited the final version.
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Chen ZHOU, Jian YANG, Yingdan ZHU, and Chendi ZHU declare that they have no conflict of interest.
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Zhou, C., Yang, J., Zhu, Y. et al. Vibration suppression of composite panel with variable angle tow design and inerter-based nonlinear energy sink. J. Zhejiang Univ. Sci. A 24, 653–672 (2023). https://doi.org/10.1631/jzus.A2200578
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DOI: https://doi.org/10.1631/jzus.A2200578