Shock vibration characteristics of fluid-structure interaction phononic crystal pipeline

Hu Bing; Yu Dian-long; Liu Jiang-wei; Zhu Fu-lei; Zhang Zhen-fang

doi:10.7498/aps.69.20200414

Abstract

Fluid-structure interaction pipeline systems are extensively adopted to transfer matter, energy and momentum, which are widely used in various fields. Due to the fluid-structure interaction effect, the pipe wall proves to produce strong vibration and noise under fluid action, which has a serious influence on the safety and concealment of the equipment, even leading to serious damages. Therefore, it is of great significance to study the vibration characteristics of fluid-structure interaction pipeline and methods to reduce the vibration of pipeline both in theory and in practice. Phononic crystal can suppress the propagation of elastic waves in a specific frequency range by their special band-gap characteristics, which have wide application prospects in the field of vibration and noise reduction. Especially, the band gap characteristics of phononic crystal pipeline used to design fluid-structure interaction pipeline system have been widely studied, thus providing a new technical approach to reducing the vibration and noise of the pipeline. In this paper, based on the theory of phononic crystal, the vibration transfer characteristics of the Bragg phononic crystal pipeline under fluid-structure interaction are studied. Combining the transfer matrix method and the finite element method, the band structure and band gap characteristics are calculated. Using the finite element method, the vibration characteristics of the phononic crystal pipeline under fluid-structure interaction effect, the shock excitation of pipe wall and the shock excitation of the fluid are considered. The influence of the fluid-structure interaction on the vibration transmission characteristics of the phononic crystal pipeline is also analyzed. The research results indicate that when the fluid velocity in the fluid-structure interaction pipeline system is small the Bragg phononic crystal pipeline has a good attenuation effect on the shock excitation of pipe wall in the band gap range, and that when the fluid velocity increases the fluid-structure interaction effect becomes significant, the attenuation effect becoming weaker. Bragg phononic crystal pipeline has a certain attenuation effect on the pipe wall vibration caused by the fluid shock excitation near the band gap. The research results are expected to be able to provide a technical reference for the vibration control of pipeline systems under fluid-structure interaction conditions.

Keywords:

Authors and contacts

1.
Laboratory of Science and Technology on Integrated Logistics Support, National University of Defense Technology, Changsha 410073, China
2.
College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, China

Corresponding author: Yu Dian-long, dianlongyu@vip.sina.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11872371) and the Major Program of the National Natural Science Foundation of China (Grant Nos. 11991032, 11991034)

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References

[1]	邵沛泽 2015 硕士学位论文 (北京: 北京工业大学) Shao P Z 2015 M. S. Thesis (Beijing: Beijing Institute of Technology) (in Chinese)
[2]	张阿漫, 戴绍仕 2011 流固耦合动力学 (北京: 国防工业出版社) 第3页 Zhang A M, Dai S S 2011 Dynamics of Solid-fluid Interaction (Beijing: National Defense Industry Press) p3 (in Chinese)
[3]	马璐 2015 硕士学位论文 (兰州: 兰州理工大学) Ma L 2015 M.S. Thesis (Lanzhou: Lanzhou University of Technology) (in Chinese)
[4]	宋学官, 蔡林, 张华 2012 ANSYS流固耦合分析与工程实例 (北京: 中国水利水电出版社)第1页 Song X G, Cai L, Zhang H 2012 ANSYS Fluid-structure Coupling Analysis and Engineering Example (Beijing: China Water & Power Press) p1 (in Chinese)
[5]	王海彦, 刘永刚 2015 ANSYS Fluent 流体数值计算方法与实例 (北京: 中国铁道出版社) 第2页 Wang H Y, Liu Y G 2015 ANSYS Numerical Calculation Method and Example of ANSYS Fluent Fluid (Beijing: China Railway Press) p2 (in Chinese)
[6]	Chimakurthi S K, Reuss S, Tooley M, Scampoli S 2018 Eng. Comput.-Germany 34 385 Google Scholar
[7]	Díaz-de-Anda A, Pimentel A, Flores J, Morales A, Gutiérrez L, Méndez-Sánchez R A 2005 J. Acoust. Soc. Am. 117 2814 Google Scholar
[8]	Yang X D, Cui Q D, Qian Y J, Zhang W, Lim C W 2018 J. Appl. Mech. T ASME 85 0610121 Google Scholar
[9]	Peiró-Torres M P, Castiñeira-Ibáñez S, Redondo J, Sánchez-Pérez J V 2019 Appl. Phys. Lett. 114 171901 Google Scholar
[10]	Iqbal M, Jaya M M, Bursi O S, Kumar A, Ceravolo R 2020 Sci. Rep. 10 85 Google Scholar
[11]	Sharma B, Sun C T 2016 J. Sandw. Struct. Mater. 18 50 Google Scholar
[12]	Chen J S, Sharma B, Sun C T 2011 Compos. Struct. 93 2120 Google Scholar
[13]	Chen J S, Sun C T 2011 J. Sandw. Struct. Mater. 13 391 Google Scholar
[14]	Chen J S, Huang Y J 2016 J. Vib. Acoust. 138 0410091 Google Scholar
[15]	Pai P F, Peng H, Jiang S 2014 Int. J. Mech. Sci. 79 195 Google Scholar
[16]	Chen Y Y, Barnhart M V, Chen J K, Hu G K, Sun C T, Huang G L 2016 Compos. Struct. 136 358 Google Scholar
[17]	Alamri S, Li B, Tan K T 2018 J. Appl. Phys. 123 95111 Google Scholar
[18]	Li B, Liu Y, Tan K 2019 J. Sandw. Struct. Mater. 21 1880 Google Scholar
[19]	Li Q Q, He Z C, Li E, Cheng A G 2018 Smart. Mater. Struct. 27 95015 Google Scholar
[20]	Li Q Q, He Z C, Li E, Cheng A G 2019 J. Appl. Phys. 125 35104 Google Scholar
[21]	Yu D L, Wang G, Liu Y Z, Wen J H, Qiu J 2006 Chin. Phys. 15 266 Google Scholar
[22]	沈惠杰, 温激鸿, 郁殿龙, 温熙森 2009 物理学报 58 8357 Google Scholar Shen H J, Wen J H, Yu D L, Wen X S 2009 Acta Phys. Sin. 58 8357 Google Scholar
[23]	Shen H, Wen J, Yu D, Wen X 2009 J. Sound Vib. 328 57 Google Scholar
[24]	Koo G K, Park Y S 1998 J. Sound Vib. 210 53 Google Scholar
[25]	Sorokina S V, Ershova O A 2004 J. Sound Vib. 278 501 Google Scholar
[26]	Sorokina S V, Ershova O A 2006 J. Sound Vib. 291 81 Google Scholar
[27]	Sorokin S, Holst-Jensen O 2012 J. Vib. Acoust 134 41001 Google Scholar
[28]	Yu D L, Wen J H, Zhao H G, Liu Y Z, Wen X S 2008 J. Sound Vib. 318 193 Google Scholar
[29]	Yu D L, Wen J H, Zhao H G, Liu Y Z, Wen X S 2011 J. Vib. Acoust 133 14501 Google Scholar
[30]	Yu D L, Wen J H, Shen H J, Wen X S 2012 Phys. Lett. A 376 3417 Google Scholar
[31]	Yu D L, Du C Y, Shen H J, Liu J W, Wen J H 2017 Chin. Phys. Lett. 34 190 Google Scholar
[32]	Yu D L, Shen H J, Liu J W, Yin J F, Zhang Z F, Wen J H 2018 Chin. Phys. B 27 285 Google Scholar
[33]	Yu D L, Paidoussis M P, Shen H J, Wang L 2014 J. Appl. Mech.-T ASME 81 11001 Google Scholar
[34]	Wen J H, Shen H J, Yu D L, Wen X S 2010 Chin. Phys. Lett. 27 133 Google Scholar
[35]	Wei Z D, Li B R, Du J M, Yang G 2016 Chin. Phys. Lett. 33 68 Google Scholar
[36]	刘东彦, 李发, 张建兴, 李宝仁 2016 机床与液压 44 74 Google Scholar Liu D Y, Li F, Zhang J X, Li B R 2016 Mach. Tool & Hydr. 44 74 Google Scholar
[37]	Shen H J, Wen J H, Yu D L, Asgari M, Wen X S 2013 J. Sound Vib. 332 4193 Google Scholar
[38]	Shen H J, Wen J H, Yu D L, Yuan B, Wen X S 2014 J. Fluid. Struct. 46 134 Google Scholar
[39]	Shen H J, Wen J H, Païdoussis M P, Yu D L, Asgari M, Wen X S 2012 Phys. Lett. A 376 3351 Google Scholar
[40]	Shen H J, Païdoussis M P, Wen J H, Yu D L, Wen X S 2014 J. Sound Vib. 333 2735 Google Scholar
[41]	Shen H J, Wen J H, Yu D L, Wen X S 2014 J. Vib. Control 21 3034 Google Scholar
[42]	Liang F, Yang X D 2020 Appl. Math. Model. 77 522 Google Scholar
[43]	尹志勇, 钟荣, 刘忠族 2006 舰船科学技术 28 23 Yin Z Y, Zhong R, Liu Z Z 2006 Ship Sci. Tech. 28 23
[44]	Khudayarov B A, Komilova K M, Turaev F Z 2019 Int. J. Appl. Mech. 11 1950090 Google Scholar
[45]	Khudayarov B A, Komilova K M, Turaev F Z, Aliyarov J A 2020 Int. J. Pres. Ves. Pip. 179 104034 Google Scholar
[46]	林磊 2005 硕士学位论文 (西安: 西北工业大学) Lin L 2005 M. S. Thesis (Xi'an: Northwestern Polytechnical University) (in Chinese)
[47]	Khudayarov B A, Komilova K M, Turaev F Z 2020 J. Nat. Gas. Sci. Eng. 75 103148 Google Scholar
[48]	张亚峰 2014 硕士学位论文 (长沙: 国防科技大学) Zhang Y F 2014 M. S. Thesis (Changsha: National University of Defense Technology) (in Chinese)
[49]	温熙森, 温激鸿, 郁殿龙, 王刚, 刘耀宗, 韩小云 2018 声子晶体 (北京: 国防工业出版社) 第207页 Wen X S, Wen J H, Yu D L, Wang G, Liu Y Z, Han X Y, 2009 Phononic Crystals (Beijing: National Defence Industry Press) p207 (in Chinese)
[50]	Liu J W, Yu D L, Zhang Z F, Shen H J, Wen J H 2019 Acta. Mech. Solida Sin. 32 173 Google Scholar
[51]	Budenkov G A and Nedzvetskaya O V 2004 Russ. J. Nondestruct T-Engl. Tr. 40 99 Google Scholar
[52]	胡兵, 郁殿龙 2019 第十三届全国振动理论及应用学术会议中国西安, 11月9−12 第7页 Hu B, Yu D L 2019 The 13th National Conference on Vibration Theory and Application Xi'an, China, November 9−12 p7 (in Chinese)
[53]	Ferràs D, Manso P A, Schleiss A J, Covas D I C 2016 Compos. Struct. 175 74 Google Scholar

Cited By

图 1 布拉格声子晶体管路结构示意图　(a)无限周期单元; (b)基本周期单元

Figure 1. Schematic diagram of Bragg phononic crystal pipeline structure: (a) Infinite periodic cell; (b) Basic periodic cell.

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图 2 未充液布拉格声子晶体管路的带隙特性　(a)能带结构; (b)振动频率响应曲线

Figure 2. Band gap characteristics of the liquid-unfilled Bragg phononic crystal pipeline: (a) Band structure; (b) Flexural vibration FRF.

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图 3 充液布拉格声子晶体管路的带隙特性　(a)能带结构; (b)振动频率响应曲线

Figure 3. Band gap characteristics of the liquid-filled Bragg phononic crystal pipeline: (a) Band structure; (b) Flexural vibration FRF.

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图 4 未充液和充液布拉格声子晶体管路弯曲振动频率响应　(a)未充液管路; (b) 充液管路

Figure 4. Frequency response of flexural vibration of liquid-unfilled and liquid-filled Bragg phononic crystal pipeline: (a) liquid-unfilled pipe; (b) liquid-filled pipe.

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图 5 未充液和充液声子晶体管路不同频率处的速度幅值　(a)未充液管路; (b) 充液管路

Figure 5. Displacement amplitude of liquid-unfilled and liquid-filled phononic crystal pipeline at different frequencies: (a) liquid-unfilled pipe; (b) liquid-filled pipe.

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图 6 ANSYS Workbench系统耦合配置方式

Figure 6. Coupling configuration of ANSYS Workbench system.

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图 7 ANSYS中建立流固耦合管路模型

Figure 7. Establishment of fluid-structure interaction pipeline model in ANSYS.

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图 8 管壁冲击脉冲响应及通过快速傅里叶变换得到的冲击模拟频域　(a) 管壁冲击时域; (b) 管壁冲击频域

Figure 8. Pipe wall shock impulse response and shock simulation frequency domain obtained by fast Fourier transform: (a) Time domain of wall impact; (b) Frequency domain of wall impact.

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图 9 未充液与充液声子晶体管路冲击振动响应　(a)未充液管路; (b) 充液管路

Figure 9. Shock vibration response of liquid-unfilled and liquid-filled phononic crystal pipeline: (a) liquid-unfilled pipe; (b) liquid-filled pipe.

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图 10 未充液和充液声子晶体管路不同时刻的速度幅值　(a)未充液管路; (b) 充液管路

Figure 10. Velocity amplitude of liquid-unfilled and liquid-filled phononic crystal pipeline at different moments: (a) liquid-unfilled pipe; (b) liquid-filled pipe.

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图 11 流固耦合声子晶体管路在不同流速下的冲击振动响应　(a)流速为0 m/s; (b) 流速为10 m/s

Figure 11. Shock vibration response of fluid-structure interaction phononic crystal pipeline at different velocities of fluid: (a) Flow velocity is 0 m/s; (b) Flow velocity is 10 m/s.

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图 12 流固耦合声子晶体管路出口处不同流速冲击振动响应

Figure 12. Shock vibration response of the outlet of fluid-structure interaction phononic crystal pipeline at different velocities of fluid.

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图 13 冲击流体激励下　(a)结构钢管和(b)声子晶体管弯曲振动响应

Figure 13. Flexural vibration response of (a) structural steel pipe and (b) phononic crystal pipe under shock fluid excitation.

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图 14 冲击流体激励下结构钢管与声子晶体管　(a) 进水口和 (b) 出水口处振动响应

Figure 14. Vibration response at (a) inlet and (b) outlet of structural steel pipe and phononic crystal pipe under shock fluid excitation.

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表 1 管路材料参数

Table 1. Pipeline material parameters.

材料名称杨氏模量/GPa 密度/kg·m^–3 泊松比

结构钢 200 7850 0.3
环氧树脂 4.35 1180 0.3672

DownLoad: CSV

[1]	邵沛泽 2015 硕士学位论文 (北京: 北京工业大学) Shao P Z 2015 M. S. Thesis (Beijing: Beijing Institute of Technology) (in Chinese)
[2]	张阿漫, 戴绍仕 2011 流固耦合动力学 (北京: 国防工业出版社) 第3页 Zhang A M, Dai S S 2011 Dynamics of Solid-fluid Interaction (Beijing: National Defense Industry Press) p3 (in Chinese)
[3]	马璐 2015 硕士学位论文 (兰州: 兰州理工大学) Ma L 2015 M.S. Thesis (Lanzhou: Lanzhou University of Technology) (in Chinese)
[4]	宋学官, 蔡林, 张华 2012 ANSYS流固耦合分析与工程实例 (北京: 中国水利水电出版社)第1页 Song X G, Cai L, Zhang H 2012 ANSYS Fluid-structure Coupling Analysis and Engineering Example (Beijing: China Water & Power Press) p1 (in Chinese)
[5]	王海彦, 刘永刚 2015 ANSYS Fluent 流体数值计算方法与实例 (北京: 中国铁道出版社) 第2页 Wang H Y, Liu Y G 2015 ANSYS Numerical Calculation Method and Example of ANSYS Fluent Fluid (Beijing: China Railway Press) p2 (in Chinese)
[6]	Chimakurthi S K, Reuss S, Tooley M, Scampoli S 2018 Eng. Comput.-Germany 34 385 Google Scholar
[7]	Díaz-de-Anda A, Pimentel A, Flores J, Morales A, Gutiérrez L, Méndez-Sánchez R A 2005 J. Acoust. Soc. Am. 117 2814 Google Scholar
[8]	Yang X D, Cui Q D, Qian Y J, Zhang W, Lim C W 2018 J. Appl. Mech. T ASME 85 0610121 Google Scholar
[9]	Peiró-Torres M P, Castiñeira-Ibáñez S, Redondo J, Sánchez-Pérez J V 2019 Appl. Phys. Lett. 114 171901 Google Scholar
[10]	Iqbal M, Jaya M M, Bursi O S, Kumar A, Ceravolo R 2020 Sci. Rep. 10 85 Google Scholar
[11]	Sharma B, Sun C T 2016 J. Sandw. Struct. Mater. 18 50 Google Scholar
[12]	Chen J S, Sharma B, Sun C T 2011 Compos. Struct. 93 2120 Google Scholar
[13]	Chen J S, Sun C T 2011 J. Sandw. Struct. Mater. 13 391 Google Scholar
[14]	Chen J S, Huang Y J 2016 J. Vib. Acoust. 138 0410091 Google Scholar
[15]	Pai P F, Peng H, Jiang S 2014 Int. J. Mech. Sci. 79 195 Google Scholar
[16]	Chen Y Y, Barnhart M V, Chen J K, Hu G K, Sun C T, Huang G L 2016 Compos. Struct. 136 358 Google Scholar
[17]	Alamri S, Li B, Tan K T 2018 J. Appl. Phys. 123 95111 Google Scholar
[18]	Li B, Liu Y, Tan K 2019 J. Sandw. Struct. Mater. 21 1880 Google Scholar
[19]	Li Q Q, He Z C, Li E, Cheng A G 2018 Smart. Mater. Struct. 27 95015 Google Scholar
[20]	Li Q Q, He Z C, Li E, Cheng A G 2019 J. Appl. Phys. 125 35104 Google Scholar
[21]	Yu D L, Wang G, Liu Y Z, Wen J H, Qiu J 2006 Chin. Phys. 15 266 Google Scholar
[22]	沈惠杰, 温激鸿, 郁殿龙, 温熙森 2009 物理学报 58 8357 Google Scholar Shen H J, Wen J H, Yu D L, Wen X S 2009 Acta Phys. Sin. 58 8357 Google Scholar
[23]	Shen H, Wen J, Yu D, Wen X 2009 J. Sound Vib. 328 57 Google Scholar
[24]	Koo G K, Park Y S 1998 J. Sound Vib. 210 53 Google Scholar
[25]	Sorokina S V, Ershova O A 2004 J. Sound Vib. 278 501 Google Scholar
[26]	Sorokina S V, Ershova O A 2006 J. Sound Vib. 291 81 Google Scholar
[27]	Sorokin S, Holst-Jensen O 2012 J. Vib. Acoust 134 41001 Google Scholar
[28]	Yu D L, Wen J H, Zhao H G, Liu Y Z, Wen X S 2008 J. Sound Vib. 318 193 Google Scholar
[29]	Yu D L, Wen J H, Zhao H G, Liu Y Z, Wen X S 2011 J. Vib. Acoust 133 14501 Google Scholar
[30]	Yu D L, Wen J H, Shen H J, Wen X S 2012 Phys. Lett. A 376 3417 Google Scholar
[31]	Yu D L, Du C Y, Shen H J, Liu J W, Wen J H 2017 Chin. Phys. Lett. 34 190 Google Scholar
[32]	Yu D L, Shen H J, Liu J W, Yin J F, Zhang Z F, Wen J H 2018 Chin. Phys. B 27 285 Google Scholar
[33]	Yu D L, Paidoussis M P, Shen H J, Wang L 2014 J. Appl. Mech.-T ASME 81 11001 Google Scholar
[34]	Wen J H, Shen H J, Yu D L, Wen X S 2010 Chin. Phys. Lett. 27 133 Google Scholar
[35]	Wei Z D, Li B R, Du J M, Yang G 2016 Chin. Phys. Lett. 33 68 Google Scholar
[36]	刘东彦, 李发, 张建兴, 李宝仁 2016 机床与液压 44 74 Google Scholar Liu D Y, Li F, Zhang J X, Li B R 2016 Mach. Tool & Hydr. 44 74 Google Scholar
[37]	Shen H J, Wen J H, Yu D L, Asgari M, Wen X S 2013 J. Sound Vib. 332 4193 Google Scholar
[38]	Shen H J, Wen J H, Yu D L, Yuan B, Wen X S 2014 J. Fluid. Struct. 46 134 Google Scholar
[39]	Shen H J, Wen J H, Païdoussis M P, Yu D L, Asgari M, Wen X S 2012 Phys. Lett. A 376 3351 Google Scholar
[40]	Shen H J, Païdoussis M P, Wen J H, Yu D L, Wen X S 2014 J. Sound Vib. 333 2735 Google Scholar
[41]	Shen H J, Wen J H, Yu D L, Wen X S 2014 J. Vib. Control 21 3034 Google Scholar
[42]	Liang F, Yang X D 2020 Appl. Math. Model. 77 522 Google Scholar
[43]	尹志勇, 钟荣, 刘忠族 2006 舰船科学技术 28 23 Yin Z Y, Zhong R, Liu Z Z 2006 Ship Sci. Tech. 28 23
[44]	Khudayarov B A, Komilova K M, Turaev F Z 2019 Int. J. Appl. Mech. 11 1950090 Google Scholar
[45]	Khudayarov B A, Komilova K M, Turaev F Z, Aliyarov J A 2020 Int. J. Pres. Ves. Pip. 179 104034 Google Scholar
[46]	林磊 2005 硕士学位论文 (西安: 西北工业大学) Lin L 2005 M. S. Thesis (Xi'an: Northwestern Polytechnical University) (in Chinese)
[47]	Khudayarov B A, Komilova K M, Turaev F Z 2020 J. Nat. Gas. Sci. Eng. 75 103148 Google Scholar
[48]	张亚峰 2014 硕士学位论文 (长沙: 国防科技大学) Zhang Y F 2014 M. S. Thesis (Changsha: National University of Defense Technology) (in Chinese)
[49]	温熙森, 温激鸿, 郁殿龙, 王刚, 刘耀宗, 韩小云 2018 声子晶体 (北京: 国防工业出版社) 第207页 Wen X S, Wen J H, Yu D L, Wang G, Liu Y Z, Han X Y, 2009 Phononic Crystals (Beijing: National Defence Industry Press) p207 (in Chinese)
[50]	Liu J W, Yu D L, Zhang Z F, Shen H J, Wen J H 2019 Acta. Mech. Solida Sin. 32 173 Google Scholar
[51]	Budenkov G A and Nedzvetskaya O V 2004 Russ. J. Nondestruct T-Engl. Tr. 40 99 Google Scholar
[52]	胡兵, 郁殿龙 2019 第十三届全国振动理论及应用学术会议中国西安, 11月9−12 第7页 Hu B, Yu D L 2019 The 13th National Conference on Vibration Theory and Application Xi'an, China, November 9−12 p7 (in Chinese)
[53]	Ferràs D, Manso P A, Schleiss A J, Covas D I C 2016 Compos. Struct. 175 74 Google Scholar

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[16]	Wang Gang, Wen Ji-Hong, Liu Yao-Zong, Yu Dian-Long, Wen Xi-Sen. Lumped-mass approach for the calculation of band structure of two-dimensional phononic crystals with high contrast of elastic constant. Acta Physica Sinica, 2005, 54(3): 1247-1252. doi: 10.7498/aps.54.1247
[17]	Zhao Fang, Yuan Li-Bo. Characteristics of the band structure in two-dimensional phononic crystals with complex lattices. Acta Physica Sinica, 2005, 54(10): 4511-4516. doi: 10.7498/aps.54.4511
[18]	Wen Ji-Hong, Wang Gang, Liu Yao-Zong, Yu Dian-Long. Lumped-mass method on calculation of elastic band gaps of one-dimensional phononic crystals. Acta Physica Sinica, 2004, 53(10): 3384-3388. doi: 10.7498/aps.53.3384
[19]	Qi Gong-Jin, Yang Sheng-Liang, Bai Shu-Xin, Zhao Xun. A study of the band structure in two-dimensional phononic crystals based on plane-wave algorithm. Acta Physica Sinica, 2003, 52(3): 668-671. doi: 10.7498/aps.52.668
[20]	Wang Gang, Wen Ji-Hong, Han Xiao-Yun, Zhao Hong-Gang. Finite difference time domain method for the study of band gap in two-dimensiona l phononic crystals. Acta Physica Sinica, 2003, 52(8): 1943-1947. doi: 10.7498/aps.52.1943

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Vol. 69, Issue 19 - 2020-10-05

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