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Dimensionless dispersion curve equation of one-dimensional periodic structure with three oscillators is deduced. It is proved by singularity theory that the topology of the dispersion curves does not change with mass and stiffness parameter. Then the equations of initial and final frequencies of the bands are presented. The method of band gap design is gained consequently. Two examples i.e., the system with the same stiffness and the system with the same mass, are given to verify it. The method may provide the reference for designing the band gap of the photonic and phononic crystals.
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Keywords:
- periodic structure /
- band gap design /
- singularity theory
[1] Chen B, Huang X C 2011 Noise and Vibration Control 31 37 (in Chinese) [陈斌,黄修长 2011 噪声与振动控制 31 37]
[2] Wen X S 2006 Theory and Technology of Photonic and Phononic Crystals (Beijing: Science Press) p4 (in Chinese) [温熙森 2006 光子/声子晶体理论与技术(北京:科学出版社)第4页]
[3] Wen J H 2005 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese) [温激鸿 2005 博士学位论文 (长沙：国防科技大学)]
[4] Asiri S, Baz A, Pines D 2006 Smart Mater. Struct. 15 1707
[5] Richards D, Pines D J 2003 J. Sound Vib. 264 317
[6] Huang X C, Feng G P, Zhang Z Y, Hua H X 2010 Noise and Vibration Control 30 9 (in Chinese) [黄修长,冯国平,张志谊,华宏星 2010 噪声与振动控制 30 9]
[7] Cheng S X 2012 M. S. Dissertation (Shanghai: Shanghai Jiao Tong University) (in Chinese) [程世祥 2012 硕士学位论文(上海:上海交通大学)]
[8] Shen H J, Wen J H, Yu D L, Wen X S 2009 Acta Phys. Sin. 58 8357 (in Chinese) [沈惠杰, 温激鸿, 郁殿龙, 温熙森 2009 58 8357]
[9] Cao Y J, Yun G H, Na R S 2011 Acta Phys. Sin. 60 077502 (in Chinese) [曹永军,云国宏, 那日苏 2011 60 077502]
[10] Kafesaki M, Sigalas M M, Garcia N 2000 Phys. Rev. Lett. 85 4044
[11] Psarobas I E, Stefanou N, Modinos A 2000 Phys. Rev. B 62 278
[12] Wang G, Wen J H, Liu Y Z 2004 Phys. Rev. B 69 184302
[13] Wen J H, Wang G, Liu Y Z, Yu D L 2004 Acta Phys. Sin. 53 3384 (in Chinese) [温激鸿,王刚,刘耀宗,郁殿龙 2004 53 3384]
[14] Baz A 2001 J. Vib. Acoust. 123 472
[15] Singh A, Pines D J, Baz A 2004 Smart Mater. Struct. 13 698
[16] Wang G, Chen S B, Wen J H 2010 Smart Mater. Struct. 20 015026
[17] Thorp O, Ruzzene M, Baz A 2001 Smart Mater. Struct. 10 979
[18] Ruzzene M, Baz A 2000 Smart Mater. Struct. 9 805
[19] Yeh J Y, Chen L W 2006 Compos. Struct. 73 53
[20] Su X L, Gao Y W 2010 J. Functional Mater. 41 368 (in Chinese) [宿星亮, 高原文 2010 功能材料 41 368]
[21] Wu M L, Wu L Y, Yang W P 2009 Smart Mater. Struct. 18 115013
[22] Huang K 1988 Solid State Physics (Beijing: Higher Education Press) p154 (in Chinese) [黄昆 1988 固体物理学(北京:高等教育出版社)第154页]
[23] Golubitsky M, Schaeffer D G 1985 Singularities and Groups in Bifurcation Theory (Vol.1) p140 (New York: Springer-Verlag)
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[1] Chen B, Huang X C 2011 Noise and Vibration Control 31 37 (in Chinese) [陈斌,黄修长 2011 噪声与振动控制 31 37]
[2] Wen X S 2006 Theory and Technology of Photonic and Phononic Crystals (Beijing: Science Press) p4 (in Chinese) [温熙森 2006 光子/声子晶体理论与技术(北京:科学出版社)第4页]
[3] Wen J H 2005 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese) [温激鸿 2005 博士学位论文 (长沙：国防科技大学)]
[4] Asiri S, Baz A, Pines D 2006 Smart Mater. Struct. 15 1707
[5] Richards D, Pines D J 2003 J. Sound Vib. 264 317
[6] Huang X C, Feng G P, Zhang Z Y, Hua H X 2010 Noise and Vibration Control 30 9 (in Chinese) [黄修长,冯国平,张志谊,华宏星 2010 噪声与振动控制 30 9]
[7] Cheng S X 2012 M. S. Dissertation (Shanghai: Shanghai Jiao Tong University) (in Chinese) [程世祥 2012 硕士学位论文(上海:上海交通大学)]
[8] Shen H J, Wen J H, Yu D L, Wen X S 2009 Acta Phys. Sin. 58 8357 (in Chinese) [沈惠杰, 温激鸿, 郁殿龙, 温熙森 2009 58 8357]
[9] Cao Y J, Yun G H, Na R S 2011 Acta Phys. Sin. 60 077502 (in Chinese) [曹永军,云国宏, 那日苏 2011 60 077502]
[10] Kafesaki M, Sigalas M M, Garcia N 2000 Phys. Rev. Lett. 85 4044
[11] Psarobas I E, Stefanou N, Modinos A 2000 Phys. Rev. B 62 278
[12] Wang G, Wen J H, Liu Y Z 2004 Phys. Rev. B 69 184302
[13] Wen J H, Wang G, Liu Y Z, Yu D L 2004 Acta Phys. Sin. 53 3384 (in Chinese) [温激鸿,王刚,刘耀宗,郁殿龙 2004 53 3384]
[14] Baz A 2001 J. Vib. Acoust. 123 472
[15] Singh A, Pines D J, Baz A 2004 Smart Mater. Struct. 13 698
[16] Wang G, Chen S B, Wen J H 2010 Smart Mater. Struct. 20 015026
[17] Thorp O, Ruzzene M, Baz A 2001 Smart Mater. Struct. 10 979
[18] Ruzzene M, Baz A 2000 Smart Mater. Struct. 9 805
[19] Yeh J Y, Chen L W 2006 Compos. Struct. 73 53
[20] Su X L, Gao Y W 2010 J. Functional Mater. 41 368 (in Chinese) [宿星亮, 高原文 2010 功能材料 41 368]
[21] Wu M L, Wu L Y, Yang W P 2009 Smart Mater. Struct. 18 115013
[22] Huang K 1988 Solid State Physics (Beijing: Higher Education Press) p154 (in Chinese) [黄昆 1988 固体物理学(北京:高等教育出版社)第154页]
[23] Golubitsky M, Schaeffer D G 1985 Singularities and Groups in Bifurcation Theory (Vol.1) p140 (New York: Springer-Verlag)
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