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运用波传播法对有限和无限周期对边简支复合板的振动带隙衰减特性进行了研究.在建立相邻板结构边界连续方程的基础上, 分别运用传递矩阵和Bloch定理建立了有限和无限周期复合板的耦合运动方程, 并详细对比分析了有限和无限周期复合板带隙衰减特性的关联关系.研究表明: 周期板结构的振动带隙频率范围与激励方式和激励位置是相关的, 若周期复合板在宽度方向按某阶模态进行线激励, 则该激励下的振动带隙与无限周期复合板在该阶模态下的振动带隙是一致的; 若周期板在点激励作用, 则该点激励下的振动带隙是参与振动的各阶模态振动带隙的交集. 此外, 还进一步研究了结构阻尼对振动衰减带隙的影响.The band gap attenuation characteristics of finite and infinite periodic compound plate simply supported along its longitudinal edges are investigated with the wave propagation approach. Base on the boundary continuum condition between two plates, the coupled equations of finite and infinite periodic compound plate are established by transfer matrix and Bloch theorem respectively, and the relations of band gap attenuation characteristics between finite and infinite periodic compound plate are analyzed in detail. It is shown that the frequency band gap of periodic compound plate is related to exciting form and position. The frequency band gap of finite compound plate is coincident with the frequency band gap of infinite compound plate with the same mode vibration if finite compound plate is excited with one mode along its longitudinal edges. If the plate is excited with a point force, the frequency band gap is the intersection of frequency band gap of all participated modes. Besides, the influence of the structural damping on band gap is also analyzed.
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Keywords:
- periodic compound plate /
- band gap attenuation characteristics /
- wave propagation approach /
- structural damping
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[2] Wen J H, Shen H J, Yu D L, Wen X S 2010 Chin. Phys. Lett. 27 114301
[3] Yu D L, Wen J H, Zhao H G, Liu Y Z, Wen X S 2008 J. Sound Vib. 318 193
[4] Shen H J, Wen J H, Yu D L, Wen X S 2009 J. Sound Vib. 328 57
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[6] Xiao Y, Wen J H, Wen X S 2012 Phys. Lett. A 376 1384
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[9] Xiao W, Zeng G W, Cheng Y S 2008 Appl. Acous. 69 255
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[11] Yu D L, Wang G, Liu Y Z, Wen J H, Qiu J 2006 Chin. Phys. 15 266
[12] Yu D L, Liu Y Z, Qiu J, Zhao H G, Liu Z M 2005 Chin. Phys. Lett. 22 1958
[13] Ruzzene M, Tsopelas P, Asce A M 2003 J. Eng. Mech. 129 975
[14] Sorokin S V, Ershova O A 2004 J. Sound Vib. 278 501
[15] Sorokin S V, Ershova O A 2006 J. Sound Vib. 291 81
[16] Wen J H, Yu D L, Wang G, Zhao H G, Liu Y Z 2007 Acta Phys. Sin. 56 2298 (in Chinese) [温激鸿, 郁殿龙, 王刚, 赵宏刚, 刘耀宗 2007 物理学报 56 2298]
[17] Gao G Q, Ma S L, Jin F, Jin D F, Lu T J 2010 Acta Phys. Sin. 59 393 (in Chinese) [高国钦, 马守林, 金峰, 金东范, 卢天健 2010 物理学报 59 393]
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[1] Mead D J 1996 J. Sound Vib. 190 495
[2] Wen J H, Shen H J, Yu D L, Wen X S 2010 Chin. Phys. Lett. 27 114301
[3] Yu D L, Wen J H, Zhao H G, Liu Y Z, Wen X S 2008 J. Sound Vib. 318 193
[4] Shen H J, Wen J H, Yu D L, Wen X S 2009 J. Sound Vib. 328 57
[5] Yu D L, Wen J H, Shen H J, Xiao Y, Wen X S 2012 Phys. Lett. A 376 626
[6] Xiao Y, Wen J H, Wen X S 2012 Phys. Lett. A 376 1384
[7] Xiao Y, Mace B R, Wen J H, Wen X S 2010 The 17th International Congress on Sound & Vibration, Cairo, July 18-22, 2010
[8] Yu D L, Liu Y Z, Wang G 2006 Chin. J. Mech. Eng. 42 150 (in Chinese) [郁殿龙, 刘耀宗, 王刚 2006 机械工程学报 42 150]
[9] Xiao W, Zeng G W, Cheng Y S 2008 Appl. Acous. 69 255
[10] Sigalas M M, Economou E N 1994 J. Appl. Phys. 75 2845
[11] Yu D L, Wang G, Liu Y Z, Wen J H, Qiu J 2006 Chin. Phys. 15 266
[12] Yu D L, Liu Y Z, Qiu J, Zhao H G, Liu Z M 2005 Chin. Phys. Lett. 22 1958
[13] Ruzzene M, Tsopelas P, Asce A M 2003 J. Eng. Mech. 129 975
[14] Sorokin S V, Ershova O A 2004 J. Sound Vib. 278 501
[15] Sorokin S V, Ershova O A 2006 J. Sound Vib. 291 81
[16] Wen J H, Yu D L, Wang G, Zhao H G, Liu Y Z 2007 Acta Phys. Sin. 56 2298 (in Chinese) [温激鸿, 郁殿龙, 王刚, 赵宏刚, 刘耀宗 2007 物理学报 56 2298]
[17] Gao G Q, Ma S L, Jin F, Jin D F, Lu T J 2010 Acta Phys. Sin. 59 393 (in Chinese) [高国钦, 马守林, 金峰, 金东范, 卢天健 2010 物理学报 59 393]
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