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本文研究一维周期性层状结构中材料弹性模量时变因素作用下的声透射临界现象, 探究了这种声学脉冲序列及全透声现象的内在机理. 考虑弹性模量时变因素的影响, 通过求解波动方程, 运用分离变量法解得特征指数, 进而得到临界现象. 当调制幅值低于或等于临界值时, 周期性结构能够将入射波转化为一系列周期的毫秒级的反射脉冲序列; 尤其在调制幅值等于临界值时, 当周期性结构的层数达到16层时, 反射脉冲序列有完整的0和1 的波形; 当大于临界值时, 反射系数在50 ms内迅速衰减至0, 此时的结构相当于完全透声, 入射波可以无损地完全透过, 产生调制透声现象. 这些特殊的现象可为声波的动态控制、声脉冲序列的产生和声波的定向传播提供重要的理论依据, 在超声换能器及调制透声方面具有实际的工程应用前景.Critical phenomenon in a one-dimensional periodic stratified structure with time-varying elastic modulus functions is found out for acoustic waves. By using the classical separation of variables method to solve the one-dimensional wave equation, and taking the time-varying elastic modulus functions into consideration, a critical value can be found of the varying amplitude of the time-varying elastic modulus functions. Near the critical value, due to the alternation of the characteristic exponent, the reflectivity of the one-dimensional periodic stratified structure changes in essence. Below or at the critical value, the incident wave can be converted into a periodic and millisecond pulse train, particularly when the varying amplitude is at the critical value. In addition, the layer number can be up to 16. Under these circumstances, complete pulse train of 0 or 1 is generated with respect to time; in the end, when above the critical value, the reflectivity decreases rapidly to 0 within 50 milliseconds, indicating that, at one moment, the incident wave can be totally transferred through the structure as if the stratified structure becomes transparent, which means a modulational transparency. In conclusion, by altering the varying amplitude of the time-varying elastic modulus functions, three different phenomena are generated. These excellent properties could find potential applications of one-dimensional periodic stratified structure in the acoustic transducer and the control of the acoustic wave.
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Keywords:
- critical phenomenon /
- acoustic pulse train /
- full transmission
[1] Yang C H, Wen Y M, Li P, Bian L X 2008 Acta Phys. Sin. 57 7292 (in Chinese) [阳昌海, 文玉梅, 李平, 卞雷祥 2008 57 7292]
[2] Wang J X, Meng G 2006 Functional Mater. 37 706 (in Chinese) [汪建晓, 孟光 2006 功能材料 37 706]
[3] Yu M, Yan X R, Xiao Y Q 2008 Functional Mater. 8 1263 (in Chinese) [余淼, 严小锐, 夏永强 2008 功能材料 8 1263]
[4] Chen S B, Han X Y, Yu D L, Wen J H 2010 Acta Phys. Sin. 59 387 (in Chinese) [陈圣兵, 韩小云, 郁殿龙, 温激鸿 2010 59 387]
[5] Li F M, Wang Y S 2004 J. Vib. Engineer. 17 828 (in Chinese) [李凤明, 汪越胜 2004 振动工程学报 17 828]
[6] Liu J, Wang J, Zhao X M, Wang X 2009 J. Wuhan Univ. Technol. 31 105 (in Chinese) [刘杰, 王钧, 赵新民, 王祥 2009 武汉理工大学学报 31 105]
[7] Liang B, Yuan Y, Cheng J C 2015 Acta Phys. Sins. 64 094305 (in Chinese) [梁彬, 袁樱, 程建春 2015 64 094305]
[8] Zhang Z, Li R Q, Liang B, Zou X Y, Cheng J C 2015 Chin. Phys. B 24 024301
[9] Wu J H, Cheng T H, Liu A Q, Wang Y X 2006 Appl. Phys. Lett. 89 263103
[10] Wu J H, Shen L 2011 J. Opt. Soc. Am. B 28 1328
[11] Wang Z X, Guo D R 1989 Special Functions (Beijing: Peking University Press) pp633-638 (in Chinese) [王竹溪, 郭敦仁 1989 特殊函数概论(北京:北京大学出版社)第633-638页]
[12] Yariv A, Yeh P 1977 J. Opt. Soc. Am. 67 423
[13] Zhang H L 2007 Theoretical Acoustics (Beijing:Higher Education Press) p225 (in Chinese) [张海澜 2007 理论声学 (北京: 高等教育出版社)第225页]
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[1] Yang C H, Wen Y M, Li P, Bian L X 2008 Acta Phys. Sin. 57 7292 (in Chinese) [阳昌海, 文玉梅, 李平, 卞雷祥 2008 57 7292]
[2] Wang J X, Meng G 2006 Functional Mater. 37 706 (in Chinese) [汪建晓, 孟光 2006 功能材料 37 706]
[3] Yu M, Yan X R, Xiao Y Q 2008 Functional Mater. 8 1263 (in Chinese) [余淼, 严小锐, 夏永强 2008 功能材料 8 1263]
[4] Chen S B, Han X Y, Yu D L, Wen J H 2010 Acta Phys. Sin. 59 387 (in Chinese) [陈圣兵, 韩小云, 郁殿龙, 温激鸿 2010 59 387]
[5] Li F M, Wang Y S 2004 J. Vib. Engineer. 17 828 (in Chinese) [李凤明, 汪越胜 2004 振动工程学报 17 828]
[6] Liu J, Wang J, Zhao X M, Wang X 2009 J. Wuhan Univ. Technol. 31 105 (in Chinese) [刘杰, 王钧, 赵新民, 王祥 2009 武汉理工大学学报 31 105]
[7] Liang B, Yuan Y, Cheng J C 2015 Acta Phys. Sins. 64 094305 (in Chinese) [梁彬, 袁樱, 程建春 2015 64 094305]
[8] Zhang Z, Li R Q, Liang B, Zou X Y, Cheng J C 2015 Chin. Phys. B 24 024301
[9] Wu J H, Cheng T H, Liu A Q, Wang Y X 2006 Appl. Phys. Lett. 89 263103
[10] Wu J H, Shen L 2011 J. Opt. Soc. Am. B 28 1328
[11] Wang Z X, Guo D R 1989 Special Functions (Beijing: Peking University Press) pp633-638 (in Chinese) [王竹溪, 郭敦仁 1989 特殊函数概论(北京:北京大学出版社)第633-638页]
[12] Yariv A, Yeh P 1977 J. Opt. Soc. Am. 67 423
[13] Zhang H L 2007 Theoretical Acoustics (Beijing:Higher Education Press) p225 (in Chinese) [张海澜 2007 理论声学 (北京: 高等教育出版社)第225页]
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