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By taking into account the macroscale nonlinear effect, quadratic and cubic microscale nonlinear effects, and microscale dispersion effect, a new model capable to describe the longitudinal wave propagation in one-dimensional microstructured solid is established based on the Mindlin theory. Using the qualitative analysis theory in the planar dynamical systems, we have analyzed the existence conditions and geometrical characteristics of solitary waves, and proved that the faces under the influence of quadratic microscale nonlinear effect, can form an asymmetric solitary wave in the microstructured solid; and under the influence of cubic microscale nonlinear effect, they can form a symmetric solitary wave in the microstructured solid, when the medium parameters and the propagation speeds of solitary waves satisfy certain appropriate conditions. Finally, the above results are further verified using a numerical method.
[1] Mindlin R D 1964 Arch. Rat. Mech. Anal. 16 51
[2] Engelbrecht J, Khamidullin Y 1988 Phys. Earth Planet. Inter. 50 39
[3] Erofeev V I 2003 Wave Processes in Solids with Microstructure (Singapore: World Scientific press) pp101-223
[4] Chen S H, Wang Z Q 2003 Advanc. Mech. 33 207(in Chinese) [陈少华, 王自强 2003 力学进展 33 207]
[5] Hu G K, Liu X N, Xun F 2004 Advanc. Mech. 34 195(in Chinese) [胡更开, 刘晓宁, 荀飞 2004 力学进展 34 195]
[6] Janno J, Engelbrecht J 2005 J. Phys. A: Math. Gen. 38 5159
[7] Peets T, Randruut M, Engelbrecht J 2008 Wave Motion 45 471
[8] Porubov A V, Pastrone F 2004 Int. J. Non-Linear Mech. 39 1289
[9] Porubov A V 2003 Amplification of Nonlinear Strain Waves in Solids (Singapore: World Scientific press) pp114-192
[10] Porubov A V, Aero E L, Maugin G A 2009 Phys. Rev. E 79 046608
[11] Janno J, Engelbrecht J 2005 Inverse Probl. 21 2019
[12] Zhang J L, Wang H X 2014 Chin. Phys. B 23 044208
[13] Gao X H, T D, Zhang C Y, Zheng H, Lu D Q, Hu W 2014 Acta Phys. Sin. 63 024204(in Chinese) [高星辉, 唐冬, 张承云, 郑晖, 陆大全, 胡巍 2014 物理学报 63 024204]
[14] Shi Y R, Zhang J, Yang H J, Duan W S 2011 Acta Phys. Sin. 60 020401(in Chinese) [石玉仁, 张娟, 杨红娟, 段文山 2011 物理学报 60 020401]
[15] Li R H, Chen W S 2013 Chin. Phys. B 22 040503
[16] Potapov A, Rodyushkin V M 2001 Acoust. Phys. 47 347
[17] Shuang S, Naranmandula 2012 Chin. J. Theore. Appl. Mech. 44 117(in Chinese) [双山, 那仁满都拉 2012 力学学报 44 117]
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[1] Mindlin R D 1964 Arch. Rat. Mech. Anal. 16 51
[2] Engelbrecht J, Khamidullin Y 1988 Phys. Earth Planet. Inter. 50 39
[3] Erofeev V I 2003 Wave Processes in Solids with Microstructure (Singapore: World Scientific press) pp101-223
[4] Chen S H, Wang Z Q 2003 Advanc. Mech. 33 207(in Chinese) [陈少华, 王自强 2003 力学进展 33 207]
[5] Hu G K, Liu X N, Xun F 2004 Advanc. Mech. 34 195(in Chinese) [胡更开, 刘晓宁, 荀飞 2004 力学进展 34 195]
[6] Janno J, Engelbrecht J 2005 J. Phys. A: Math. Gen. 38 5159
[7] Peets T, Randruut M, Engelbrecht J 2008 Wave Motion 45 471
[8] Porubov A V, Pastrone F 2004 Int. J. Non-Linear Mech. 39 1289
[9] Porubov A V 2003 Amplification of Nonlinear Strain Waves in Solids (Singapore: World Scientific press) pp114-192
[10] Porubov A V, Aero E L, Maugin G A 2009 Phys. Rev. E 79 046608
[11] Janno J, Engelbrecht J 2005 Inverse Probl. 21 2019
[12] Zhang J L, Wang H X 2014 Chin. Phys. B 23 044208
[13] Gao X H, T D, Zhang C Y, Zheng H, Lu D Q, Hu W 2014 Acta Phys. Sin. 63 024204(in Chinese) [高星辉, 唐冬, 张承云, 郑晖, 陆大全, 胡巍 2014 物理学报 63 024204]
[14] Shi Y R, Zhang J, Yang H J, Duan W S 2011 Acta Phys. Sin. 60 020401(in Chinese) [石玉仁, 张娟, 杨红娟, 段文山 2011 物理学报 60 020401]
[15] Li R H, Chen W S 2013 Chin. Phys. B 22 040503
[16] Potapov A, Rodyushkin V M 2001 Acoust. Phys. 47 347
[17] Shuang S, Naranmandula 2012 Chin. J. Theore. Appl. Mech. 44 117(in Chinese) [双山, 那仁满都拉 2012 力学学报 44 117]
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