Behavior of one-dimensional elastic waves at a unilateral contact interface between two piezoelectric solids
-
摘要: 弹性波与压电材料接触界面的相互作用问题是工程应用中常见而复杂的问题，入射波足够强会引起界面出现滑移和分离，但滑移和分离的边界未知，边界条件具有非线性特性。通过Fourier分析，将混合边值问题的求解转化为非线性代数方程，利用软件通过迭代修正的方法进行了求解；给出3种状态边界的求解，分析入射波强度、外加应力及电场对界面状态的影响，并对高频谐波的特性进行分析，通过实例对理论推导进行验证，结果显示：入射波强度、外加荷载和电场的大小及摩擦因数均会影响到界面，通过改变这些条件可以控制界面状态，另外检测高频谐波的信号也可以反映界面状态。Abstract: The behavior of one-dimensional elastic waves at a unilateral frictional contact piezoelectric material interface was studied theoretically in this thesis. When the incident wave is strong enough, the contact interface will separate or slip in local interface areas and non-linearity (boundary non-linearity) will pose as a serious problem, and high harmonics will be generated due to this non-linearity, thus not only causing difficulties in mathematics but giving rise to some new phenomena in physics. In this paper one-dimensional problems were discussed in details using the Fourier analysis, and the mix-boundary value problems with unknown regions were converted to a set of non-linear algebraic equations for a one-dimensional case. An iterative method was developed to determine the extent and location of the separation, slip and stick regions which vary with the external mechanical-electrical loads. The interface tractions, relative slip velocities and the amplitudes of the reflected and refracted high harmonics due to the boundary non-linearity were calculated. Their variation with the applied mechanical-electrical loads was discussed. It was found that, due to the mechanical-electrical coupling, the non-linearity of mechanical parameters would induce the non-linearity of electrical parameters, and the applied electrical fields would influence the interface states by changing the mechanical loads. The present research may enrich the wave theory of piezoelectricity and facilitate its practical application. For instance, we could evaluate the contact state and modulate an interface by detecting the mechanical or electrical information carried by high harmonics.
-
Key words:
- piezoelectric material /
- frictional contact /
- elastic waves /
- high frequency harmonics /
- separation zones /
- slip zones
-
图 1 一维弹性波透过压电介质摩擦接触界面的传播
Figure 1. Propagation of one-dimensional elastic wave through a frictional contact interface between two piezoelectric media
图 2 界面张开位移与参数关系
Figure 2. Relation between the interface opening displacement and the parameter
图 5 P波入射，分离状态分布区间与Pz/A3(0)的变化关系
Figure 5. Distribution of separation zones for different －Pz/A3(0) when the incident wave is P wave
图 6 P波入射，分离、滑移和黏着状态分布区间随Tx/A3(0)的变化关系
Figure 6. Distribution of separation, slip, stick state zones for different Tx/A3(0)when the incident wave is P wave
-
[1] Sezawa K, Kanai K.A fault surface or a block absorbs seismic wave energy[J].Bulletin of the Earthquake Research Institute Imperial University of Tokyo, 1940(18):465-482. http://cn.bing.com/academic/profile?id=695538fbd1007f8b770b0eb34f634c99&encoded=0&v=paper_preview&mkt=zh-cn [2] 卢文波.应力波与可滑移岩石界面的相互作用研究[J].岩土力学, 1996, 17(3):70-75. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QK199600621922Lu Wenbo.A sdudy on interaction between stress wave and slipping rock interface[J].Rock and Soil Meckanics, 1996, 17(3):70-75. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QK199600621922 [3] Chevalier Y, Louzar M, Maugin G A.Surface-wave characterization of the interface between two anisotropic media[J].Journal of the Acoustical Society of America, 1991, 90(6):3218-3227. doi: 10.1121/1.401431 [4] 李夕兵.论岩体软弱结构面对应力波的影响[J].爆炸与冲击, 1993, 13(4):334-342. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QK000001148819Li Xibing.Influence of the structural weakness planes in rock mass on the propagation of stress waves[J].Explosion and Shock Waves, 1993, 13(4):334-342. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QK000001148819 [5] Comniou M, Dundurs J, Chez E L.Total reflection of SH waves in presence of slip and friction[J].Journal of the Acoustical Society of America, 1979, 66(3):789-793. doi: 10.1121/1.383681 [6] Comninou M, Dundurs J.Interaction of elastic waves with a unilateral interface[J].Proceedings of the Royal Society A, 1979, 368(1732):141-154. doi: 10.1098/rspa.1979.0120 [7] Comninou M, Dundurs J.Elastic interface waves and sliding between two solids[J].Journal of Applied Mechanics, 1978, 45(2):325-330. doi: 10.1115/1.3424296 [8] Wang Y S, Yu G L, Gai B Z.Slip with friction between a layer and a substrate caused by SH pulse[J].Mechanics Research Communications, 1997, 64(4):85-91. doi: 10.1016-S0093-6413(96)00082-1/ [9] Wang Y S, Yu G L, Gai B Z.Propagation of SH waves in a layered half-space with a frictional contact interface[J].Bulletin of the Seismological Society of America, 1998, 88(5):1300-1310. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=cff36e4600029aa6e5ee393d6868c7f2 [10] Wang Y S, Yu G L.Re-polarization of elastic waves at a frictional contact interface of a P or SV wave[J].International Journal of Solids and Structures, 1999, 36(30):4563-4586. doi: 10.1016/S0020-7683(98)00208-X [11] Wang Y S, Yu G L, Dai H H.Transmission of elastic waves through a frictional contact interface between two anisotropic dissimilar media[J].Wave Motion, 2003, 37(37):137-156. doi: 10.1016-S0165-2125(02)00039-2/ [12] 于桂兰, 汪越胜, 李楠.一般各向异性单侧接触界面上波的反射和折射[J].力学学报, 2003, 35(5):561-568. doi: 10.3321/j.issn:0459-1879.2003.05.007Yu Guilan, Wang Yuesheng, Li Nan.Reflection and refraction of elastic waves at a unilateral contact interface between two generally anisotropic media[J].Chinese Journal of Theoretical and Applied Mechanics, 2003, 35(5):561-568. doi: 10.3321/j.issn:0459-1879.2003.05.007 [13] 李楠, 汪越胜, 于桂兰.基于表面阻抗张量的界面滑移波动失稳分析[J].应用数学和力学, 2004, 25(9):935-942. doi: 10.3321/j.issn:1000-0887.2004.09.008Li Nan, Wang Yuesheng, Yu Guilan.Analysis of dynamic instability of interfacial slip waves based on the surface impedance tensor[J].Applied Mathematics and Mechanics, 2004, 25(9):935-942. doi: 10.3321/j.issn:1000-0887.2004.09.008 [14] 白玉柱, 于桂兰, 许丽敏.压电体光滑接触界面上滑移界面波理论分析[J].北京交通大学学报, 2007, 31(4):10-13. doi: 10.3969/j.issn.1673-0291.2007.04.003Bai Yuzhu, Yu Guilan, Xu Limin.Theoretical analysis of slip waves propagating along the frictionless contact interface of piezoelectric solids[J].Journal of Beijing Jiaotong University, 2007, 31(4):10-13. doi: 10.3969/j.issn.1673-0291.2007.04.003 [15] 白玉柱, 汪越胜, 于桂兰.压电体光滑接触界面有局部分离时滑移脉冲波传播[J].应用数学与力学, 2007, 28(9):1095-1101. http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX200709012.htmBai Yuzhu, Wang Yuesheng, Yu Guilan.Propagation of slip pulse along a frictionless contact interface with local separation between two piezoelectric solids[J].Applied Mathematics and Mechanics, 2007, 28(9):1095-1101. http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX200709012.htm [16] 路桂华, 汪越胜, 于桂兰.弹性波在压电介质摩擦接触界面上的反射与投射[J].应用基础与工程科学学报, 2006, 14(1):77-83. doi: 10.3969/j.issn.1005-0930.2006.01.010Lu Guihua, Wang Yuesheng, Yu Guilan.Reflection and transmission of elastic waves at a fricton contact interface between two piezoelectric media[J].Journal of Basic Science and Engineering, 2006, 14(1):77-83. doi: 10.3969/j.issn.1005-0930.2006.01.010 [17] 路桂华, 于桂兰, 汪越胜.弹性波投过压电介质接触界面的传播特性[J].科学技术与工程, 2005, 3(3):174-176. doi: 10.3969/j.issn.1671-1815.2005.03.011Lu Guihua, Yu Guilan, Wang Yuesheng.Behavior of elastic waves propagation through a contact interface between two piezoelectricity solids[J].Science Technology and Engineering, 2005, 3(3):174-176. doi: 10.3969/j.issn.1671-1815.2005.03.011 [18] 汪越胜, 于桂兰, 章子茂.复杂界面(界面层)条件下的弹性波传播问题研究综述[J].力学进展, 2000, 30(3):378-390. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=CAS201303040000429246Wang Yuesheng, Yu Guilan, Zhang Zimao.Review on elastic wave propagation under complex interface (interface layer) conditions[J].Advances in Mechanics, 2000, 30(3):378-390. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=CAS201303040000429246 -
下载:
图(7)
计量
- 文章访问数: 4407
- HTML全文浏览量: 1327
- PDF下载量: 251
- 被引次数: 0