流固耦合条件下压电层合柱的共振断裂分析
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摘要
建立了轴向剪切振动条件下,流固耦合压电层合柱的断裂力学分析模型。运用分离变量法、无穷三角级数、柯西奇异积分、Bessel函数和Lobatto–Chebyshev配点法等方法,得到了应力强度因子随频率变化的数值结果。分析了裂纹角度、弹性模量、压电系数、介电系数、密度等对SIF (stress intensity factor)一阶共振频率的影响规律。
The fracture behavior of a fluid-structure piezoelectric laminated column is studied under the condition of the axial shear vibration. The problem is solved by the variable separation method, the infinite trigonometric series, the Cauchy singular integral equation, the Bessel function and the Lobatto-Chebyshev collocation. The numerical results of the stress intensity factor(SIF) against the frequency are obtained,as well as the effects of the crack angle, the elastic modulus, the piezoelectric coefficient, the dielectric coefficient and the density on the first order resonance behavior of the stress intensity factor.
The fracture behavior of a fluid-structure piezoelectric laminated column is studied under the condition of the axial shear vibration. The problem is solved by the variable separation method, the infinite trigonometric series, the Cauchy singular integral equation, the Bessel function and the Lobatto-Chebyshev collocation. The numerical results of the stress intensity factor(SIF) against the frequency are obtained,as well as the effects of the crack angle, the elastic modulus, the piezoelectric coefficient, the dielectric coefficient and the density on the first order resonance behavior of the stress intensity factor.
引文
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10 Li YD,Xiong T,Zhao H.Interfacial fracture analysis of a piezoelectric-polythene composite cylindrical shell patch under axial shear.Acta Mechanica,2014,225(2):543-551
11 Zaitsev BD,Kuznetsova IE,Joshi SG,et al.Acoustic waves in piezoelectric plates bordered with viscous and conductive liquid.Ultrasonics,2001,39(1):45-50
2何超,陈文革.压电材料的制备应用及其研究现状.功能材料,2010,41(s1):11-13He Chao,Chen Wenge.Fabrication and research and application of piezoelectric materials.Journal of Functional Materials,2010,41(s1):11-13(in Chinese)
3汪越胜,于桂兰,章梓茂等.复杂界面(界面层)条件下的弹性波传播问题研究综述.力学进展,2000,30(3):378-390Wang Yuesheng,Yu Guilan,Zhang Zimao,et al.Review on elastic wave propagation under complex interface(interface layer)conditions.Advances in Mechanics,2000,30(3):378-390(in Chinese)
4 Li YD,Xiong T,Zhao H.Interfacial fracture analysis of a piezoelectric-polythene composite cylindrical shell patch under axial shear.Acta Mechanica,2014,225(2):543-551
5 Yuan L,Du J,Ma T,et al.Study on SH-SAW in imperfectly bonded piezoelectric structures loaded with viscous liquid.Acta Mechanica,2014,225(1):1-11
6王晖,孟广伟,周立明等.含裂纹压电材料的扩展无网格伽辽金法.华中科技大学学报(自然科学版),2015(3):42-47Wang Hui,Meng Guangwei,Zhou Liming,et al.Enriched element-free Galerkin method for piezoelectric materials with crack.Journal of Huazhong University of Science and Technology(Natural Science Edition),2015(3):42-47(in Chinese)[7]
7赵鹏,秦太验,张琳楠.压电材料动态裂纹问题的奇异积分方程法.力学与实践,2014,36(4):433-436Zhao Peng,Qin Taiyan,Zhang Linnan.Analysis of a transient elastodynamic crack in piezoelectric materials using a singular integral equation method.Mechanics in Engineering.2014,36(4):433-436(in Chinese)
8 Li YD,Lee KY,Zhang N.A generalized hypergeometric function method for axisymmetric vibration analysis of a piezoelectric actuator.European Journal of Mechanics,2012,31(1):110-116
9 Li YD,Lee KY.Effect of an imperfect interface on the SHwave propagating in a cylindrical piezoelectric sensor.Ultrasonics,2010,50(4):473-478
10 Li YD,Xiong T,Zhao H.Interfacial fracture analysis of a piezoelectric-polythene composite cylindrical shell patch under axial shear.Acta Mechanica,2014,225(2):543-551
11 Zaitsev BD,Kuznetsova IE,Joshi SG,et al.Acoustic waves in piezoelectric plates bordered with viscous and conductive liquid.Ultrasonics,2001,39(1):45-50