Please wait a minute...
浙江大学学报(工学版)
浙江大学学报(工学版)  2018, Vol. 52 Issue (6): 1185-1193    DOI: 10.3785/j.issn.1008-973X.2018.06.018
工程力学     
基于L-S理论的压电球壳广义热冲击分析
刘承斌1, 刘文耀2, 陈伟球3,4,5, 王惠明3,4,5, 吕朝锋1,4,5
1. 浙江大学 土木工程学系, 浙江 杭州 310058;
2. 宁波职业技术学院 海天学院, 浙江 宁波 315800;
3. 浙江大学 工程力学学系, 浙江 杭州 310027;
4. 浙江大学 浙江省软体机器人与智能器件研究重点实验室, 浙江 杭州 310027;
5. 浙江大学 软物质科学研究中心, 浙江 杭州 310027
Generalized thermal shock analysis of piezoelectric spherical shell based on L-S theory
LIU Cheng-bin1, LIU Wen-yao2, CHEN Wei-qiu3,4,5, WANG Hui-ming3,4,5, LV Chao-feng1,4,5
1. Department of Civil Engineering, Zhejiang University, Hangzhou 310058, China;
2. Haitian School, Ningbo Polytechnic, Ningbo 315800, China;
3. Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, China;
4. Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou 310027, China;
5. Soft Matter Research Center, Zhejiang University, Hangzhou 310027, China
 全文: PDF(1182 KB)   HTML
摘要：

基于L-S广义热弹性理论，针对压电球壳受表面球对称热冲击作用下的热弹性问题进行分析.从三维压电弹性理论基本方程出发，利用Laplace变换，建立耦合的6阶状态方程；采用层合近似模型，将状态方程转化为关于径向坐标的常系数状态方程.利用界面连续条件得到球壳内、外状态变量的整体传递关系，结合球壳内、外边界条件，可以确定频域内所有状态变量，通过数值反变换获得时域解.数值算例给出热冲击作用下压电球壳的位移、应力、电势和温度等物理量的分布规律，考察热松弛时间对热冲击作用效果的影响.
Abstract:

The spherically symmetric problem of a piezoelectric spherical shell subjected to thermal shock was analyzed based on the L-S generalized thermoelasticity. A sixth-order homogeneous state equation was established by Laplace transform based on the three-dimensional theory of piezoelectricity. The state equation was transferred to the one with constant coefficients using the approximate laminate model. A transfer relation was obtained between the state vectors at the inner and outer surfaces of the spherical shell by using the continuity conditions at each interface between two adjacent layers. Then the state variables were exactly determined by incorporating the prescribed boundary conditions. All time-domain physical variables of the coupled field were obtained by using the numerical inverse Laplace transform. Numerical examples were performed to analyze the distributions of the temperature, stress, displacement, and electric potential, and in particularly, the influences of thermal relaxation time on the thermal shock effects.
收稿日期: 2017-03-21 出版日期: 2018-06-20
CLC:  O343  
基金资助:

国家自然科学基金创新研究群体资助项目（11621062）.
通讯作者: 吕朝锋,男,教授、博导.orcid.org/0000-0003-2846-1266.     E-mail: lucf@zju.edu.cn
作者简介: 刘承斌(1978-),男,高级工程师,博士,从事压电弹性力学研究.orcid.org/0000-0003-4131-4092.E-mail:lcb@zju.edu.cn
服务　　
把本文推荐给朋友
加入引用管理器
E-mail Alert
作者相关文章　　

引用本文:

刘承斌, 刘文耀, 陈伟球, 王惠明, 吕朝锋. 基于L-S理论的压电球壳广义热冲击分析[J]. 浙江大学学报(工学版), 2018, 52(6): 1185-1193.

LIU Cheng-bin, LIU Wen-yao, CHEN Wei-qiu, WANG Hui-ming, LV Chao-feng. Generalized thermal shock analysis of piezoelectric spherical shell based on L-S theory. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 2018, 52(6): 1185-1193.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2018.06.018    或    http://www.zjujournals.com/eng/CN/Y2018/V52/I6/1185

[1] CATTANEO C. Sulla conduzionedelcalore[J]. Attisem Mat Fis Univ Modena, 1948, 3:83-101.
[2] VERNOTTE P. Les paradoxes de la theorie continue de I'equation de la chaleur[J]. Compute Rendus, 1958, 246(22):3154-3155.
[3] LORD H W, SHULMAN Y. A generalized dynamical theory of thermoelasticity[J]. Journal of the Mechanics and Physics of Solids, 1967, 15(5):299-309.
[4] GREEN A E, LINDSAY K A. Thermoelasticity[J]. Journal of Elasticity, 1972, 2(1):1-7.
[5] GREEN A E, NAGHDI P M. Thermoelasticity without energy dissipation[J]. Journal of Elasticity, 1993,31(3):189-208.
[6] JIANG F M, SOUSA A C M. Analytical solution for hyperbolic heat conduction in a hollow sphere[J]. Journal of Thermophysics and Heat Transfer, 2005, 19(4):595-598.
[7] BABAEI B H, CHEN Z T. Hyperbolic heat conduction in a functionally graded hollow sphere[J]. International Journal of Thermophysics, 2008, 29(4):1457-1469.
[8] 赵伟涛,吴九汇.球体表面受任意周期热扰动时非傅里叶导热的求解与分析[J].西安交通大学学报,2014,4(1):13-18. ZHAO Wei-tao, WU Jiu-hui. Solution and analysis of non-Fourier heat conduction in a solid sphere under arbitrary periodic surface thermal disturbance[J]. Journal of Xi'an Jiaotong University, 2014, 4(1):13-18.
[9] ZHAO W T, WU J H, CHEN Z. Analysis of non-Fourier heat conduction in a solid sphere under arbitrary surface temperature change[J]. Archive of Applied Mechanics, 2014, 84(4):z505-518.
[10] SHIRMOHAMMADI R. Temperature transients in spherical medium irradiated by laser pulse[J]. International Communications in Heat and Mass Transfer, 2008, 35(8):1017-1023.
[11] TSAI C S, HUNG C I. Thermal wave propagation in a bi-layered composite sphere due to a sudden temperature change on the outer surface[J]. International Journal of Heat and Mass Transfer, 2003, 46(26):5137-5144.
[12] TARIQ T D, MALAK N, MOH'D AIN. Transient thermal stresses in an orthotropic cylinder under the hyperbolic heat conduction model[J]. Heat Transfer Engineering, 2008, 29(7):632-642.
[13] 赵伟涛,吴九汇,白宇,等.受热冲击时球体的广义热弹性分析[J].西安交通大学学报,2013,47(7):108-113. ZHAO Wei-tao, WU Jiu-hui, BAI Yu, et al. Generalized thermoelastic analysis for sphere under thermal shock[J]. Journal of Xi'an Jiaotong University, 2013, 47(7):108-113.
[14] SHI X Y, SHANG X C. Transient response of thermoelastic hollow sphere under thermal shocks[J]. Journal of Thermal Stresses, 2014, 37:707-726.
[15] KIANI Y, ESLAMI M R. The GDQ approach to thermally nonlinear generalized thermoelasticity of a hollow sphere[J]. International Journal of Mechanical Sciences, 2016, 118:195-204.
[16] CHANDRASEKHARAIAH D S. A general linear thermoelasticity theory for piezoelectric media[J]. ActaMechanica, 1988, 71(1-4):39-49.
[17] AOUADI M. Generalized thermo-piezoelectric problems with temperature dependent properties[J]. International Journal of Solids and Structures, 2006, 43:6347-6358.
[18] BABAEI M H, CHEN Z T. The transient coupled thermo-piezoelectric response of a functionally graded piezoelectric hollow cylinder to dynamic loadings[C]//Proceedings of the Royal Society A. London:[s.n.], 2009:1-15.
[19] 田晓耕,张婕,沈亚鹏.不同理论下广义压电热弹性问题的有限元求解[J].力学学报,2006,38(4):553-558. TIAN Xiao-geng, ZHANG Jie, SHEN Ya-peng. Sloving generalized piezothermoelastic problem by FEM with different theories[J]. Chinese Journal of Theoretical and Applied Mechanics, 2006, 38(4):553-558.
[20] 田晓耕,沈亚鹏.广义热弹性问题研究进展[J].力学进展,2012,42(1):18-28. TIAN Xiao-geng, SHEN Ya-peng. Research progress in generalized thermoelasticproblems[J].Advances in Mechanics, 2012, 42(1):18-28.
[21] TIAN X G, ZHANG J, SHEN Y P, et al. Finite element method for generalized piezothermoelastic problems[J]. International Journal of Solids and Structures, 2007, 44:6330-6339.
[22] CHEN W Q, SHIOYA T. Piezothermoelastic behavior of a pyroelectric spherical shell[J]. Journal of Thermal Stresses, 2001, 24(2):105-120.
[23] DING H J, CHEN W Q. Three dimensional problems of piezoelasticity[M]. New York:Nova Science Publishers, 2001.
[24] 刘承斌.压电球壳的若干多场耦合问题研究[D].杭州:浙江大学,2016. LIU Cheng-bin. Multifield coupling analysis of piezoelectric spherical shell[D]. Hangzhou:Zhejiang University, 2016.
[25] DURBIN F. Numerical inversion of Laplace transformation:an efficient improvement to Durbin and Abate's method[J]. Computer Journal, 1974, 17(4):371-376.
[26] HONG G, HIRDES U. A method for the numerical inversion of Laplace transform[J]. Journal of Computational and Applied Mathematics, 1984, 10(1):113-132.
[27] DAVIES B, MARTIN B. Numerical inversion of the Laplace transform:a survey and comparison of methods[J]. Journal of Computational Physics. 1979,33(1):1-32.
[28] CRUMP K S. Numerical inversion of Laplace transforms using a Fourier series approximation[J]. Journal of the Association for Computing Machinery, 1976, 23(1):89-96.
[29] 韩光松,余志勇.Laplace变换数值反演的参数选择[J].兰州大学学报:自然科学版,2009,45(增1):116-119. HAN Guang-song, YU Zhi-yong. Parameters determination in numerical inversion of Laplace transforms[J].Journal of Lanzhou University:Natural Science, 2009, 45(supple.1):116-119.
[30] 郭攀,吴文华,吴志刚.非傅里叶热弹性的时域间断迦辽金有限元方法[J].力学学报,2013,45(3):447-450. GUO Pan, WU Wen-hua, WU Zhi-gang. Time discontinuous Galerkin finite element method for generalized thermo-elastic wave of non-Fourier effects[J].Chinese Journal of Theoretical and Applied Mechanics, 2013,45(3):447-450.
[31] 张浙,刘登瀛.超急速传热时球体内非稳态热传导的非傅里叶效应[J].工程热物理学报,1998,19(5):601-605. ZHANG Zhe, LIU Deng-ying. Non-Fourier effects in rapid transient heat conduction in a spherical medium[J]. Journal of Engineering Thermo-physics, 1998,19(5):601-605.
[1] 解王惠明, 肖艳萍. 旋转功能梯度压电空心圆柱的精确[J]. J4, 2009, 43(6): 1172-1176.