A time discontinuous Galerkin finite element method for the solution of impact problem of laminated piezoelectric material

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Journal of Vibration and Shock ›› 2018, Vol. 37 ›› Issue (24) : 195-200.

GUO Pan1,WEI Hongtao1,WU Wenhua2,XU Guangtao3,ZHAO Jun1

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Abstract

A time discontinuous Galerkin finite element method (DGFEM) is used to simulate the problem of laminated piezoelectric material subjected to the high-frequency impulsive load.At present, the traditional numerical method for solving the dynamic problem of piezoelectric solid subjected to high frequency impulsive load generally fails to properly capture discontinuities of waves in space and interface between two layers, and produces spurious numerical oscillations in the simulation of high modes and sharp gradients.In order to filter out the spurious oscillations, an artificial damping scheme, which based on the DGFEM, was implemented in the final finite element formula.Numerical results of one dimension and two dimension show that the developed DGFEM presents good abilities and provides much more accurate solutions for piezoelectric problem.It can capture the discontinuities effectively at the wave front and wave after and filter out the effects of spurious numerical oscillation induced by high-frequency impulsive load.

Key words

time discontinuous Galerkin finite element method / impulsive load / laminated piezoelectric material / numerical oscillation

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GUO Pan1,WEI Hongtao1,WU Wenhua2,XU Guangtao3,ZHAO Jun1. A time discontinuous Galerkin finite element method for the solution of impact problem of laminated piezoelectric material[J]. Journal of Vibration and Shock, 2018, 37(24): 195-200

References

[1] Ilgar Jafarsadeghi-Pournaki, Ghader Rezazadeh, Mohammadreza Zamanzadeh, Rasoul Shabani. Parametric Thermally Induced Vibration of an Electrostatically Deflected FGM Micro-Beam[J]. International Journal of Applied Mechanics, 2016, 8(8):1-22.
[2] Kefi AAbdel, Nayfeh AH, Hajj MR. Effects of nonlinear piezoelectric coupling on energy harvesters under direct excitation[J]. Nonlinear Dynamics, 2012, 67(8):1221-1232.
[3] Nanthakumar SS., Lahmer Tom, Zhuang Xiaoying, Park Harold S, Rabczuk Timon. Topology optimization of piezoelectric nanostructures[J]. Journal of the Mechanics and Physics of Solids, 2016, 94(8):316-335
[4] 林鹏,王长利,李迅,王登旺. 压杆式压电应力传感器在爆炸冲量测试中的应用[J]. 应用数学和力学, 2015, 36:29-35.
LIN Peng, WANG Chang-li, LI Xun, WANG Deng-wang. Application of the Piezoelectric Pressure Bar Gauge to Blast Im pulse Measurement[J]. Applied Mathematics and Mechanics, 2015, 36, 29-35
[5] 朱劲松, 高志玉. 基于PZT波传播法的混凝土内部钢筋锈蚀监测方法[J].建筑材料学报, 2016, 1(19):166-170.
Zhu Jinsong, Gao Zhiyu. Monitoring method for corrosion of reinforcement in concrete based on wave propagation method with PZT[J]. Journal of building materials. 2016, 19(1): 166-170.
[6] Sorokin B.P., Kvashnin G.M., Novoselov A.S., Bormashov V.S., Golovanov A.V., Burkov S.I., Blank V.D.. Excitation of hypersonic acoustic waves in diamond-based piezoelectric layered structure on the microwave frequencies up to 20 GHz[J]. Ultrasonics, 2017, 78:162-165.
[7] Mahmoudpour Masihollah, Zabihollah Abolghassem, Vesaghi Mohammad, Mohadese Kolbadinejad. Design and analysis of an innovative light tracking device based on opto-thermo-electro-mechanical actuators[J]. Microelectronic Engineering. 2014, 119:37-43.
[8] Sairajan KK, Aglietti GS, Mani KM. A review of multifunctional structure technology for aerospace applications[J]. Acta Astronautica, 2016, 120:30-42.
[9] Abdelkefi A. Aeroelastic energy harvesting:A review[J]. International Journal of Engineering Science, 2016, 100: 112-135.
[10] Williams RP, Kim D, Gawalt DP, Hall NA. Surface micromachined differential piezoelectric shear-stress sensors[J]. Journal of Micromechanics and Microengineering, 2017, 27(1):015011.
[11] Rouhollah Hosseini, Mohsen Hamedi, Jongbeom Im, Jaehwan Kim, Jedol Dayou. Analytical and experimental investigation of partially covered piezoelectric cantilever energy harvester[J]. International Journal of Precision Engineering and Manufacturing. 2017, 18(3):415-424.
[12] 匡震邦.电弹性理论[M].上海交通大学出版社, 上海, 2010.
Kuang ZhenBang. Theory of Electroelasticity[M], Profile of Shanghai Jiao Tong University Press, Shang Hai, 2010
[13] Jan Sladek, Vladimir, Sladek Peter Stanak, Ernian Pan. FEM formulation for size-dependent theory with application to micro coated piezoelectric and piezomagnetic fiber-composites[J]. Comput Mech, 2017, 59:93-105.
[14] Tinh Quoc Bui,Chuanzeng Zhang. Extended finite element simulation of stationary dynamic cracks in piezoelectric solids under impact loading[J]. Computational Materials Science, 2012, 62:243-257.
[15] Dziatkiewicz Grzegorz. Complex variable step method for sensitivity analysis of effective properties in multi-field micromechanics[J]. Acta Mech, 2016, 227:11-28.
[16] Marquez Renteria IA, Bolborici V. A dynamic model of the piezoelectric traveling wave rotary ultrasonic motor stator with the finite volume method[J]. Ultrasonics. 2017, 77:69-78.
[17] Tinh Quoc Bui. Extended isogeometric dynamic and static fracture analysis for cracks in piezoelectric materials using NURBS[J]. Comput Methods Appl Mech Engrg. 2015, 295: 470-509.
[18] Hughes TJR, Hulbert GM. Space-time finite element methods for elastodynmaics: Fomurlations and error estimates[J]. Computer Methods in Applied Mechanics and Engineering, 1988, 66:339-363.
[19] Wiberg NE, Li XD. Adaptive finite element procedures for linear and non- linear dynamics[J]. International Journal for Numerical Methods in Engineering, 1999, 46:1781-1802.
[20] Mancuso M, Ubertini F. An efficient time discontinuous Galerkin procedure for nonlinear structural dynamics[J]. Computer Methods in Applied Mechanics and Engineering, 2006, 195:44-47.
[21] Li XK, Yao DM, Lewis RW. A discontinuous Galerkin finite element method for dynamic and wave propagation problems in non-linear solids and saturated porous media[J]. International Journal for Numerical Methods in Engineering, 2003, 57(3): 1775-1800.
[22] Wenhua Wu, Xikui Li. Application of the time discontinuous Galerkin finite element method to heat wave simulation. I.J heat and Mass transfer. 2006,49:1679-1684.
[23] 郭攀, 武文华,吴志刚. 改进时域间断Galerkin有限元方法在弹塑性波传播数值模拟中的应用, 固体力学学报, 2013, 34(3):1-6.
GUO Pan, WU Wen-Hua, WU Zhi-Gang. Application of the modified time discontinuous Galerkin finite element method to elasto-plastic wave propagation simulation[J]. Chinese Joural of Solid Mechanics, 2013, 34(3):1-6.
[24] GUO Pan,WU Wen-Hua,WU Zhi-Gang. A time discontinuous Galerkin finite element method for generalized thermo-elastic wave analysis, considering non-Fourier effects[J]. Acta Mechanica, 2014, 225:299-307.
[25] Li DH, Zheng XJ, Wu B, Zhou YC. Fracture analysis of a surface through-thickness crack in PZT thin film under a continuous laser irradiation[J]. Engineering Fracture Mechanics, 2009, 76:525-532.