Spherical-Symmetric Steady-State Response of Piezoelectric Spherical Shell Under External Excitation

LI Hong-yun; LIU Zheng-xing; LIN Qi-rong

Volume 21 Issue 8

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 2000 > 21(8): 852-860

LI Hong-yun, LIU Zheng-xing, LIN Qi-rong. Spherical-Symmetric Steady-State Response of Piezoelectric Spherical Shell Under External Excitation[J]. Applied Mathematics and Mechanics, 2000, 21(8): 852-860.

Citation:

PDF( 355 KB)

Spherical-Symmetric Steady-State Response of Piezoelectric Spherical Shell Under External Excitation

Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200030, P R China

Received Date: 1999-08-12
Rev Recd Date: 2000-04-18
Publish Date: 2000-08-15

Abstract

Abstract

Spherical-symmetric steady-state response problem of piezoelectric spherical shell in the absence of body force and free charges is discussed. The steady-state response solutions of mechanical displacement, stresses, strains, potential and electric displacement were derived from constitutive relations, geometric and motion equations for the piezoelectric medium under external excitation (i.e. applied surface traction and potential)in spherical coordinate system. As an application of the general solutions, the problem of an elastic spherical shell with piezoelectric actuator and sensor layers was solved. The results could provide good theoretical basis for the spherical-symmetric dynamic control problem of piezoelectric intelligent structure. Furthermore, the solutions can serve as reference for the research of general dynamic control problem.
- piezoelectric material,
- steady-state response,
- spherical coordinate system,
- actuator layer,
- sensor layer

FullText(HTML)

References(12)

References

[1]	Tani J, Takagi T, Qiu J.Intelligent material systems:application of functional materials[J].Applied Mechanics Reviews,1998,51(8);505-519.
[2]	Chee C Y, Tong L Y, Steven G P.A review on the modelling of piezoelectric sensors and actuators incorporated in intelligent structures[J].Journal of Intelligent Material Systems and Structures,1998,9(1);3-19.
[3]	李山青,杨耀文,刘正兴.压电材料在智能结构形状和振动控制中的应用[J].力学进展,1999,29(1);66-76.
[4]	Chandrashekhara K, Smyser C P.Dynamic modeling and neutral control of composite shells using piezoeletric devices[J].Journal of Intelligent Material Systems and Structures,1998,9(1);29-43.
[5]	Tzou H S, Zhong J P.Electromechanics and vibrations of piezoelectric shell distributed systems[J].Journal of Dynamic Systems, Measurement and Control, ASME,1993,115(3);506-517.
[6]	Wang Z K, Zheng B L.The general solution of three-dimensional problems in piezoelectric media[J].Internat J Solids and Structures,1995,32(1);105-115.
[7]	王子昆,陈庚超.压电材料空间轴对称问题的通解及其应用[J].应用数学和力学,1994,15(7);587-598.
[8]	姚林泉,俞焕然.压电材料球对称问题的通解[J].兰州大学学报(自然科学版);1998,34(1);30-33.
[9]	孙慷,张福学.压电学[M].北京;国防工业出版社,1984.
[10]	Sun J, Norris M, Rossetti D, et al.Distributed piezoelectric actuators for shell interior noise control[J].Journal of Vibration and Acoustics,1996,118(4);676-681.
[11]	奚定平.贝塞尔函数[M].北京;高等教育出版社,1998.
[12]	Tzou H S, Tseng C I.Distributed piezoelectric sensor/actuator design for dynamic measurement/control of the distributed parameter systems:a piezoelectric finite element approach[J].J Sound Vibr,1990,138(1);17-34.

Relative Articles

[1]	LÜ Xin, KE Liaoliang, SU Jie. An Axisymmetric Contact Problem of Piezoelectric Materials Based on the Couple Stress Theory[J]. Applied Mathematics and Mechanics, 2024, 45(10): 1268-1278. doi: 10.21656/1000-0887.450190
[2]	MA Lan, TIAN Lili, LIU Li. Stochastic Responses and Stability Analysis of Vibro-Impact Systems With Friction Under Wideband Noise Excitation[J]. Applied Mathematics and Mechanics, 2024, 45(9): 1235-1242. doi: 10.21656/1000-0887.440313
[3]	CHEN Shenshen, WANG Juan. Application of a Coupled Interpolating Element-Free Galerkin Scaled Boundary Method and Finite Element Method in Fracture Analysis of Piezoelectric Materials[J]. Applied Mathematics and Mechanics, 2018, 39(11): 1258-1267. doi: 10.21656/1000-0887.390129
[4]	BIAN Wen-feng, WANG Biao. Dual Equations and Solutions of Ⅰ-Type Crack of Dynamic Problems in Piezoelectric Materials[J]. Applied Mathematics and Mechanics, 2007, 28(6): 651-658.
[5]	ZHOU Zhen-gong, WANG Biao. Basic Solution of Two Parallel Non-Symmetric Permeable Cracks in Piezoelectric Materials[J]. Applied Mathematics and Mechanics, 2007, 28(4): 379-390.
[6]	HE Yuan-jun, MA Xing-rui, WANG Ben-li. Stable Response of the Low-Gravity Liquid Non-Linear Sloshing in a Circle Cylindrical Tank[J]. Applied Mathematics and Mechanics, 2007, 28(10): 1135-1145.
[7]	QING Guang-hui, QIU Jia-jun, LIU Yan-hong. Hamiltonian Parametric Element and Semi-Analytical Solution for Smart Laminated Plates[J]. Applied Mathematics and Mechanics, 2007, 28(1): 45-52.
[8]	ZHOU Zhen-gong, WANG Biao. Investigation of the Behavior of a Model-Ⅰ Interface Crack in Piezoelectric Materials by Using the Schmidt Method[J]. Applied Mathematics and Mechanics, 2006, 27(7): 765-774.
[9]	QU Gui-min, ZHOU Zhen-gong, WANG Biao. Dynamic Behavior of Two Collinear Permeable Cracks in a Piezoelectric Layer Bonded to Two Half Spaces[J]. Applied Mathematics and Mechanics, 2005, 26(10): 1152-1160.
[10]	SUN Jian-liang, ZHOU Zhen-gong, WANG Biao. Dynamic Behavior of Two Unequal Parallel Permeable Interface Cracks in a Piezoelectric Layer Bonded to Two Half Piezoelectric Materials Planes[J]. Applied Mathematics and Mechanics, 2005, 26(2): 145-154.
[11]	LIU You-wen, FANG Qi-hong. Electroelastic Interaction Between a Piezoelectric Screw Dislocation and a Circular Inhomogeneity With Interfacial Cracks[J]. Applied Mathematics and Mechanics, 2004, 25(12): 1305-1312.
[12]	ZHONG Zheng. Analysis of a Partially Debonded Elliptic Inhomogeneity in Piezoelectric Materials[J]. Applied Mathematics and Mechanics, 2004, 25(4): 405-416.
[13]	WU Jun, CHEN Li-qun. Steady-State Responses and Their Stability of Nonlinear Vibration of an Axially Accelerating String[J]. Applied Mathematics and Mechanics, 2004, 25(9): 917-926.
[14]	ZHOU Zhen-gong, WANG Biao. Investigation of the Dynamic Behavior of Two Collinear Anti-Plane Shear Cracks in a Piezoelectric Layer Bonded to Two Half Spaces by a New Method[J]. Applied Mathematics and Mechanics, 2003, 24(1): 1-11.
[15]	ZHANG Lin-nan, SHI Zhi-fei. Analytical Solution of a Simply Supported Piezoelectric Beam Subjected to a Uniformly-Distributed Loading[J]. Applied Mathematics and Mechanics, 2003, 24(10): 1075-1082.
[16]	LI Hong-yun, LIN Qi-yong, LIU Zheng-xing, WANG Chao. Active Control of the Piezoelastic Laminated Cylindrical Shell’s Vibration Under Hydrostatic Pressure[J]. Applied Mathematics and Mechanics, 2003, 24(2): 163-174.
[17]	ZHOU Zhen-gong, WANG Biao. The Behavior of Two Parallel Symmetric Permeable Cracks in Piezoelectric Materials[J]. Applied Mathematics and Mechanics, 2002, 23(12): 1211-1219.
[18]	GAO Cun-fa, FAN Wei-xun. An Interface Inclusion Between Two Dissimilar Piezoelectric Materials[J]. Applied Mathematics and Mechanics, 2001, 22(1): 85-92.
[19]	LIU Jin-xi, JIANG Zhi-qing, FENG Wen-jie. On the Electroelastic Interaction of a Piezoelectric Screw Dislocation With an Elliptical Inclusion in Piezoelectric Materials[J]. Applied Mathematics and Mechanics, 2000, 21(11): 1185-1190.
[20]	Wang Zi-kung, Chen Geng-chao. A General Solution And the Applicatlon of Space Axisymmetric Problem in Piezoelectric Material[J]. Applied Mathematics and Mechanics, 1994, 15(7): 587-598.