|
Abstract: An element model including 4 displacement nodes, 2 electric potential nodes and 8 temperature nodes is presented. Its displacement field is defined by means of plane shell element model, and its electric potential field and temperature field are both defined by means of linear interpolation, the detailed element equations are deduced by using virtual work principle. Through the analytic solutions of sensitivities with respect to random parameters and first order second moment method, the numerical characteristics of natural frequencies, mode shapes, temperature field, displacement field and output voltages are solved in turn. Finally , an intelligent cantilever plate is taken as an example. The numerical results are compared with those of Monte Carlo method, the results show that the computing process presented is feasible and has very good precision.
Key words: Piezothermoelasticity Finite element method Random paramete r Sensitivity First order second moment method Monte Carlo method Numerical simulation
CLC No:
O242.21
国家高技术研究发展计划 (863计划, 2006AA04Z402) 和陕西省自然 科学基金(2005A009)资助项目,
received
in
revised
form
20070417,
received
in
revised
form
20071203
|
| References
[1] TZOU H S, YE R. Piezothermoelasticity and precision
control of piezoelectric systems: theory and finite element analysis[J].
Journal of Vibration and Acoustics, 1994, 116: 489-495.
[2] GU Haozhong, CHATTOPADHYAY Aditi, LI Jingmei, et al. A higher order
temperature theory for coupled thermopiezoelectric-mechanical modeling
of smart composites[J]. International Journal of Solids and Structures,
2000, 37: 6 479-6 497.
[3] KIM Heung Soo, CHATTOPADHYAY Aditi. Dynamic response of smart
composite shell using a coupled thermo-piezoelectric-mechanical model[C]//
43rd AIAA/ ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and
Materials Con. Colorado, Denver, 22-25 Apr., 2002: 1-11.
[4]
CHEN Jianjun, WANG Xiaobing. Analysis of the dynamic characteristic for
the intelligent plate with random parameters[J]. Journal of Xidian
University, 2004, 31(5): 661-665.
[5] GAO Wei, KESSISSOGLOU N J. Seismic random vibration analysis of
stochastic structures using random factor method[J]. Chinese Journal of
Mechanical Engineering, 2006, 19(1): 1-8.
[6]
WU Xiangfa, YANG Guoshu. Statistical analysis of the dynamic
characteristics of structures including random parameters[J]. Journal of
Beijing Institute of Technology, 1996, 16(1): 43-47.
[7]
CAO Jiayu, FANG Zhichu. Study on the random eigen-problem of engineering
structures and its application to beam[J]. Chinese Journal of Applied
Mechanics, 2002, 19(4): 71-74.
[8]
ZHANG Yimin, WEN Bangchun. Eigenvalues and Eigenvectors Analysis of
Random Structure Systems[J]. Journal of Vibration and Shock, 2002,
21(1): 77-78.
[9]
ZHANG Yimin, LIU Qiaoling, WEN Bangchun. Probability analysis of
eigenvalue problem with general real matrices in random structural
systems[J]. Chinese Quarterly of Mechanics, 2003, 24(4): 522-527.
[10] LIEW K M, HE X Q, NG T Y, et al. Finite element piezothermoelasticty
analysis and the active control of FGM plates with integrated
piezoelectric sensors and actuators[J]. Computational
Mechanics, 2003, 31: 350-358.
[11] WANG. Dongwei. Dynamics and distributed control of geometrically
nonlinear active piezothermoelastic structronic systems using the finite
element technique[D]. Kentucky: University of Kentucky, 2003.
[12]
ZHONG Wanxie. On precise time-integration method for structural
dynamics[J]. Journal of Dalian University of Technology, 1994,
4(2): 131-136.
[13]
CHENG Lejin, XUE Mingde, TANG Yuye, et al. Thermal- dynamic analysis of
large scale space structures by FEM[J]. Cinese Journal of Applied
Mechanics, 2004, 21(2): 1-9.
|