Hamiltonian Parametric Element and Semi-Analytical Solution for Smart Laminated Plates

QING Guang-hui; QIU Jia-jun; LIU Yan-hong

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2007 > 28(1): 45-52

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.

Citation:

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.

Citation:

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.

PDF( 334 KB)

Hamiltonian Parametric Element and Semi-Analytical Solution for Smart Laminated Plates

1.
Aeronautical Mechanics and Avionics Engineering College, Civil Aviation University of China, Tianjin 300300, P. R. China;

Received Date: 2005-03-29
Rev Recd Date: 2006-10-27
Publish Date: 2007-01-15

Abstract

Abstract

Based on the Hellinger-Reissner (H-R) mixed variational principle for piezoelectric material, a unified 4-node Hamiltonian isoparametric element of anisotropy piezoelectric material was established. A new semi-analytical solution for the natural vibration of smart laminated plates and the transient response of the laminated cantilever with piezoelectric patch was presented. The major steps of mathematical model are as follows: the piezoelectric layer and host layer of laminated plate were considered as unattached three-dimensional bodies and discretized by the Hamiltonian isoparametric elements. The control equation of whole structure was derived by considering the compatibility of generalized displacements and generalized stresses on the interface between layers. There is no restriction for the side-face geometrical boundaries, the thickness and the number of layers of plate by the use of the present isoparametric element. The present method has a wide application a.
- piezoelectric material,
- smart laminated plate,
- vibration analysis,
- Hamiltonian isoparametric element,
- semi-analytical solution

FullText(HTML)

References(12)

References

[1]	冯康，秦孟兆. Hamilton动力体系的Hamilton算法[J].自然科学进展-国家重点实验室,1990,试刊(2)：110-120.
[2]	钟万勰.条形城平面弹性问题和哈密尔顿体系[J].大连理工大学学报,1991,31(4)：373-384.
[3]	唐立民.弹性力学的混合方程和Hamilton正则方程[J].计算结构力学及其应用，1991,8(4)：343-349.
[4]	钟万勰. 弹性力学求解新体系[M].大连：大连理工大学出版社,1995,155-159.
[5]	卿光辉,邱家俊,塔娜.压电体的变分原理及叠层板的自由振动分析[J].振动工程学报,2004，17(3)：285-290.
[6]	Benjeddou A. Advances in piezoelectric finite element modeling of adaptive structural elements:a survey[J].Computers & Structures,2000,76(1)：347-363.
[7]	Saravanos D A, Heyliger P R,Hopkins D A. Layerwise mechanics and finite element for the dynamic analysis of piezoelectric composite plates[J].International Journal of Solids and Structures,1997,34(3):359-378. doi: 10.1016/S0020-7683(96)00012-1
[8]	唐立民,褚致中,王治国,等.混合状态Hamiltonian元的半解析解和叠层板的计算 [J].计算结构力学及其应用,1992,9(4)：347-360.
[9]	邹贵平.复合材料层合板壳的混合状态方程、Hamilton正则方程及其半解析法[D]. 博士论文.大连：大连理工大学，1994,11-240.
[10]	Reddy J N. Dynamic (transient) analysis of layered anisotropic composite material plates[J].International Journal Numeric Method and Engineering,1983,19(2):237-255. doi: 10.1002/nme.1620190206
[11]	Lim Y H,Varandan V. Finite-element modeling of the transient response of MEMS sensors[J].Smart Material and Structures,1997,6(1):53-61. doi: 10.1088/0964-1726/6/1/007
[12]	卿光辉,邱家俊,塔娜.正则方程和整体加筋板的固有频率分析[J].力学学报,2004，[STHZ]. 36[STBZ]. (6):749-756.