Hamiltonian parametric element and semi-analytical solution for smart laminated plates
- 36 Downloads
Based on the Hellinger-Reissner (H-R) mixed variational principle for piezoelectric material, a unified 4-node Hamiltonian isoparametric element of anisotropy piezoelectric material is 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 is presented. The major steps of mathematical model are as follows: the piezoelectric layer and host layer of laminated plate are considered as unattached three-dimensional bodies and discretized by the Hamiltonian isoparametric elements. The control equation of whole structure is 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. Present method has wide application area.
Key wordspiezoelectric material smart laminated plate vibration analysis Hamiltonian isoparametric element semi-analytical solution
Chinese Library ClassificationO343.2 O176
2000 Mathematics Subject Classification74B99 49S05
Unable to display preview. Download preview PDF.
- Feng Kang, Qin Mengzao. Hamilton method for Hamilton dynamics systematic methodology[J]. Advance in Natural Science-State Key Laboratory Communication, 1990, Test(2):110–120 (in Chinese).Google Scholar
- Tang Limin. Mixed formulation and Hamilton canonical equations of theory of elasticity[J]. Computational Structural Mechanics and Applications, 1991, 8(4):343–349 (in Chinese).Google Scholar
- Zhong Wanxie. A new systematic methodology for theory of elasticity[M]. Dalian: Dalian University of Technology Press, 1995, 155–159 (in Chinese).Google Scholar
- Qing Guanghui, Qiu Jiajun, Ta Na. Modified H-R mixed variational principle for piezoelectric material and free vibration analysis of composite laminates with piezoelectric layers[J]. Journal of Vibration Engineering, 2004, 17(3):285–290 (in Chinese).Google Scholar
- Tang Limin, Chu Zhizhong, Wang Zhiguo, et al. The semi-analytical solutions of mixed state Hamiltonian element and the computation laminated plates[J]. Computational Structural Mechanics and Applications, 1992, 9(4):347–360 (in Chinese).Google Scholar
- Zou Guiping. The mixed state equation, hamilton canonical equation and a semi-analytical solution for the analysis of laminated composite plate and shells[D]. Ph D Dissertation. Dalian: Dalian University of Technology, 1994, 11–240 (in Chinese).Google Scholar
- Qing Guanghui, Qiu Jiajun, Ta Na. Hamilton canonical equation for elastic bodies and natural frequencies analysis of integral stiffened plates[J]. Acta Mechanica Sinica, 2004, 36(6):749–756 (in Chinese).Google Scholar