Abstract
A method based on newly presented state space formulations is developed for analyzing the bending, vibration and stability of laminated transversely isotropic rectangular plates with simply supported edges. By introducing two displacement functions and two stress functions, two independent state equations were constructed based on the three-dimensional elasticity equations for transverse isotropy. The original differential equations are thus decoupled with the order reduced that will facilitate obtaining solutions of various problems. For the simply supported rectangular plate, two relations between the state variables at the top and bottom surfaces were established. In particular, for the free vibration (stability) problem, it is found that there exist two independent classes: One corresponds to the pure in-plane vibration (stability) and the other to the general bending vibration (stability). Numerical examples are finally presented and the effects of some parameters are discussed.
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References
Das Y C, Setlur A V. Method of initial functions in two-dimensional elastodynamic problems[J].J Appl Mech, 1970,7(1):137–140.
Fan J R, Ye J Q. An exact solution for the statics and dynamics of laminated thick plate with orthotropic layers[J].Int J Solids Struct, 1990,26(5/6):655–662.
DING Hao-jiang, XU Rong-qiao, CHEN Wei-qiu, Chi Y W. Free axisymmetric vibration of transversely isotropic laminated circular plates[J].Acta Mechanica Solida Sinica, 1998,11(3):209–215.
DING Hao-jiang, LIANG Jian, ZOU Dao-qin.Transversely Isotropic Elasticity[M]. Hangzhou: Zhejiang University Press, 1997. (in Chinese)
DING Hao-jiang, Chen B, Liang J. On the general solutions for coupled equation for piezoelectric media[J].Int J Solids Struct, 1996,33(16):2283–2298.
LUO Jia-hong.Introduction to the Matrix Analysis[M]. Guangzhou:Press of Huanan University of Science and Technology, 1992. (in Chinese)
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(Paper from DING Hao-jiang, Member of Editorial Committee, AMM)
Foundation item: the National Natural Science Foundation of China (19872060)
Biography: DING Hao-jiang (1934−), Professor, Doctor Director
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Hao-jiang, D., Wei-qiu, C. & Rong-qiao, X. On the bending, vibration and stability of laminated rectangular plates with transversely isotropic layers. Appl Math Mech 22, 17–24 (2001). https://doi.org/10.1007/BF02437941
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DOI: https://doi.org/10.1007/BF02437941