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| Chaos of thin circular functionally graded plate in thermal environment |
| Received:July 26, 2010 Revised:November 09, 2011 |
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| DOI：10.7511/jslx20122020 |
| KeyWord:functionally graded material thin circular thermal load chaos bifurcation |
| Author | Institution |
| 胡宇达 |
燕山大学 河北省重型装备与大型结构力学可靠性重点实验室, 秦皇岛 |
| 张志强 |
燕山大学 河北省重型装备与大型结构力学可靠性重点实验室, 秦皇岛 |
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| Abstract: |
| A ceramic/metal functionally graded circular plate was considered in this study. The effect of geometric nonlinearity and temperature-dependent material properties are both taken into account. The material properties of the functionally graded plate are assumed to vary continuously through the thickness, according to a power law distribution of the volume fraction of the constituents. Using the principle of virtual work, the nonlinear partial differential equations of FGM plate subjected to transverse harmonic excitation force and thermal load are derived. For the circular plate with clamped immovable edge, the Duffing nonlinear forced vibration equation is deduced by using Galerkin method. The criterion of existence of chaos is given with Melnikov method. Numerical simulation is carried out to plot the bifurcation curves for the homolinic orbits. Effect of the material volume fraction index and temperature to the criterion are discussed and the existence of chaos is validated by plotting phase portraits Poincare map. Also, the bifurcation diagram and the corresponding maximum Lyapunov exponent are plotted. It was found that periodic, multiplier periodic solutions and chaotic motions exist for the FGM plate under certain conditions. |
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