| QUALITATIVE ANALYSIS OF DYNAMICAL BEHAVIOR FOR AN IMPERFECT INCOMPRESSIBLE NEO-HOOKEAN SPHERICAL SHELL |
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| 作者姓名： | YUAN Xue-gang |
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| 作者单位： | Shanghai Institute of Applied Mathematics and Mechanics，Shanghai University，Shanghai Institute of Applied Mathematics and Mechanics，Shanghai University，Department of Mathematics and Information Science，Yantai University Shanghai 200072，P.R.China，Department of Mathematics and Information Science，Yantai University，Yantai 264005，Shandong Province，P.R.China，Shanghai 200072，P.R.China，Yantai 264005，Shandong Province，P.R.China |
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| 基金项目： | Project supported by the National Natural Science Foundation of China （ No. 10272069 ） and the Municipal Key Subject Program of Shanghai |
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| 摘 要： | IntroductionIn applications, it is commonly considered that the phenomena of cavity formation,growth and run-through of adjacent cavities occur in materials as precursors to failure. Thesephenomena are mainly due to instability of materials. On the other …
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| 关 键 词： | NEO-HOOKEAN材料 动态特性 临界值 非线性周期振动 定性分析 |
| 文章编号： | 0253-4827（2005）08-0973-09 |
| 收稿时间： | 2003-12-20 |
| 修稿时间： | 2005-03-22 |
Qualitative analysis of dynamical behavior for an imperfect incompressible neo-Hookean spherical shell |
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| Yuan Xue-gang,Zhu Zheng-you,Cheng Chang-jun.QUALITATIVE ANALYSIS OF DYNAMICAL BEHAVIOR FOR AN IMPERFECT INCOMPRESSIBLE NEO-HOOKEAN SPHERICAL SHELL[J].Applied Mathematics and Mechanics(English Edition),2005,26(8):973-981. |
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| Authors: | Yuan Xue-gang Zhu Zheng-you Cheng Chang-jun |
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| Institution: | 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University,Shanghai 200072, P. R. China;Department of Mathematics and Information Science, Yantai University,Yantai 264005, Shandong Province, P. R. China
2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University,Shanghai 200072, P. R. China |
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| Abstract: | The radial symmetric motion problem was examined for a spherical shell composed of a class of imperfect incompressible hyper-elastic materials, in which the materials may be viewed as the homogeneous incompressible isotropic neo-Hookean material with radial perturbations. A second-order nonlinear ordinary differential equation that describes the radial motion of the inner surface of the shell was obtained.And the first integral of the equation was then carried out. Via analyzing the dynamical properties of the solution of the differential equation, the effects of the prescribed imperfection parameter of the material and the ratio of the inner and the outer radii of the underformed shell on the motion of the inner surface of the shell were discussed, and the corresponding numerical examples were carried out simultaneously. In particular, for some given parameters, it was proved that, there exists a positive critical value, and the motion of the inner surface with respect to time will present a nonlinear periodic oscillation as the difference between the inner and the outer presses does not exceed the critical value. However, as the difference exceeds the critical value, the motion of the inner surface with respect to time will increase infinitely.That is to say, the shell will be destroyed ultimately. |
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| Keywords: | imperfect incompressible neo-Hookean material dynamical behavior critical value nonlinear periodic oscillation |
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