【作者】 张军柯；

【导师】 王知人；

【作者基本信息】 燕山大学 ， 概率论与数理统计， 2009， 硕士

【摘要】 电磁固体力学是研究在弹性固态物质中,电磁场与变形场相互作用的理论。板壳磁弹性非线性振动问题在工程实际中比较常见,其控制方程的建立和求解具有很大难度,因此研究板壳磁弹性非线性振动具有重要的理论和实际意义。论文首先在建立薄板磁弹性非线性振动方程的基础上,得到梁式板的非线性振动方程,运用中心流形定理和方法对其分岔行为进行了具体分析,画出了分岔图,并运用Melnikov函数方法得到发生全局分岔的条件。其次,对梁式板的振动方程引入参数进行变换,运用多尺度方法求出梁式板主共振下的二阶定常解,用奇异性理论得到分岔方程并求出转迁集,导电梁式板在不同的转迁集的条件下发生分岔的条件是不相同的,求解可得到歧集和双极限点集内分岔条件是不存在,分岔只发生在滞后集内,在滞后集条件下求出了分岔条件。最后,将两边简支的边界条件带入圆柱薄壳振动方程,得到了圆柱薄壳的带立方和平方项的振动微分方程,用多尺度方法求出主共振解的分岔方程,分析了系统运动中解的稳定性,运用奇异性理论得到分岔方程的转迁集,导电圆柱薄壳在不同的转迁集区域内有不同的分岔条件,圆柱薄壳在歧集和滞后集内分岔条件不存在。分岔只发生在双极限点集内,在双极限点集的条件下求出了分岔条件。更多还原

【Abstract】 Electromagnetism solid mechanics study electromagnetic field and deformation field interoperable theory of flexibility solid matter, Plate and Shell magnetoelasticity nonlinear vibrational subject is relatively common of engineering reality, Establish and Solve of governing equation have very great difficulty, So to study Plate and Shell magnetoelasticity nonlinear vibrational subject have important theory and reality meaning.This paper firstly according to equation of magnetoelasticity nonlinear vibration, Gain nonlinear vibrational equation of Beam-plate, Specific analyse bifurcation factor of Beam-plate by Center-manifold-theorem, And gain exist factor of global bifurcation by Melnikov function.Secondly adhibit parameter to vibrational equation of the conductive Beam-plate and transform, Gain master syntonic single and second order stable common solution by Multi-scale means, Gain equation of bifurcation and Anslyze behaviour of bifurcation by Strangeness-theory, Different change sum of sequences have different bifurcation of the conductive Beam-plate.volume. Solving and Gain factor of bifurcation is not exist of fork volume and double limit point volume, Bifurcation only exist of lag volume, Gain factor of bifurcation at lag volume field.Finally adhibit boundary condition to vibrational equation of simply supported on both bides of Column-thin-shell, Gain vibrational differential equation of Column-thin-shell and This equation have cubic and squared term, Find master syntonic solutional equation of bifurcation. Gain equation of bifurcation and Anslyze behaviour of bifurcation by Strangeness-theory, Different change sum of sequences have different bifurcation volume of the conductive Column-thin-shell. Factor of bifurcation is not exist of fork volume and lag volume, Bifurcation only exist of double limit point volume, Gain factor of bifurcation at double limit point volume field.更多还原