共查询到16条相似文献,搜索用时 439 毫秒
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具有缺陷的不可压缩neo-Hookean球壳的动力学行为的定性分析 总被引:3,自引:0,他引:3
研究了一类具有缺陷的不可压缩超弹性材料球壳的径向对称运动问题,该类材料可以看作是带有径向摄动的均匀各向同性不可压缩的neo-Hookean材料.得到了描述球壳内表面运动的二阶非线性常微分方程,并给出了方程的首次积分.通过对微分方程的解的动力学行为的分析,讨论了材料的缺陷参数和球壳变形前的内外半径的比值对解的定性性质的影响,并给出了相应的数值算例.特别地,对于一些给定的参数,证明了存在一个正的临界值,当内压与外压之差小于临界值时,球壳内表面随时间的演化是非线性周期振动;当内压与外压之差大于临界值时,球壳的内表面半径随时间的演化将无限增大,即球壳最终将被破坏. 相似文献
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周期载荷下超弹性圆柱壳的动力响应 总被引:4,自引:2,他引:2
研究了不可压超弹性圆柱壳在内表面周期载荷及突加常值载荷作用下的运动与破坏等动力响应问题.通过对所得描述圆柱壳内表面运动的非线性常微分方程解的数值计算和动力学定性分析,发现存在一个临界载荷;当突加常值载荷或周期载荷的平均载荷值小于这一临界值时,圆柱壳的运动随时间的演化是周期性的或拟周期性的非线性振动,而当其大于这一临界值时,圆柱壳将被破坏.另外,准静态问题的解可作为突加常值载荷作用下系统动力响应解的不动点,且不动点的性质与动力响应解及圆柱壳运动的性质有关.讨论了圆柱壳的厚度和载荷等参数对临界载荷值和圆柱壳运动特性的影响. 相似文献
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一个非线性微分方程的周期边值问题 总被引:2,自引:0,他引:2
本文考虑作为卫星绕椭圆轨道作周期运动模型的一个二阶非线性微分方程的周期边值问题.用迭代方法证明了奇函数周期解的存在性,并且扩大了文[3]中给出的参数范围. 相似文献
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本文利用变分方法给出了具不对称非线性项的二阶常微分方程周期解的存在性的充分条件,通过例子说明本文的主要结果可看作是Landesman-Lazer条件的补充。 相似文献
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二阶多时滞非线性微分方程的周期解 总被引:2,自引:0,他引:2
张保生 《纯粹数学与应用数学》1998,14(4):62-66
研究二阶系数非线性多时滞微分方程ω周期解的存在性,得到了ω周期解存在的充分条件。 相似文献
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在Banach中,本文在很弱条件下,通过迭代序列得到了不连续二阶非线性微分方程的周期边值问题的唯一解存在性的一个充分条件,而且给出了迭代序列近代解的误差估计. 相似文献
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研究了一类含参泛函微分方程反周期解的存在性.获得了当参数在一定范围取值时反周期解的存在性结果,得到了反周期解存在的充分条件,并通过例子表明结果的可行性.主要工具为Leray-Schauder非线性抉择. 相似文献
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本运用Liapunov函数方法,研究了一类四阶非线性微分方程的周期解,得到了存在唯一渐近稳定的周期解的充分条件。 相似文献
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一类非线性微分方程的概周期解 总被引:1,自引:0,他引:1
运用Leray-Schauder不动点定理和Liapunov函数方法,研究了一类非线性微分方程的概周期解,得到了该微分方程概周期解存在的充分条件. 相似文献
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Nonlinear vibration analysis of circular cylindrical shells has received considerable attention from researchers for many decades. Analytical approaches developed to solve such problem, even not involved simplifying assumptions, are still far from sufficiency, and an efficient numerical scheme capable of solving the problem is worthy of development. The present article aims at devising a novel numerical solution strategy to describe the nonlinear free and forced vibrations of cylindrical shells. For this purpose, the energy functional of the structure is derived based on the first-order shear deformation theory and the von–Kármán geometric nonlinearity. The governing equations are discretized employing the generalized differential quadrature (GDQ) method and periodic differential operators along axial and circumferential directions, respectively. Then, based on Hamilton's principle and by the use of variational differential quadrature (VDQ) method, the discretized nonlinear governing equations are obtained. Finally, a time periodic discretization is performed and the frequency response of the cylindrical shell with different boundary conditions is determined by applying the pseudo-arc length continuation method. After revealing the efficiency and accuracy of the proposed numerical approach, comprehensive results are presented to study the influences of the model parameters such as thickness-to-radius, length-to-radius ratios and boundary conditions on the nonlinear vibration behavior of the cylindrical shells. The results indicate that variation of fundamental vibrational mode shape significantly affects frequency response curves of cylindrical shells. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2007,12(4):496-518
The dynamics of a circular cylindrical shell carrying a rigid disk on the top and clamped at the base is investigated. The Sanders–Koiter theory is considered to develop a nonlinear analytical model for moderately large shell vibration. A reduced order dynamical system is obtained using Lagrange equations: radial and in-plane displacement fields are expanded by using trial functions that respect the geometric boundary conditions.The theoretical model is compared with experiments and with a finite element model developed with commercial software: comparisons are carried out on linear dynamics.The dynamic stability of the system is studied, when a periodic vertical motion of the base is imposed. Both a perturbation approach and a direct numerical technique are used. The perturbation method allows to obtain instability boundaries by means of elementary formulae; the numerical approach allows to perform a complete analysis of the linear and nonlinear response. 相似文献
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扁锥面网壳非线性动力分岔与混沌运动 总被引:2,自引:0,他引:2
对曲面为正三角形网格的3向扁锥面单层网壳,用拟壳法建立了轴对称非线性动力学方程.在几何非线性范围内给出了协调方程.网壳在周边固定条件下,通过Galerkin作用得到一个含2次、3次的非线性微分方程,通过求Floquet指数讨论了分岔问题.为了研究混沌运动,对一类非线性动力系统的自由振动方程进行了求解,继之给出了单层扁锥面网壳非线性自由振动微分方程的准确解,通过求Melnikov函数,给出了发生混沌的临界条件,通过数值仿真也证实了混沌运动的存在. 相似文献
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两自由度非线性振动系统周期运动及其稳定性研究 总被引:1,自引:0,他引:1
运用Liapunov函数方法,对一类两自由度非线性振动系统周期运动及其稳定性进行了研究,得到了存在唯一渐近稳定的周期解的充分条件. 相似文献