排序方式: 共有43条查询结果,搜索用时 15 毫秒
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本文研究一类含小参数的Hill方程的初值问题,利用边值问题可解性条件及摄动理论中的伸缩参数法,给出寻求该初值问题近似周期解的方法,并以Mathieu方程为例作了具体计算. 相似文献
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本文用奇异摄动理论多尺度法的导数展开法[1],求解了在微粘性阻尼作用下,连结在一个非线性弹簧上的一个质点的受迫振动方程.研究的是四次非线性问题,讨论了四种情况:非共振的软激发;非共振的硬激发;共振的软激发;共振的硬激发. 相似文献
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本文首先给出变厚度圆薄板大挠度方程,用小参数方法和修正迭代法联合求解此问题,得到三次近似解;给出特征曲线同线性理论进行了比较. 相似文献
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IntroductionTheproblemofnonlinearvibrationisveryimportantnotonlyintheorybutalsoinapplication .Theconicshellplaysanimportantroleinarchitecture ,navigation ,spaceflightandwasusedastheelasticcomponentoftheinstrumentwidely .Thenonlinearvibrationofshellisacomplicatedproblemanditisdifficulttosolveinmechanicsandmathematics .Itismoredifficultiftheactionofouterloads (staticload ,thermalload ,magnetic)istakenintoaccount[1~7].Thereisdifferentinterestineventhenonlinearvibrationundertheactionofstaticload… 相似文献
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By using the method of quasi-shells,the nonlinear dynamic equations of three-dimensional single-layer shallow cylindrical reticulated shells with equilateral tri- angle cell are founded.By using the method of the separating variable function,the transverse displacement of the shallow cylindrical reticulated shells is given under the conditions of two edges simple support.The tensile force is solved out from the compati- ble equations,a nonlinear dynamic differential equation containing second and third order is derived by using the method of Galerkin.The stability near the equilibrium point is discussed by solving the Floquet exponent and the critical condition is obtained by using Melnikov function.The existence of the chaotic motion of the single-layer shallow cylin- drical reticulated shell is approved by using the digital simulation method and Poincarémapping. 相似文献
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扁薄球壳非对称大变形问题 总被引:7,自引:3,他引:7
本文用修正选代法研究了扁球壳非对称大变形问题,求得了在线性液体载荷作用下的扁球壳变形的二次近似解析解并绘出了摄动点的挠度与载荷的特征曲线族.应用本文方法还可对其他板壳的非轴对称大变形问题进行讨论.本文通过算例对平板及不同初挠度的扁球壳大挠度变形进行了讨论. 相似文献
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In this paper, we consider the initial value problem of a class of Hill’s equation having a small parameter. Using the solvable condition of boundary value problem and the stretched parameter method in the perturbation techniques, we present the method which can be applied to obtain asymptotic periodic solution of the initial value problem. As an example, we consider Mathieu equation and present its computational result. 相似文献
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To begin with, in this paper, the displacement governing equations and the boundary conditions of nonsymmetrical large deflection problem of circular thin plates are derived. By using the transformation and the perturbation method, the nonlinear displacement equations are linearized, and the approximate boundary value problems are obtained. As an example, the nonlinear bending problem of circular thin plates subjected to comparatively complex loads is studied. 相似文献