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1.
范存旭 《应用数学和力学(英文版)》1990,11(12):1175-1185
This paper deals with the research of accuracy of differential equations of deflections.The basic idea is as follows.Firstly,considering the boundary effect the meridianmidsurface displacement u=0,thus we derive the deflection differential equations;secondly we accurately prove that by use of the deflection differential equations or theoriginal differential equations the same inner forces solutions are obtained;finally,weaccurately prove that considering the boundary effect the meridian surface displacementu=0 is an exact solution.In this paper we give the singular perturbation solution of thedeflection differential equations.Finally we check the equilibrium condition and prove theinner forces solved by perturbation method and the outer load are fully equilibrated.Itshows that perturbation solution is accurate.On the other hand,it shows again that thedeflection differential equation is an exact equation.The features of the new differential equations are as follows:1.The accuracies of the new differentia 相似文献
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引入分数因子和分数增量,给出了分数阶微积分的定义和性质;基于分数阶导数的定义,证明了含有分数因子的等时变分与分数阶算子的交换关系;提出了分数阶完整保守和非保守系统的Hamilton原理;建立了分数阶完整保守系统和非保守系统的运动微分方程;得到了分数阶完整保守系统的循环积分;并利用分数阶循环积分导出分数阶罗兹方程.最后给出了两个例子.研究表明利用分数因子给出的分数阶微分方程是一个含有分数因子的通常的微分方程,那么分数阶系统运动微分方程的求解都可以采用通常微分方程的求解方法. 相似文献
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Quaternion Regularization of the Equations of the Perturbed Spatial Restricted Three-Body Problem: I
Yu. N. Chelnokov 《Mechanics of Solids》2017,52(6):613-639
We develop a quaternion method for regularizing the differential equations of the perturbed spatial restricted three-body problem by using the Kustaanheimo–Stiefel variables, which is methodologically closely related to the quaternion method for regularizing the differential equations of perturbed spatial two-body problem, which was proposed by the author of the present paper.A survey of papers related to the regularization of the differential equations of the two- and threebody problems is given. The original Newtonian equations of perturbed spatial restricted three-body problem are considered, and the problem of their regularization is posed; the energy relations and the differential equations describing the variations in the energies of the system in the perturbed spatial restricted three-body problem are given, as well as the first integrals of the differential equations of the unperturbed spatial restricted circular three-body problem (Jacobi integrals); the equations of perturbed spatial restricted three-body problem written in terms of rotating coordinate systems whose angular motion is described by the rotation quaternions (Euler (Rodrigues–Hamilton) parameters) are considered; and the differential equations for angular momenta in the restricted three-body problem are given.Local regular quaternion differential equations of perturbed spatial restricted three-body problem in the Kustaanheimo–Stiefel variables, i.e., equations regular in a neighborhood of the first and second body of finite mass, are obtained. The equations are systems of nonlinear nonstationary eleventhorder differential equations. These equations employ, as additional dependent variables, the energy characteristics of motion of the body under study (a body of a negligibly small mass) and the time whose derivative with respect to a new independent variable is equal to the distance from the body of negligibly small mass to the first or second body of finite mass.The equations obtained in the paper permit developing regular methods for determining solutions, in analytical or numerical form, of problems difficult for classicalmethods, such as the motion of a body of negligibly small mass in a neighborhood of the other two bodies of finite masses. 相似文献
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Lie??s linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing transformations but also the solutions of the nonlinear equations. Here, complex methods for a scalar ordinary differential equation are used for linearizing systems of two second-order ordinary and partial differential equations, which can use the power of the geometric method for writing the solutions. Illustrative examples of mechanical systems including the Lane?CEmden type equations which have roots in the study of stellar structures are presented and discussed. 相似文献
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《International Journal of Solids and Structures》1999,36(19):2807-2824
A semi-analytic method is presented for the analysis of transient response of one-dimensional distributed parameter systems. Replacing time differentials by finite difference, the governing partial differential equations are reduced to difference–differential equations. The solutions of derived ordinary differential equations are given in exact and closed form by distributed transfer function method. Complex systems that contain many one-dimensional sub-systems are also studied. Numerical results show that the efficiency and accuracy of the method are excellent. 相似文献
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压电复合材料层合梁的分岔、混沌动力学与控制 总被引:1,自引:0,他引:1
研究了简支压电复合材料层合梁在轴向、横向载荷共同作用下的非线性动力学、分岔和混沌动力学响应. 基于vonKarman理论和Reddy高阶剪切变形理论,推导出了压电复合层合梁的动力学方程. 利用Galerkin法离散偏微分方程,得到两个自由度非线性控制方程,并且利用多尺度法得到了平均方程. 基于平均方程,研究了压电层合梁系统的动态分岔,分析了系统各种参数对倍周期分岔的影响及变化规律. 结果表明,压电复合材料层合梁周期运动的稳定性和混沌运动对外激励的变化非常敏感,通过控制压电激励,可以控制压电复合材料层合梁的振动,保持系统的稳定性,即控制系统产生倍周期分岔解,从而阻止系统通过倍周期分岔进入混沌运动,并给出了控制分岔图. 相似文献
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The paper systematically investigates the plane elasticity problems of two-dimensional quasicrystals with noncrystal rotational symmetry. First, applying their independent elastic constants, the equilibrium differential equations of the problems in terms of displacements are derived and it is found that the plane elasticity of pentagonal quasicrystals is the same as that of decagonal. Then by introducing displacement functions, huge numbers of complicated partial differential equations of the problems are simplified to a single or a pair of partial differential equations of higher order, which is called governing equations, such that the problems can be easily solved. Finally, some solving methods of these governing equations obtained are introduced briefly. 相似文献
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ARC-length method for differential equations 总被引:1,自引:0,他引:1
IntroductionTheordinaryandpartialdiferentialequationsofcontinuumproblemareoftenwithcertaintypesofsingularityasstifproperty,or... 相似文献
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针对圆柱体的三维温度场分析,提出了一种高效的半解析-精细积分法。将温度场展开为环向坐标的Fourier级数,并对径向坐标进行差分离散,从而把三维热传导方程简化为一系列二阶常微分方程;将这些二阶常微分方程转化为哈密顿体系下的一阶状态方程,并利用两点边值问题的精细积分法求解。由于该方法仅对径向坐标进行差分离散,故相对于传统的数值方法离散规模大幅度减少,不仅提高了计算效率、降低了存贮量,而且缓解了代数方程的病态问题。此外,针对Fourier半解析解,根据热平衡原理推导出了两种材料衔接面的半解析差分方程,从而为求解复合材料层合柱问题打下了基础。算例结果表明,即使对于细长比高达400的圆柱杆件,此方法仍然可以给出精度较高的解答。 相似文献
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A new two-eigenfunctions theory, using the amplitude deflection and the generalized curvature as two fundamental eigenfunctions, is proposed for the free vibration solutions of a rectangular Mindlin plate. The three classical eigenvalue differential equations of a Mindlin plate are reformulated to arrive at two new eigenvalue differential equations for the proposed theory. The closed form eigensolutions, which are solved from the two differential equations by means of the method of separation of variables are identical with those via Kirchhoff plate theory for thin plate, and can be employed to predict frequencies for any combinations of simply supported and clamped edge conditions. The free edges can also be dealt with if the other pair of opposite edges are simply supported. Some of the solutions were not available before. The frequency parameters agree closely with the available ones through pb-2 Rayleigh-Ritz method for different aspect ratios and relative thickness of plate. 相似文献
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M. N. Tufail A. S. Butt A. Ali 《Journal of Applied Mechanics and Technical Physics》2016,57(5):900-907
An investigation has been conducted on the MHD Casson fluid and heat transfer over an unsteady stretching sheet with viscous dissipation effects. With suitable dimensionless variables, partial differential equations are reduced to ordinary differential equations, which are then solved by the homotopy analysis method. Dependences of flow characteristics on various parameters involved into the equations are obtained. 相似文献
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I. Bosch Vivancos P. Chossat I. Melbourne 《Archive for Rational Mechanics and Analysis》1995,131(3):199-224
Dionne & Golubitsky [10] consider the classification of planforms bifurcating (simultaneously) in scalar partial differential equations that are equivariant with respect to the Euclidean group in the plane. In particular, those planforms corresponding to isotropy subgroups with one-dimensional fixed-point space are classified.Many important Euclidean-equivariant systems of partial differential equations essentially reduce to a scalar partial differential equation, but this is not always true for general systems. We extend the classification of [10] obtaining precisely three planforms that can arise for general systems and do not exist for scalar partial differential equations. In particular, there is a class of one-dimensional pseudoscalar partial differential equations for which the new planforms bifurcate in place of three of the standard planforms from scalar partial differential equations. For example, the usual rolls solutions are replaced by a nonstandard planform called anti-rolls. Scalar and pseudoscalar partial differential equations are distinguished by the representation of the Euclidean group. 相似文献
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导出了扇形截面杆扭转问题偏微分方程的差分线法常微分方程组, 并解析求解了该方程组,
得到了扭转应力函数的半解析解, 计算了扭转应力及扭转刚度. 计算过程中, 用追赶法计算
常微分方程组的特解, 用公式计算三对角矩阵的特征值与特征向量, 利用实对阵矩阵的特征
向量相互正交的特性避免矩阵求逆计算, 利用复化梯形公式计算扭转刚度. 整个求解过程在
角度方向离散微分方程和用复化梯形公式进行面积积分时引入了误差, 其他求解过程是精确
的. 计算结果与已有结果进行了对比, 显示了算法的正确性. 该算法对工程中扇形截面扭
转杆的设计有一定的实用价值. 相似文献
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Based on the Timoshenko beam model the equations of motion are obtained for large deflection of off-center impact of a column by a rigid mass via Hamilton's principle. These are a set of coupled nonlinear partial differential equations. The Newmark time integration scheme and differential quadrature method are employed to convert the equations into a set of nonlinear algebraic equations for displacement components. The equations are solved numerically and the effects of weight and velocity of the rigid mass and also off-center distance on deformation of the column are studied. 相似文献
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IntroductionAsweknow ,intheinvestigationofthepropertiesofsolutionsfornonlineardifferentialequations,themethodofvariationofparametersisaneffectivetoolinthecasethatthecorrespondingunperturbedtermsarelinearorofcertainsmoothnessthoughtheyarenonlinear.Onthe… 相似文献
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Criteria are established for higher order ordinary differential equations to be compatible with lower order ordinary differential equations. Necessary and sufficient compatibility conditions are derived which can be used to construct exact solutions of higher order ordinary differential equations subject to lower order equations. We provide the connection to generalized groups through conditional symmetries. Using this approach of compatibility and generalized groups, new exact solutions of non-linear flow problems arising in the study of Newtonian and non-Newtonian fluids are derived. The ansatz approach for obtaining exact solutions for non-linear flow models of Newtonian and non-Newtonian fluids is unified with the application of the compatibility and generalized group criteria. 相似文献
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Oscillatory properties of the solutions of nonlinear delay hyperbolic differential equations of neutral type 总被引:2,自引:0,他引:2
Thenewly—developedtheoryofnonlineardelaypartialfunctionaldifferentialequationsareappliedinmanyfields,suchasinengineering ,biology,medicine,physicsandchemistry .Aseriesofsufficientconditions,necessaryandsufficientconditionsforoscillationsoftheequationswer… 相似文献