共查询到20条相似文献,搜索用时 38 毫秒
1.
M. Sajid T. Hayat S. Asghar K. Vajravelu 《Archive of Applied Mechanics (Ingenieur Archiv)》2008,78(2):127-134
An analysis is performed for the boundary-layer flow of a viscous fluid over a nonlinear axisymmetric stretching sheet. By
introducing new nonlinear similarity transformations, the partial differential equations governing the flow are reduced to
an ordinary differential equation. The resulting ordinary differential equation is solved using the homotopy analysis method
(HAM). Analytic solution is given in the form of an infinite series. Convergence of the obtained series solution is explicitly
established. The solution for an axisymmetric linear stretching sheet is obtained as a special case. 相似文献
2.
This study investigates the nonlinear dynamics of a rotating circular string subjected to a spring force fixed in space. The governing equation for out-of-plane vibration is developed using Hamilton's principle. The nonlinearities of the string deformation and the spring stiffness are considered in the governing equation. Applying Galerkin's method, the governing equation is transformed from a nonlinear partial differential equation into a set of coupled nonlinear ordinary differential equations through orthogonal trigonometric shape functions. Butenin's method is adopted to develop a closed-form analytical solution for single-mode oscillations of the system. Comparison shows that the closed-form solution is in a good agreement with the numerical results over a wide range of the nonlinearities. Multi-mode responses of the string are investigated by means of numerical integration. Based on the results, the nonlinear dynamics of the string are discussed. 相似文献
3.
INTEGRABLETYPESOFNONLINEARORDINARYDIFFERENTIALEQUATIONSETSOFHIGHERORDERSTangGuangsong(汤光宋)(MathematicsDepartment,JianghanUniv... 相似文献
4.
Energy conservation of nonlinear Schrodinger ordinary differential equation was proved through using continuous finite element methods of ordinary differential equation; Energy integration conservation was proved through using space-time continuous fully discrete finite element methods and the electron nearly conservation with higher order error was obtained through using time discontinuous only space continuous finite element methods of nonlinear Schrodinger partial equation. The numerical results are in accordance with the theory. 相似文献
5.
Energy conservation of nonlinear Schrodinger ordinary differential equation was proved through using continuous finite element methods of ordinary differential equation; Energy integration conservation was proved through using space-time continuous fully discrete finite element methods and the electron nearly conservation with higher order error was obtained through using time discontinuous only space continuous finite element methods of nonlinear Schrodinger partial equation. The numerical results are in accordance with the theory. 相似文献
6.
汪懋骅 《应用数学和力学(英文版)》1986,7(3):255-258
It is very difficult to obtain an exact analytical solution to a nonlinear ordinary differential equation, so till now analytical solutions are rare in this area. The author has obtained the exact analytical solutions of this type of nonlinear oscillations. In this paper as an example, the exact analytical solution of nonlinear oscillation of a two-dimen-sional lift body, which has attracted the attention of research workers for a long time, is given. 相似文献
7.
The nonlinear responses of planar motions of a fluid-conveying pipe embedded in nonlinear elastic foundations are investigated via the differential quadrature method discretization (DQMD) of the governing partial differential equation. For the analytical model, the effect of the nonlinear elastic foundation is modeled by a nonlinear restraining force. By using an iterative algorithm, a set of ordinary differential dynamical equations derived from the equation of motion of the system are solved numerically and then the bifurcations are analyzed. The numerical results, in which the existence of chaos is demonstrated, are presented in the form of phase portraits of the oscillations. The intermittency transition to chaos has been found to arise. 相似文献
8.
Yu. A. Mitropol’skii G. Matarazzo A. Pompei V. G. Samoilenko 《Nonlinear Oscillations》2004,7(4):461-472
The object of this paper is to study the problem of constructing an approximate solution of a first-order weakly nonlinear ordinary differential equation with deviating argument and slowly varying coefficients. On the basis of asymptotic techniques in nonlinear mechanics, we construct an algorithm for the asymptotic integration of the differential equation under consideration.__________Published in Neliniini Kolyvannya, Vol. 7, No. 4, pp. 475–486, October–December, 2004. 相似文献
9.
The boundary-layer flow and heat transfer in a viscous fluid containing metallic nanoparticles over a nonlinear stretching sheet are analyzed. The stretching velocity is assumed to vary as a power function of the distance from the origin. The governing partial differential equation and auxiliary conditions are reduced to coupled nonlinear ordinary differential equations with the appropriate corresponding auxiliary conditions. The resulting nonlinear ordinary differential equations (ODEs) are solved numerically. The effects of various relevant parameters, namely, the Eckert number Ec, the solid volume fraction of the nanoparticles φ, and the nonlinear stretching parameter n are discussed. The comparison with published results is also presented. Different types of nanoparticles are studied. It is shown that the behavior of the fluid flow changes with the change of the nanoparticles type. 相似文献
10.
Two-dimensional magnetohydrodynamic (MHD) boundary layer flow of an upper-convected Maxwell fluid is investigated in a channel. The walls of the channel are taken as porous. Using the similarity transformations and boundary layer approximations, the nonlinear partial differential equations are reduced to an ordinary differential equation. The developed nonlinear equation is solved analytically using the homotopy analysis method. An expression for the analytic solution is derived in the form of a series. The convergence of the obtained series is shown. The effects of the Reynolds number Re, Deborah number De and Hartman number M are shown through graphs and discussed for both the suction and injection cases. 相似文献
11.
IntroductionCablesareveryefficientstructuralmembersandhencehavebeenwidelyusedinmanylong_spanstructures,includingcable_supportbridges,guyedtowersandcable_supportroofs.Sincecablesarelight,veryflexibleandlightlydamped ,structuresutilizingcables,i.e .,cable_structuresystems,usuallyhavevariousdynamicproblems.Theirmodelsarethereforeverimportantinpredictingandcontrollingtheirresponses.Inthelastdecade,thenonlineardynamicvibrationandstabilitybehaviorofcablesandcable_structureshavedrawntheattentionofman… 相似文献
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14.
This study investigates the rotating magnetohydrodynamic (MHD) flow of a third-grade fluid in a porous space. Modified Darcy's
law has been utilized for the flow modeling. The Hall effects are taken into consideration. The basic equations governing
the flow are reduced to a highly nonlinear ordinary differential equation. This equation has been solved analytically by employing
the homotopy analysis method (HAM). The effects of the various interesting parameters on the velocity distribution have been
discussed. 相似文献
15.
Steady flow of a viscous incompressible fluid in a channel, driven by suction or injection of the fluid through the channel walls, is investigated. The velocity equation of this problem is reduced to nonlinear ordinary differential equation with two boundary conditions by appropriate transformation and convert the two‐point boundary‐value problem for the similarity function into an initial‐value problem in which the position of the upper channel. Then obtained differential equation is solved analytically using differential transformation method and compare with He's variational iteration method and numerical solution. These methods can be easily extended to other linear and nonlinear equations and so can be found widely applicable in engineering and sciences. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
16.
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
17.
功能梯度板的非线性动力分析 总被引:3,自引:1,他引:3
非线性材料功能梯度板件的动力分析是属于在数学方程上同时具有变系数、非线性、非定常特征的固体力学问题.文中首先将问题的变系数非线性偏微分方程组转化为各向异性常系数非线性常微分方程,然后用小参数法求得解析解,适用于各种形状、边界及功能梯度分布的板件非线性弹性振动分析. 相似文献
18.
In this article, the multi-step differential transform method (MsDTM) is applied to give approximate solutions of nonlinear ordinary differential equation such as fractional-non-linear oscillatory and vibration equations. The results indicate that the method is very effective and sufficient for solving nonlinear differential equations of fractional order. 相似文献
19.
In this paper, the nonlinear free vibration of the nanotube with damping effects is studied. Based on the nonlocal elastic theory and Hamilton principle, the governing equation of the nonlinear free vibration for the nanotube is obtained. The Galerkin method is employed to reduce the nonlinear equation with the integral and partial differential characteristics into a nonlinear ordinary differential equation. Then the relation is solved by the multiple scale method and the approximate analytical solution is derived. The nonlinear vibration behaviors are discussed with the effects of damping, elastic matrix stiffness, small scales and initial displacements. From the results, it can be observed that the nonlinear vibration can be reduced by the matrix damping. The elastic matrix stiffness has significant influences on the nonlinear vibration properties. The nonlinear behaviors can be changed by the small scale effects, especially for the structure with large initial displacement. 相似文献
20.
This paper investigates longtime dynamical behaviors of an axially accelerating viscoelastic string with geometric nonlinearity.
Application of Newton's second law leads to a nonlinear partial-differential equation governing transverse motion of the string.
The Galerkin method is applied to truncate the partial-differential equation into a set of ordinary differential equations.
By use of the Poincare maps, the dynamical behaviors are presented based on the numerical solutions of the ordinary differential
equations. The bifurcation diagrams are presented for varying one of the following parameter: the mean transport speed, the
amplitude and the frequency of transport speed fluctuation, the string stiffness or the string dynamic viscosity, while other
parameters are fixed. 相似文献