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A New Approach to Nonlinear Partial Differential Equations

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Communications in Nonlinear Science and Numerical Simulation 1997年第4期2卷 230-235页

作者： Jihuan HE (shanghai University,shanghai institute of applied mathematics and mechanics,shanghai 2 0 0 0 72 ,china) shanghai University Shanghai Institute of Applied Mathematics and Mechanics Shanghai 200072 China

In this paper,a novel method called variational iteration method is proposed to solve nonlinear partial differential equations without linearization or small *** this method,a correction functional is constructed by a general Lagrange multiplier,which can be identified via variational *** analytical solution can be obtained from its trial- function with possible unknown constants,which can be identified by imposing the boundary conditions,by successively iteration.

关键词： Nonlinear Problems Partial Differential Equations Variational Iteration Method Variational Theory

Weakly nonlinear stability of ultra-thin slipping films

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Progress in Natural Science:Materials International 2005年第9期15卷 827-831页

作者： HU Guohui(shanghai institute of applied mathematics and mechanics, shanghai University, shanghai 200072, china) shanghai institute of applied mathematics and mechanics Shanghai University Shanghai 200072 China

A weakly nonlinear theory is presented to study the effects of slippage on the stability of the ultra-thin polymer films. The nonlinear mathematical model is constructed for perturbations of small finite amplitude based on hydrodynamic equations with the long wave approximation. Results reveal that the nonlinearity always accelerates the rupture of the films. The influences of the slip length, film thickness, and initial amplitude of perturbations on the rupture of the films are investigated.

关键词： ultra-thin film weakly nonlinear theory hydrodynamic stability rupture of thin film.

Steady-state responses of axially accelerating viscoelastic beams: Approximate analysis and numerical confirmation

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Science china(Physics,mechanics & Astronomy) 2008年第11期51卷 1707-1721页

作者： CHEN LiQun1,2 & DING Hu2 1 Department of mechanics, shanghai University, shanghai 200444, china 2.shanghai institute of applied mathematics and mechanics, shanghai 2.0070, china Department of mechanics Shanghai University Shanghai China shanghai institute of applied mathematics and mechanics Shanghai China

Nonlinear parametric vibration of axially accelerating viscoelastic beams is inves-tigated via an approximate analytical method with numerical confirmations. Based on nonlinear models of a finite-small-stretching slender beam moving at a speed with a periodic fluctuation, a solvability condition is established via the method of multiple scales for subharmonic resonance. Therefore, the amplitudes of steady-state periodic responses and their existence conditions are derived. The amplitudes of stable steady-state responses increase with the amplitude of the axial speed fluctuation, and decrease with the viscosity coefficient and the nonlinear coefficient. The minimum of the detuning parameter which causes the existence of a stable steady-state periodic response decreases with the amplitude of the axial speed fluctuation, and increases with the viscosity coefficient. Nu-merical solutions are sought via the finite difference scheme for a nonlinear par-tial-differential equation and a nonlinear integro-partial-differential equation. The calculation results qualitatively confirm the effects of the related parameters pre-dicted by the approximate analysis on the amplitude and the existence condition of the stable steady-state periodic responses. Quantitative comparisons demonstrate that the approximate analysis results have rather high precision.

关键词： nonlinearity parametric vibration axially accelerating beam method of multiple scales numerical confir-mation

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Variational Iteration Method for Delay Differential Equations

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Communications in Nonlinear Science and Numerical Simulation 1997年第4期2卷 235-236页

作者： Jihuan HE (shanghai University,shanghai institute of applied mathematics and mechanics,shanghai 2 0 0 0 72 ,china) shanghai University Shanghai Institute of Applied Mathematics and Mechanics Shanghai 200072 China

The variational iteration method is shown to be applicable to delay differential equations for analytical approximate solutions

关键词： Variational Iteration Method for Delay Differential Equations

A New Cellular Automaton Model for TrafficFlow

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Communications in Nonlinear Science and Numerical Simulation 1999年第4期4卷 264-267页

作者： Yongtao HU(shanghai institute of applied mathematics and mechanics, shanghai University,shanghai 200072, china) shanghai institute of applied mathematics and mechanics Shanghai University Shanghai 200072 China

IntroductionCellularautomaton(CA)***,thesemodelSareremaxkable***]introdu... 详细信息

IntroductionCellularautomaton(CA)***,thesemodelSareremaxkable***]introdu...

关键词： traffic model transportation simulation cellular automata

A uniformly valid series solution to the unsteady stagnation-point flow towards an impulsively stretching surface

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Science china(Physics,mechanics & Astronomy) 2010年第3期53卷 521-526页

作者： CHENG Jun & DAI ShiQiang shanghai institute of applied mathematics and mechanics, shanghai University, shanghai 200072, china shanghai institute of applied mathematics and mechanics Shanghai University Shanghai China

The paper studies the problem of the unsteady two-dimensional stagnation-point flow of an incompressible viscous fluid over a flat deformable sheet. The flow is started impulsively from rest and the sheet is suddenly stretched in its own plane with a velocity proportional to the distance from the stagnation point. An analytical series solution is obtained by means of the homotopy analysis method (HAM). Also, the homotopy-Pade′ technique is employed. An explicit formula for the local friction coefficient is provided. The present formula, different from the perturbation solution, is accurate and uniformly valid for all dimensionless time in the whole spatial region and for all possible values of physical parameter λ, defined as the ratio of the potential flow velocity to the sheet sudden stretching velocity. Numerical tests are done to verify the present formula for its validity and accuracy.

关键词： unsteady boundary-layer flows stagnation point stretching sheet homotopy analysis method

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On two transverse nonlinear models of axially moving beams

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Science china(Technological Sciences) 2009年第3期52卷 743-751页

作者： DING Hu1 & CHEN LiQun1,2 1 shanghai institute of applied mathematics and mechanics, shanghai University, shanghai 200072, china 2 Department of mechanics, shanghai University, shanghai 200444, china shanghai institute of applied mathematics and mechanics Shanghai University Shanghai China Department of mechanics Shanghai University Shanghai China

Nonlinear models of transverse vibration of axially moving beams are computationally investigated. A partial-differential equation is derived from the governing equation of coupled planar motion by omit- ting its longitudinal terms. The model can be reduced to an integro-partial-differential equation by av- eraging the beam disturbed tension. Numerical schemes are respectively presented for the governing equations of coupled planar and the two governing equations of transverse motion via the finite dif- ference method and differential quadrature method under the fixed boundary and the simple support boundary. A steel beam and a copper beam are treated as examples to demonstrate the deviations of the solutions to the two transverse equations from the solution to the coupled equation. The numerical results indicate that the differences increase with the amplitude of vibration and the axial speed. Both models yield almost the same precision results for small amplitude vibration and the inte- gro-partial-differential equation gives better results for large amplitude vibration.

关键词： axially moving beam nonlinearity transverse vibration finite difference method differential quadrature method

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Effect of Material Property of Interply Film on the Delamination in Laminated Composites

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Communications in Nonlinear Science and Numerical Simulation 1999年第1期4卷 39-42页

作者： Wei FENG and Qian HUANG (shanghai institute of applied mathematics and mechanics, shanghai University, shanghai 200072, china) shanghai institute of applied mathematics and mechanics Shanghai University Shanghai 200072 China

The delamination is one of the main failure modes in laminated composites. In order to suppress and/or delay it, considerable research has been devoted to the reduction of the interlaminar stresses at the interfaces between two different plies. This paper studies the effect of isotropic layers placed at ply interface on the interlaminar behaviour of the angle-ply laminated composites. The results of the experiment and numerical analysis show that the material properties of interply film have strong influence on the interlaminar behaviour of laminated composites. In order to suppress delamination, the material of interply film has to been selected carefully due to the fact that different matrials have different results. Some materials may increase the stress values at the interfaces. Some materials may reduce the stress concertration.

关键词： laminated composite interply film stress concentration

Some New Approaches to Duffing Equation with Strongly and High Order Nonlinearity (II) Parametrized Perturbation Technique

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Communications in Nonlinear Science and Numerical Simulation 1999年第1期4卷 78-83页

作者： Jihuan HE (shanghai institute of applied mathematics and mechanics, shanghai University, shanghai 200072, china) Email: glliu@*** shanghai institute of applied mathematics and mechanics Shanghai University Shanghai 200072 China

For the strongly nonlinear equations without small parameter, a transformation u = v can be introduced for the nonlinear equation L(u) + N(u) = 0, where L and N are general linear and nonlinear differential operators respectively, P is sufficiently small. Therefore, a strongly non-linear system is transformed into a small parameter system with respect to the new introduced parameter P, thus various traditional perturbation techniques can be applied. By Lindstedt-Poincare method, a perturbation solution for Duffing equation with sib order nonlinearity is obtained, which is valid not only for the small parameter E in the equation, but also for very large values of E.

关键词： perturbation technique nonlinear equation