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1.
I.IntroductionAlthoughtherapiddevelopmentofdigitalcomputersmakesiteasierandeasiertonumericallysolvenolllinearproblems,itisstillratherditliculttogivethed'analyticapproximations.Currently,mostofour11onlinearanalytictechlliquesill'cunsatislllctory.Forinstance,althoughpel.turbatiolltechlliquesarewidelyappliedtoalZalyzcnolllillcarproblcllisillscienceandengineerillg,theyarehoweversostronglydependentonsmall13arall,etersappearedinequatiollsunderconsiderationthattheyarerestrictedonlytoweLlklynolllinea… 相似文献
2.
I.IntroductionInthispaper,onthebasisofRefll],usingtheinterPotationPerturbationmethod,theauthorseekstosolveseveralnon-Iinearproblems.Itsmainpointsare:Introducinganinterpolationfunction,wedeterminethisfunctionbyusingtheperturbationmethodandthenproceedtoseek… 相似文献
3.
Summary A mathematical model for a hydraulic servomechanism is constructed. It is shown that the model, in general, reduces to a nonlinear third-order equation of the form xx+( 1+ xx+– 2
x= p(t). Under certain conditions imposed on the constants involved, it is proved that above equation possesses a periodic solution. 相似文献
4.
IntroductionThestronglynonlinearoscillationproblem¨u ω20 u =εf(u , u ,¨u) , (1 )wherethesymbol“·”denotesthedifferentiationwithrespecttotheindependentvariabletandω0andεareallthearbitraryconstants,haveintherecentyearsseveralimprovedL_Pmethodswhenεisnotsmall (stro… 相似文献
5.
IntroductionInthispaper,westudiedakindofboundaryvalueproblems (BVPs)forsemi_linearretardeddifferentialequationwithnonlinearboundarycondition : εx″(t) =f(t,x(t) ,x(t-ε) ,ε) , t∈(0 ,1 ) ,(1 ) x(t) =φ(t,ε) , t∈[-ε0 ,0 ] ,h(x(1 ) ,x′(1 ) ,ε) =A(ε) ,(2 )whereε>0isasmallparameterandε0 isasufficientlysmallpositiveconstant.ThereweremanyresultsofstudyingonsingularlyperturbedboundaryvalueproblemforretardeddifferentialequationinRefs.[1~5] .Butthosestudiespossessedanesse… 相似文献
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A generalized hyperbolic perturbation method is presented for homoclinic solutions of strongly nonlinear autonomous oscillators,in which the perturbation procedure is improved for those systems whose exact homoclinic generating solutions cannot be explicitly derived.The generalized hyperbolic functions are employed as the basis functions in the present procedure to extend the validity of the hyperbolic perturbation method.Several strongly nonlinear oscillators with quadratic,cubic,and quartic nonlinearity are studied in detail to illustrate the efficiency and accuracy of the present method. 相似文献
7.
Based on the random perturbation technique for reliability sensitivity design,some realistic reliability-based sensitivity issues are discussed,some of which have a structure of high nonlinear performance functions.Combining the related theories of the moment method of the reliability analysis,the matrix differential,and the Kronecker algebra,the reliability-based sensitivity method based on the perturbation method is modified if the first four moments of random variables are given.Meanwhile,a reliability-based sensitivity computation method is proposed.Some examples are used to show that using this method can effectively improve the accuracy of the reliability-based sensitivity computation and offer a reliable theoretic basis in engineering. 相似文献
8.
The finite-element-displacement-perturbation method (FEDPM)for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes (Ⅰ) was employed to calculate the stress distributions and the stiffness of the bellows. Firstly, by applying the first-order perturbation solution (the linear solution)of the FEDPM to the bellows, the obtained results were compared with those of the general solution and the initial parameter integration solution proposed by the present authors earlier, as well as of the experiments and the FEA by others.It is shown that the FEDPM is with good precision and reliability, and as it was pointed out in (Ⅰ) the abrupt changes of the meridian curvature of bellows would not affect the use of the usual straight element. Then the nonlinear behaviors of the bellows were discussed. As expected, the nonlinear effects mainly come from the bellows ring plate,and the wider the ring plate is, the stronger the nonlinear effects are. Contrarily, the vanishing of the ring plate, like the C-shaped bellows, the nonlinear effects almost vanish. In addition, when the pure bending moments act on the bellows, each convolution has the same stress distributions calculated by the linear solution and other linear theories, but by the present nonlinear solution they vary with respect to the convolutions of the bellows. Yet for most bellows, the linear solutions are valid in practice. 相似文献
9.
In order to analyze bellows effectively and practically, the finite-element-displacement-perturbation method (FEDPM) is proposed for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes. The formulations are mainly based upon the idea of perturba-tion that the nodal displacement vector and the nodal force vector of each finite element are expanded by taking root-mean-square value of circumferential strains of the shells as a perturbation parameter. The load steps and the iteration times are not as arbitrary and unpredictable as in usual nonlinear analysis. Instead, there are certain relations between the load steps and the displacement increments, and no need of iteration for each load step. Besides, in the formulations, the shell is idealized into a series of conical frusta for the convenience of practice, Sander’s nonlinear geometric equations of moderate small rotation are used, and the shell made of more than one material ply is also considered. 相似文献
10.
The purpose of this paper is to develop a finite analytic (FA) numerical solution for the elasto-plastic problem of the total theory. Schemes for the FA method in local coordinates for solving non-linear governing equations in the form of Navier equations are derived, which can be utilized to solve the problem in a domain of arbitrary geometry. Numerical illustration shows that the schemes are effective and practical. 相似文献
11.
(黄家寅)(秦圣立)THEPROBLEMSOFNONLINEARBENDINGFORORTHOTROPICRECTANGULARPLATEWITHFOURCLAMPEDEDGES¥HuangJiayin;QinShengli(QufuNormalUn... 相似文献
12.
In this paper, we consider a singularly perturbed problem of a kind of quasilinear hyperbolic-parabolic equations, subject
to initial-boundary value conditions with moving boundary:
When certain assumptions are satisfied and ε is sufficiently small, the solution of this problem has a generalized asymptotic
expansion (in the Van der Corput sense), which takes the sufficiently smooth solution of the reduced problem as the first
term, and is uniformly valid in domain Q where the sufficiently smooth solution exists. The layer exists in the neighborhood
of t=0. This paper is the development of references [3–5].
The Project supported by the National Natural Science Foundation of China. 相似文献
13.
In this paper we present a spectral technique for building asymptotic expansions which describe periodic processes in conservative and self-excited systems without assuming the oscillations to be weakly nonlinear. The small parameter of the expansion is connected with the ratio of the amplitudes of higher than the first harmonics in contrast to the traditional parameter connected with weak nonlinearity. In the case of an oscillator with power nonlinearity the frequency of the main harmonic and the complex amplitudes of higher harmonics are computed as the expansions of either integer (for weakly nonlinear oscillations) or algebraic (for strong nonlinearity) functions of the complex amplitude of the first harmonic depending on the character of the initial conditions and the maximum power of the nonlinear term in the equation. In the simplest case of weakly nonlinear oscillations the complete asymptotic expansion is shown to be valid in the whole domain of the periodic motions of definite type until the separatrix is reached. The expressions for the first terms of the expansion for concrete examples coincide with the expressions obtained both with the use of other methods and by expanding the exact solutions. For some special cases of the strongly nonlinear oscillations the comparison of the results with known exact solutions is carried out as well as the criteria of convergence of the expansions are determined. 相似文献
14.
The initial layer phenomena for a class of singular perturbed nonlinear system with slow variables are studied. By introducing stretchy variables with different quantity levels and constructing the correction term of initial layer with different “ thickness“, the Norder approximate expansion of perturbed solution concerning small parameter is obtained, and the “ multiple layer“ phenomena of perturbed solutions are revealed. Using the fixed point theorem, the existence of perturbed solution is proved, and the uniformly valid asymptotic expansion of the solutions is given as well. 相似文献
15.
SINGULAR PERTURBATIONS FOR A CLASS OF BOUNDARY VALUE PROBLEMS OF HIGHER ORDER NONLINEAR DIFFERENTIAL EQUATIONSShiYuaning(史玉明)... 相似文献
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In this paper, according to the form of the asymptotic solution of papers [1, 2], the asymptotic method is extended to the following a class of more general strong nonlinear vibration systems where g and f are the nonlinear analytical-functions of x and x, and ε>0 is a small parameter. We assume that the derivative system corresponding to ε=0 has periodic solution. The recurrence equations of the asymptotic solution for the system(0.1)are deduced in this paper, and they are applied to practical examples. 相似文献
17.
A 3-D nonlinear problem of supercavitating flow past an axisymmetric body at a small angle of attack is investigated by means
of the perturbation method and Fourier-cosine-expansion method. The first three order perturbation equations are derived in
detail and solved numerically using the boundary integral equation method and iterative techniques. Computational results
of the hydrodynamic characteristics and cavity shapes of each order are presented for nonaxisymmetric supercavitating flow
past cones with various apex-angles at different cavitation numbers. The numerical results are found in good agreement with
experimental data.
The project supported by the National Natural Science Foundation of China 相似文献
18.
A class of nonlinear nonlocal for singularly perturbed Robin initial boundary value problems for reaction diffusion equations
is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using
the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed,
finally, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value
problems are studied and educing some relational inequalities the existence and uniqueness of solution for the original problem
and the uniformly valid asymptotic estimation is discussed.
Foundation items: the National Natural Science Foundation of China (10071048); the “Hunfred Talents Project” by Chinese Academy of Sciences
Biography: Mo Jia-qi (1937−) 相似文献
19.
SINGULARPERTURBATIONFORANONLINEARBOUNDARYVALUEPROBLEMOFFIRSTORDERSYSTEMChenSonglin(陈松林)(ReceivedApril8,1984;RevisedApril15,19... 相似文献
20.
The wavelet multiresolution interpolation for continuous functions defined on a finite interval is developed in this study by using a simple alternative of transformation matrix. The wavelet multiresolution interpolation Galerkin method that applies this interpolation to represent the unknown function and nonlinear terms independently is proposed to solve the boundary value problems with the mixed Dirichlet-Robin boundary conditions and various nonlinearities, including transcendental ones, in which the discretization process is as simple as that in solving linear problems, and only common two-term connection coefficients are needed. All matrices are independent of unknown node values and lead to high efficiency in the calculation of the residual and Jacobian matrices needed in Newton’s method, which does not require numerical integration in the resulting nonlinear discrete system. The validity of the proposed method is examined through several nonlinear problems with interior or boundary layers. The results demonstrate that the proposed wavelet method shows excellent accuracy and stability against nonuniform grids, and high resolution of localized steep gradients can be achieved by using local refined multiresolution grids. In addition, Newton’s method converges rapidly in solving the nonlinear discrete system created by the proposed wavelet method, including the initial guess far from real solutions. 相似文献
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