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991.
在用渐近法求解任意旋转薄壳(圆柱壳和球壳除外)的轴对称自由振动方程时,在一定的频率参数范围内,存在转点问题。其中,对于存在唯一简单转点的情况,至今未获解决。本文解决了这一问题。 相似文献
992.
Based on the successive iteration in the Taylor series expansion method, a three-point explicit compact difference scheme with arbitrary order of accuracy is derived in this paper. Numerical characteristics of the scheme are studied by the Fourier analysisl Unlike the conventional compact difference schemes which need to solve the equation to obtain the unknown derivatives in each node, the proposed scheme is explicit and can achieve arbitrary order of accuracy in space. Application examples for the convectiondiffusion problem with a sharp front gradient and the typical lid-driven cavity flow are given. It is found that the proposed compact scheme is not only simple to implement and economical to use, but also is effective to simulate the convection-dominated problem and obtain high-order accurate solution in coarse grid systems. 相似文献
993.
We show how one can construct conservation laws of Euler-Lagrange-type equations via Noether-type symmetry operators associated with what we term partial Lagrangians. This is even in the case when a system does not directly have a usual Lagrangian, e.g. scalar evolution equations. These Noether-type symmetry operators do not form a Lie algebra in general. We specify the conditions under which they do form an algebra. Furthermore, the conditions under which they are symmetries of the Euler-Lagrange-type equations are derived. Examples are given including those that admit a standard Lagrangian such as the Maxwellian tail equation, and equations that do not such as the heat and nonlinear heat equations. We also obtain new conservation laws from Noether-type symmetry operators for a class of nonlinear heat equations in more than two independent variables. 相似文献
994.
基于Reisner板理论,通过对混合能变分原理的修正,建立了更一般的哈密尔顿型广义变分原理,并给出了Reisner板问题的哈密尔顿正则方程及其共轭辛正交解析法 相似文献
995.
Matched asymptotics are used formally in the linearized Navier–Stokes equations, the so-called Oseen approximation, to derive a nonlinear law for the flow of a single-phase, incompressible Newtonian fluid through a rigid porous medium. A suitable choice of the linear term gives, to order a Forchheimer-type law. 相似文献
996.
二维介质参数的大扰动反演方法 总被引:2,自引:0,他引:2
对非均匀介质参数反演问题进行了研究,并提出了用于反演二维介质参数的广义射线近似方法.利用参考场量和扰动变量对声波方程中的介质参数进行处理,并利用Green函数理论得到扰动参数比的积分方程.基于非均匀介质中波函数的局部理论和射线理论,引入了全波场的广义射线近似形式,通过定义介质参数函数,把反演目标归结为其第一类Fredholm积分方程.利用积分变换方法得到二维介质的介质参数函数,从而得到介质参数,在Born近似方法中,反演的介质参数扰动不能超过20%,但是在本文中介绍的方法能够有效地反演其扰动比不超过50%的变化情况 相似文献
997.
A closed form solution to the second order elasticity problem, when an isotropic compressible elastic half-space undergoes a deformation owing to a non-uniformly distributed normal load, is presented. The method of integral transform is employed and the case when loading is distributed, in accordance with Hertz's law, is discussed. The limiting solution for incompressible isotropic elastic material is also derived. Numerical calculations for the second order elastic material for the displacement and the normal stress in thez-direction are carried out. It is found that, in comparision to the linear elastic case, the displacement increases and the normal stress decreases in the second order elastic material
Sommario Si presenta una soluzione del secondo ordine in forma chiusa del problema di un semi-spazio elastico isotropo compressibile soggetto a un carico normale distribuito non uniformemente, ottenuta mediante il metodo delle trasformate integrali. Si discute il caso del carico distribuito secondo la legge di Hertz; si deriva anche la soluzione limite per materiale elastico isotropo incompressibile. Si ottengono numericamente alcuni risultati relativi a spostamenti e tensioni normali nella direzione z: si trova che, a paragone del caso elastico lineare, gli spostamenti aumentano e le tensioni diminuiscono nel materiale elastico del secondo ordine.相似文献
998.
Chia-Shun Yih 《Acta Mechanica Sinica》1993,9(2):97-101
A general solution of the Boussinesq equation is presented which solves the problem of interaction of any number of right-going
and left-going solitary waves. The solution relies on the exact solution of Gardner, Greene, Kruskal, and Miura (1967), and
has the same degree of accuracy as that solution, but has a wider scope of application. It is much simpler than, but as accurate
as, Hirota's exact solution (1973) of the Boussinesq equation, to which the present solution is compared for the simplest
case of two solitary waves in head-on collision. 相似文献
999.
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
1000.
In this paper an initial-boundary value problem for a weakly nonlinear string(or wave) equation with non-classical boundary conditions is considered. Oneend of the string is assumed to be fixed and the other end of the string isattached to a spring-mass-dashpot system, where the damping generated by thedashpot is assumed to be small. This problem can be regarded as a rather simple model describing oscillationsof flexible structures such as suspension bridges or overhead transmission lines in a windfield. A multiple-timescales perturbation method will be usedto construct formal asymptotic approximations of the solution. It will also beshown that all solutions tend to zero for a sufficiently large value of thedamping parameter. For smaller values of the damping parameter it will be shownhow the string-system eventually will oscillate. 相似文献