共查询到18条相似文献,搜索用时 15 毫秒
1.
本文从小涡球的随机运动出发研究壁湍流的流动特征。建立了这个随机过程所满足的随机微分方程。解此方程再次导出了著名的对数律,并从理论上决定了对数律中的Kármán常数,K=1/6~(1/2)=0.408。 相似文献
2.
By means of a variational approach we rigorously deduce three one-dimensional models for elastic ribbons from the theory of von Kármán plates, passing to the limit as the width of the plate goes to zero. The one-dimensional model found starting from the “linearized” von Kármán energy corresponds to that of a linearly elastic beam that can twist but can deform in just one plane; while the model found from the von Kármán energy is a non-linear model that comprises stretching, bendings, and twisting. The “constrained” von Kármán energy, instead, leads to a new Sadowsky type of model. 相似文献
3.
C. Schmieden 《Archive of Applied Mechanics (Ingenieur Archiv)》1936,7(4):215-221
Ohne Zusammenfassung 相似文献
4.
《European Journal of Mechanics - B/Fluids》2001,20(1):145-153
The instantaneous velocity field of a circular cylinder wake is built using a PIV technique when a small amount of viscoelastic liquid is introduced through the cylinder. It is shown that the viscoelastic fluid slows down the vorticity concentration and produces a street of partially rolled-up vortices. The underlying mechanism appears very analogous to that of a surface tension in the Kelvin–Helmholtz instability. The partial roll-up is studied in terms of the Weiss determinant. This quantity is a local measurement of the spatial separation between the strain and vorticity. In the viscoelastic wake, the Weiss determinant reaches much lower values than in the Newtonian wake. This result shows that the elasticity prevents the clear separation between vorticity and strain during the roll-up process. Since the Weiss determinant is directly related to the pressure field, it suggests that elasticity can drastically modify the pressure levels even when vorticity and strain levels are unaffected. 相似文献
5.
Using techniques from formal asymptotic analysis, the first two authors have recently identified generalized von Kármán equations, which constitute a two-dimensional model for a nonlinearly elastic plate where only a portion of the lateral face is subjected to boundary conditions of von Kármán's type, the remaining portion being free. In this paper, we establish an existence theorem for these equations. To this end, we first reduce them to a single equation, which generalizes a cubic operator equation introduced by M.S. Berger and P. Fife. We then directly solve this equation, notably by adapting a crucial compactness method due to J.-L. Lions.
Résumé. En utilisant les techniques de l'analyse asymptotique formelle, les deux premiers auteurs ont récemment identifié des équations de von Kármán généralisées, qui constituent un modèle bi-dimensionnel de plaque non linéairement élastique dont une partie seulement de la face latérale est soumise à des conditions aux limites de von Kármán, la partie restante étant libre. Dans cet article, on établit un théorème d'existence pour ces équations. À cette fin, elles sont d'abord réduites à une seule équation, qui généralise une équation faisant intervenir un opérateur cubique, introduite par M.S. Berger et P. Fife. On résout ensuite directement cette équation, en adaptant notamment une méthode cruciale de compacité due à J.-L. Lions. 相似文献
6.
C. Schmieden 《Archive of Applied Mechanics (Ingenieur Archiv)》1936,7(5):337-341
Ohne Zusammenfassung 相似文献
7.
Zhang Jianwu Professor Doctor Humboldt Research Fellow Li Qi Shu Yongping 《应用数学和力学(英文版)》2000,21(5):529-536
A new refined first-order shear-deformation plate theory of the Kármán type is presented for engineering applications and
a new version of the generalized Kármán large deflection equations with deflection and stress functions as two unknown variables
is formulated for nonlinear analysis of shear-deformable plates of composite material and construction, based on the Mindlin/Reissner
theory. In this refined plate theory two rotations that are constrained out in the formulation are imposed upon overall displacements
of the plates in an implicit role. Linear and nonlinear investigations may be made by the engineering theory to a class of
shear-deformation plates such as moderately thick composite plates, orthotropic sandwich plates, densely stiffened plates,
and laminated shear-deformable plates. Reduced forms of the generalized Kármán equations are derived consequently, which are
found identical to those existe in the literature.
Foundation item: the National Natural Science Foundation of China (59675027)
Biography: Zhang Jianwu (1954-) 相似文献
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9.
含孔von Kármán板中的高次谐波散射现象 总被引:2,自引:0,他引:2
基于vonKarman板大挠度弯曲理论,利用谐波平衡法及小参数振动法,研究了含孔vonKarman板的非线性波散射问题.通过分析发现:由于弯曲应力与中面力的非线性耦合,vonKarman板中会出现高次谐波散射现象. 相似文献
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11.
In a recent work in the static case, Gratie (Appl. Anal. 81:1107–1126, 2002) has generalized the classical Marguerre-von Kármán equations studied by Ciarlet and Paumier in (Comput. Mech. 1:177–202, 1986), where only a portion of the lateral face of the shallow shell is subjected to boundary conditions of von Kármán type, while the remaining portion is subjected to boundary conditions of free edge. Then Ciarlet and Gratie (Math. Mech. Solids 11:83–100, 2006) have established an existence theorem for these equations. In Chacha et al. (Rev. ARIMA 13:63–76, 2010), we extended formally these studies to the dynamical case. More precisely, we considered a three-dimensional dynamical model for a nonlinearly elastic shallow shell with a specific class of boundary conditions of generalized Marguerre-von Kármán type. Using technics from formal asymptotic analysis, we showed that the scaled three-dimensional solution still leads to two-dimensional dynamical boundary value problem called the dynamical equations of generalized Marguerre-von Kármán shallow shells. In this paper, we establish the existence of solutions to these equations using a compactness method of Lions (Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Dunod, Paris, 1969). 相似文献
12.
In this paper, modified von Kármán equations are derived for Kirchhoff nanoplates with surface tension and surface tension-induced residual stresses. The simplified Gurtin-Murdoch model which does not contain non-strain displacement gradients in surface stress-strain relations is adopted, so that the von Kármán strain-compatibility equation can be expressed in terms of the stress function and deflection. The modified von Kármán equations derived here are different than the existing related models especially for elastic plates with in-plane movable edges. Unlike the existing models which predict a surface tension-induced tensile pre-stress for an elastic plate with in-plane movable edges, the present model predicts that this tensile pre-stress is actually cancelled by the surface tension-induced residual compressive stress. Our this result is consistent with recent clarification on similar issue for cantilever beams with surface tension, which implies that the existing models have incorrectly predicted an invalid tensile pre-stress for an elastic plate with in-plane movable edges which leads to significant overestimation of postbuckling load and free vibration frequencies. In addition, our numerical examples indicated that surface stresses can moderately increase or decrease postbuckling load and free vibration frequency of Kirchhoff nanoplate with all in-plane movable edges, depending on the surface elasticity parameters and the geometrical dimensions of nanoplates. 相似文献
13.
Since their formulation almost 100 years ago, the von Kármán (vK) plate equations have been frequently used both by engineers
and by analysts to study thin elastic bodies, in particular their stability behaviour under applied loads. At the same time
the derivation of these equations met some harsh criticism and their precise mathematical status has been unclear until very
recently. Following up on a recent variational derivation of the vK theory by Friesecke, James and Müller from three-dimensional
nonlinear elasticity we study the predictions and the validity of the vK equation in the presence of in-plane compressive
forces. The first main result is a stability alternative: either the load leads to instability already in the nonlinear bending
theory of plates (Kirchhoff–Love theory), or it leads to an instability in a geometrically linear KL theory (‘linearized instability’),
or vK theory is valid. The second main result states that under suitable conditions the critical loads for nonlinear stability
and linearized instability coincide. The third main result asserts this critical load also agrees with the load beyond which
the infimum of the vK functional is −∞. The main ingredients are a sharp rigidity estimate for maps with low elastic energy
and a study of the properties of isometric immersions from a set in to and their geometrically linear counterparts. 相似文献
14.
Meccanica - We propose a mixed variational principle for deducing the generalized Marguerre–von Kármán equations, governing the relatively large deflections of thin elastic shallow... 相似文献
15.
A new mathematical model is presented to study the heat and mass transfer characteristics of magnetohydrodynamic (MHD) Maxwell fluid flow over a convectively heated stretchable rotating disk. To regulate the fluid temperature at the surface, a simple isothermal model of homogeneous-heterogeneous reactions is employed. The impact of nonlinear thermal radiative heat flux on thermal transport features is studied. The transformed nonlinear system of ordinary differential equations is solved numerically with an efficient method, namely, the Runge-Kutta-Felberg fourth-order and fifth-order (RKF45) integration scheme using the MAPLE software. Achieved results are validated with previous studies in an excellent way. Major outcomes reveal that the magnetic flux reduces the velocity components in the radial, angular, and axial directions, and enhances the fluid temperature. Also, the presence of radiative heat flux is to raise the temperature of fluid. Further, the strength of homogeneous–heterogeneous reactions is useful to diminish the concentration of reaction. 相似文献
16.
This research paper analyzes the transport of thermal and solutal energy in the Maxwell nanofluid flow induced above the disk which is rotating with a constant angular velocity.The significant features of thermal and solutal relaxation times of fluids are studied with a Cattaneo-Christov double diffusion theory rather than the classical Fourier’s and Fick’s laws.A novel idea of a Buongiorno nanofluid model together with the Cattaneo-Christov theory is introduced for the first time for the Maxwel... 相似文献
17.
We are concerned with the deformation of thin, flat annular plates under a force applied orthogonally to the plane of the plate. This mechanical process can be described via a radial formulation of the Föppl – von Kármán equations, a set of nonlinear partial differential equations describing the deflections of thin flat plates. We are able to obtain analytical solutions for the radial Föppl – von Kármán equations with boundary conditions relevant for clamped, loosely clamped, and free inner and outer. This permits us to study the qualitative behavior of the out-of-plane deflections as well as the Airy stress function for a number of cases. Provided that an appropriate non-dimensionalization is taken, we find that the perturbation solutions are surprisingly valid for a wide variety of parameters, and compare favorably with numerical simulations in all cases (rather than just for small parameters). The results demonstrate that the ratio of the inner to outer radius of the annular plate will strongly influence the properties of the solutions, as will the specific boundary data considered. For instance, one may choose to fix the plate in place with a specific set of boundary conditions, in order to minimize the out-of-plane deflections. Other boundary conditions may result in undesirable behaviors. 相似文献
18.
Robert A. Van Gorder 《International Journal of Non》2012,47(3):1-6
We discuss the method of linearization and construction of perturbation solutions for the Föppl–von Kármán equations, a set of non-linear partial differential equations describing the large deflections of thin flat plates. In particular, we present a linearization method for the Föppl–von Kármán equations which preserves much of the structure of the original equations, which in turn enables us to construct qualitatively meaningful perturbation solutions in relatively few terms. Interestingly, the perturbation solutions do not rely on any small parameters, as an auxiliary parameter is introduced and later taken to unity. The obtained solutions are given recursively, and a method of error analysis is provided to ensure convergence of the solutions. Hence, with appropriate general boundary data, we show that one may construct solutions to a desired accuracy over the finite bounded domain. We show that our solutions agree with the exact solutions in the limit as the thickness of the plate is made arbitrarily small. 相似文献