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New method to solve electromagnetic parabolic equation ZHAO Xiao-Feng;HUANG Si-Xun;KANG Lin-Chun Applied Mathematics and Mechanics (English Edition)    2013, 34 (11): 1373-1382.   DOI: 10.1007/s10483-013-1752-6 Abstract （591）      PDF（pc） （484KB）（500）       Knowledge map    Save This paper puts forward a new method to solve the electromagnetic parabolic equation (EMPE) by taking the vertically-layered inhomogeneous characteristics of the atmospheric refractive index into account. First, the Fourier transform and the convolution theorem are employed, and the second-order partial differential equation, i.e., the EMPE, in the height space is transformed into first-order constant coefficient differential equations in the frequency space. Then, by use of the lower triangular characteristics of the coefficient matrix, the numerical solutions are designed. Through constructing analytical solutions to the EMPE, the feasibility of the new method is validated. Finally, the numerical solutions to the new method are compared with those of the commonly used split-step Fourier algorithm. Related Articles | Metrics | Comments（0） Cited: Baidu(3)

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THE WARP AND STRESS TRANSMISSION IN THE JOINT OF AN OPEN THIN WALL BEAM Yang Gin-linag Applied Mathematics and Mechanics (English Edition)    1985, 6 (4): 331-342.   Abstract （545）      PDF（pc） （860KB）（318）       Knowledge map    Save The regularities of the war p in the sections of on open thin-wall beam have been discussed using the MODERN ENGINEERING THEORY OF BEAM.Thus, the transmission relationship between the warp displacements and the double-moments in the joints of open thin-wall beams which are connected in different ways hos been deduced.Meanwhile.experiments conducted by the author and some conclusions reached from these experiments as well as the tentative idea for further perfection are briefly presented here. Reference | Related Articles | Metrics | Comments（0）

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OSCILLATORY CORRELATIONS BETWEEN EXTERNAL FORCE AND DAMPING Zou Feng-wu Applied Mathematics and Mechanics (English Edition)    1986, 7 (6): 609-613.   Abstract （483）      PDF（pc） （270KB）（323）       Knowledge map    Save In this paper we shall examine the correlations among the external froce, variable damping and variable restoring force. Some new results are obtained. Reference | Related Articles | Metrics | Comments（0）

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VARIATIONAL PRINCIPLES IN ELASTICITY WITH NONLINEAR STRESS-STRAIN RELATION Chien Wei-zang Applied Mathematics and Mechanics (English Edition)    1987, 8 (7): 589-601.   Abstract （534）      PDF（pc） （725KB）（987）       Knowledge map    Save Since 1979, a series of papers have been published concerning the variational principles and generalized variational principles in elasticity such as [1](1979), [6](1980), [2,3](1983) and[4,5](1984). All these papers deal with the elastic body with linear stress-strain relations. In 1985, a book was published on generalized variational principles dealing with some nonlinear elastic body, but never going into detailed discussion. This paper discusses particularly variational principles and generalized variational principles for elastic body with nonlinear stress-strain relations. In these discussions, we find many interesting problems worth while to pay some attention. At the same time, these discussions are also instructive for linear elastic problems. When the strain is small, the high order terms may be neglected, the results of this paper may be simplified to the well-known principles in ordinary elasticity problems. Reference | Related Articles | Metrics | Comments（0）

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LEIBNIZ' FORMULA OF GENERALIZED DIFFERENCE WITH RESPECT TO A CLASS OF DIFFERENTIAL OPERATORS AND RECURRENCE FORMULA OF THEIR GREEN’S FUNCTION Xu Yue-sheng Applied Mathematics and Mechanics (English Edition)    1984, 5 (3): 1359-1364.   Abstract （538）      PDF（pc） （657KB）（1779）       Knowledge map    Save In this paper, Leibniz’ formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green function about the operators is also given. Reference | Related Articles | Metrics | Comments（0）

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THE IMPROVEMENT OF THE GENERAL EXPRESSION FOR THE STRESS FUNCTION Φ OF THE TWO-DIMENSIONAL PROBLEM Zhao Xing-hua Applied Mathematics and Mechanics (English Edition)    1990, 11 (3): 207-214.   Abstract （540）      PDF（pc） （394KB）（547）       Knowledge map    Save In this paper, it is pointed that the general expression for the stress function of the plane problem in polar coordinates is incomplete. The problems of the curved bar with an arbitrary distributive load at the boundries can’t he solved by this stress function. For this reason, we suggest two new stress functions and put them into the general expression. Then, the problems of the curved bar applied with an arbitrary distributive load at r=a,b boundaries can be solved. This is a new stress function including geometric boundary constants. Reference | Related Articles | Metrics | Comments（0）

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APPROXIMATION THEORY OF THREE DIMENSIONAL ELASTIC PLATESAND ITS BOUNDARY CONDITIONS WITHOUT USINGKIRCHHOFF-LOVE ASSUMPTIONS Chien Wei-zang Applied Mathematics and Mechanics (English Edition)    1995, 16 (3): 203-224.   Abstract （475）      PDF（pc） （999KB）（532）       Knowledge map    Save The classical small deflection theory of elastic plates id based on the Kirchhoff-Lore assumptions[1,2].Ther are used on the basis of the thinness of plate and the smallness of deflection.In terms of Cartesian tensor coordinates xi(i=0, 12)these basic assumptions are:(1)the transversal normal strain may be neglected i.e.00=0;(2)the transversal shear strain may be neglected i.e.e0α=0(α= 1, 2)(3)the transversal normal stress may be neglected i.e.. σ00=0.In classical theory of elastic plates,the strain-displacement relations and the corresponding stress-displacement relations are established on the basis of these assumptions. And the equations of the classical theory for a set of undetermined quantities defined on the middle surface are established through integrating the three dimensional equations of equilibrium of stress over the thickness.In the previous papers[3,4,5],an approximation theory is given on the basis of Ihree dimensional theory of elastic plates without using Kirchhoff-Love assumptions.However,no uniqueness study is given,and also the boundary conditions have never been studied. In this paper.the same problems are studied on the basis of generalizedvariational principle of the three dimensional theory of elastic bodies￣[6].The stationary conditions of variation give an unique and complete set of field equations and the related boundary conditions for the approximation theory.In this paper,the first order approximation theory is studied in detail. Related Articles | Metrics | Comments（0）

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CURVE CRACKS LYING ALONG A PARABOLIC CURVE IN ANISOTROPIC BODY Hu Yuan-tai;Zhao Xing-hua Applied Mathematics and Mechanics (English Edition)    1995, 16 (2): 115-124.   Abstract （610）      PDF（pc） （482KB）（476）       Knowledge map    Save A general solutions for the stress and displacement of curve cracks distributingalong a parabolic curve Ω in an infinite homogeneous anisotropic medium subjected tounifrom loading a infinity have been given in this paper by using the Stroh’s formalism and the mapping method. The solutions are valid not only for plane problems but also for antiplane problems and the problems whose inplane andantiplane deformations couple each other. A closed form solution for the stress and dispacement in the entire domain is obtained for one curve crack or two curve cracks along the parabolic curve. The simple explicit form solution for the stress intensity factors and the crack opening displacement are presented. Reference | Related Articles | Metrics | Comments（0）

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THE METHOD OF THE RECIPROCAL THEOREM OF FORCED VIBRATION FOR THE ELASTIC THIN RECTANGULAR PLATES (II)-RECTANGULAR PLATES WITH TWO ADJACENT CLAMPED EDGES Fu Bao-lian;Li Nong Applied Mathematics and Mechanics (English Edition)    1990, 11 (11): 1043-1054.   Abstract （528）      PDF（pc） （653KB）（311）       Knowledge map    Save In this paper, applying the method of reciprocal theorem, we give the distributions of the amplitude of bending moments along clamped edges and the amplitude of deflections along free edges of rectangular plates with two adjacent clamped edges under harmonic distributed and concentrated loads. Reference | Related Articles | Metrics | Comments（0）

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LATERAL INSTABILITY OF RECTANGULAR PLATES Cheng Xiang-sheng Applied Mathematics and Mechanics (English Edition)    1989, 10 (1): 87-92.   Abstract （455）      PDF（pc） （372KB）（468）       Knowledge map    Save This paper investituites the problems of lateral buckling of rectangular plates. In the text we discuss the minimum critical load of the lateral buckling occurring on under a concentrated force, uniformly distributed load and the concentrated couples, respectively. The energy method is used in this article. Reference | Related Articles | Metrics | Comments（0）

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CANONICAL REPRESENTATIONS AND DEGREE OF FREEDOM FORMULAE OF ORTHOGONAL TENSORS IN N-DIMENSIONAL EUCLIDEAN SPACE Xiong Zhu-hua;Zheng Quan-shui Applied Mathematics and Mechanics (English Edition)    1989, 10 (1): 93-101.   Abstract （437）      PDF（pc） （493KB）（500）       Knowledge map    Save In this paper, with the help of the eigenvalue properties of orthogonal tensors in n-dimensional Euclidean space and the representations of the orthogonal tensors in 2-dimensional space, the canonical representations of orthogonal tensors in n-dimensional Euclidean space are easily gotten. The paper also gives all the constraint relationships among the principal invariants of arbitrarily given orthogonal tensor by use of Cayley-Hamilton theorem; these results make it possible to solve all the eigenvalues of any orthogonal tensor based on a quite reduced equation of m-th order, where m is the integer part of n/2. Finally, the formulae of the degree of freedom of orthogonal tensors are given. Reference | Related Articles | Metrics | Comments（0）

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SINGULARLY PERTURBED PHENOMENA OF SEMILINEAR SECOND ORDER SYSTEMS Lin Zong-chi;Lin Su-rong Applied Mathematics and Mechanics (English Edition)    1988, 9 (12): 1131-1138.   Abstract （423）      PDF（pc） （484KB）（447）       Knowledge map    Save In this paper we consider singular perturbed phenomena of semilinear second ordersystems, under appropriate assumptions, the existence and asymptotic behavior asε→0+ of solution of vector boundary value problem are proved by constructing specialinvariant regions in which solutions display so-called boundary layer phenomena andangular layer phenomena. Reference | Related Articles | Metrics | Comments（0）

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THE EXPRESSION OF FREE ENERGY FOR THERMOELASTIC MATERIAL AND ITS RELATION TO THE VARIABLE MATERIAL COEFFICIENTS Wang Hong-gang Applied Mathematics and Mechanics (English Edition)    1988, 9 (12): 1139-1144.   Abstract （435）      PDF（pc） （366KB）（588）       Knowledge map    Save The expression of free energy is expanded in a power series, in which there aren ’t any terms of order higher than third in the temperature increments θ and second in the strains γii in this paper. The regular patterns of the material coefficients changing with temperature increments can be derived from this expression. These regulations accord with the experimental graph in references but the constants in the expression of free energy must be determined by experimental data.It is pointed out that the variable modulus of elasticity E and shearing modulus of elasticity G are independent of each other, but the rest of the coefficients are related to them. Reference | Related Articles | Metrics | Comments（0）

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SPACE VARIABLE TRANSFORM METHOD FOR FREE VIBRATION ANALYSIS OF THICK CYLINDRICAL SHELL WITH ARBITRARY BOUNDARY CONDITIONS Ni Hai-ying;Weng Zhi-yuan Applied Mathematics and Mechanics (English Edition)    1988, 9 (12): 1145-1151.   Abstract （444）      PDF（pc） （485KB）（731）       Knowledge map    Save In this paper, a general analytical method-space variable transform method is presented fur solving free vibration problems of thick cylindrical shell with arbitrary boundary conditions. Free vibration characteristics of cantilever thick cylindrical shell are evaluated by the presented method, and the numerical results are compared with the corresponding results of thin shell theory and experimental values. Theoretical analysis and calculating results show that the method presented in this paper has good convergence and accuracy and can be extended to analyze free vibration of beams, plates and shells. Reference | Related Articles | Metrics | Comments（0）

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ANALYSIS OF NONLINEAR LARGE DEFORMATION PROBLEMS BY BOUNDARY ELEMENT METHOD Xie He-ping Applied Mathematics and Mechanics (English Edition)    1988, 9 (12): 1153-1162.   Abstract （448）      PDF（pc） （475KB）（503）       Knowledge map    Save In this paper, the author deduces an approximate solution of nonlinear influence function in rate form for two-dimensional elastic problems on current configuration by the method of comoving coordinate system.Here BEM formulation of large deformation based on Chen’s theory[1] is given. The computational processes of nonlinear boundary integral equation is discussed. The author also compiles a nonlinear computing program NBEM. Numerical examples show that the results presented here is available to the solution of engineering problems. Reference | Related Articles | Metrics | Comments（0）

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SOME PROBLEMS OF SECOND METHOD OF LYAPUNOV. IN DISCRETE SYSTEMS Li Zhong;Huang Lin Applied Mathematics and Mechanics (English Edition)    1988, 9 (12): 1175-1181.   Abstract （470）      PDF（pc） （381KB）（406）       Knowledge map    Save The geometric properties of the solution set of Lyapunov equation of linear time-invariant discrete system are discussed. Furthermore,the stabitility of piecewise linear discrete systems is studied and some sufficient conditions are obtained for the asymptotical stability of piecewise linear discrete systems in which each sub-system is stable. The results are applied to second order piecewise linear systems. Reference | Related Articles | Metrics | Comments（0）

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FREE VIBRATION OF NONLINEAR DEFORMATION RING-AND STRINGER-STIFFENED NONUNIFORM CYLINDRICAL SHELL Yeh Kai-yuan;Ji Zhen-yi Applied Mathematics and Mechanics (English Edition)    1988, 9 (11): 1025-1037.   Abstract （439）      PDF（pc） （691KB）（491）       Knowledge map    Save Cylindrical shells stiffened with rings and stringers are used in many structural application with as pipes conveying fluids or gases and aerospace.In this paper, the eral solulin is obtained for free vibration of nonlinear deformation ring-and stringer-stiffened cylindrical shell with arbitrary boundary condition by step reduction method[1].Finally, it is only necessary to solve a nonlinearl gebraic equation.This equation is expressed as an analytic form.Its convergence is proved.Three numerical examples are given at the end of the paper which indicate that satisfactory results can he obtained by step reduction method. Reference | Related Articles | Metrics | Comments（0）

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PERTURBATION METHOD TO SOLVE THE COUPLE PROBLEM AMONG HARMONIC WAVES Gao Shi-qiao;Loo Wen-da Applied Mathematics and Mechanics (English Edition)    1988, 9 (11): 1039-1044.   Abstract （477）      PDF（pc） （340KB）（402）       Knowledge map    Save In this paper, in terms of the characteristics of weak coupling problems between different harmonic waves, a perturbation method was presented to solve the coupling problem among harmonic waves. Reference | Related Articles | Metrics | Comments（0）

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DEVELOPING FLOWS AND DEVELOPED FLOWS Cen Ren-jing;Liu Bao-sen Applied Mathematics and Mechanics (English Edition)    1988, 9 (11): 1045-1056.   Abstract （495）      PDF（pc） （663KB）（432）       Knowledge map    Save This paper puts emphasis on the problem of the developing flows in the circular tube under oscillatory conditions.According to the Navier-Stokes' equation and using the method of Bessel function of imaginary argument, a system of formulas is obtained.Comparing the formulas obtained in this paper with A tabek's formulas, it may be seen that the former is simpler and more convenient.When both the formulas obtained in this paper and A tabek's formulas are reduced to the representation of developed flows, both of them are consistent.Numerical calculation results show that the computed results obtained in this paper are rather consistent with both A tabek's computed results and the experimental results. Reference | Related Articles | Metrics | Comments（0）

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THE GLOBAL STRUCTURAL STABILITY AND APPLICATION OF THE TOROIDAL DIFFERNTIAL EQUATIONS Zhou Rong-xing Applied Mathematics and Mechanics (English Edition)    1988, 9 (11): 1067-1077.   Abstract （459）      PDF（pc） （700KB）（436）       Knowledge map    Save In this paper, the global structural stability of the toroidal differential equationshas  been obtained, and applied to the cross-coupled phase - locked loop, where Δω≥0 Reference | Related Articles | Metrics | Comments（0）