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RESEARCH ON THE COMPANION SOLUTION FOR A THIN PLATE IN THE MESHLESS LOCAL BOUNDARY INTEGRAL EQUATION METHOD LONG Shu-yao;XIONG Yuan-bo Applied Mathematics and Mechanics (English Edition)    2004, 25 (4): 418-423.   Abstract （592）      PDF（pc） （384KB）（341）       Knowledge map    Save The meshless local boundary integral equation method is a currently developed numerical method, which combines the advantageous features of Galerkin finite element method(GFEM), boundary element method(BEM) and element free Galerkin method(EFGM), and is a truly meshless method possessing wide prospects in engineering applications. The companion solution and all the other formulas required in the meshless local boundary integral equation for a thin plate were presented, in order to make this method apply to solve the thin plate problem. Reference | Related Articles | Metrics | Comments（0）

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Numerical investigation of flow over a two-dimensional square cylinder with a synthetic jet generated by a bi-frequency signal Yiran LU, Yuan QU, Jiangsheng WANG, Jinjun WANG Applied Mathematics and Mechanics (English Edition)    2022, 43 (10): 1569-1584.   DOI: 10.1007/s10483-022-2919-6 Abstract （503）   HTML （0）    PDF（pc） （3489KB）（94）       Knowledge map    Save The flow around a square cylinder with a synthetic jet positioned at the rear surface is numerically investigated with the unsteady Reynolds-averaged Navier-Stokes (URANS) method. Instead of the typical sinusoidal wave, a bi-frequency signal is adopted to generate the synthetic jet. The bi-frequency signal consists of a basic sinusoidal wave and a high-frequency wave. Cases with various amplitudes of the high-frequency component are simulated. It is found that synthetic jets actuated by bi-frequency signals can realize better drag reduction with lower energy consumption when appropriate parameter sets are applied. A new quantity, i.e., the actuation efficiency Ae, is used to evaluate the controlling efficiency. The actuation efficiency Ae reaches its maximum of 0.266 8 when the amplitude of the superposed high-frequency signal is 7.5% of the basic signal. The vortex structures and frequency characteristics are subsequently analyzed to investigate the mechanism of the optimization of the bi-frequency signal. When the synthetic jet is actuated by a single-frequency signal with a characteristic velocity of 0.112 m/s, the wake is asymmetrical. The alternative deflection of vortex pairs and the peak at half of the excitation frequency in the power spectral density (PSD) function are detected. In the bi-frequency cases with the same characteristic velocity, the wake gradually turns to be symmetrical with the increase in the amplitude of the high-frequency component. Mean-while, the deflection of the vortex pairs and the peak at half of the excitation frequency gradually disappear as well. Reference | Related Articles | Metrics | Comments（0）

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ONE TYPE OF SOLUTIONS OF CONDUCTION OF NERVOUS PULSES AND THE STABILITY OF ACTION POTENTIAL Tang Wen-liang Applied Mathematics and Mechanics (English Edition)    1983, 4 (1): 117-126.   Abstract （746）      PDF（pc） （476KB）（877）       Knowledge map    Save This paper reports a type of laws which governs action potential of nervous impulses,and it is discussed by general form -nonlinear dispersive process. We find that the nervous wave is a slowly varying amplitude solitary wave in the small dispersive case. He prove that the solitary wave is not generated in the ordinary dispersion,but a travelling wave with varying amplitudes may be obtained. The stability of various possible action potentials and bifurcation in overdamped case are also discussed in this paper. Reference | Related Articles | Metrics | Comments（0）

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Bifurcation and pattern formation in a coupled higher autocatalator reaction diffusion system ZHANG Li;LIU San-yang Applied Mathematics and Mechanics (English Edition)    2007, 28 (9): 1235-1248.   DOI: 10.1007/s10483-007-0912-1 Abstract （1371）      PDF（pc） （284KB）（678）       Knowledge map    Save Spatiotemporal structures arising in two identical cells, which are governed by higher autocatalator kinetics and coupled via diffusive interchange of autocatalyst, are discussed. The stability of the unique homogeneous steady state is obtained by the linearized theory. A necessary condition for bifurcations in spatially non-uniform solutions in uncoupled and coupled systems is given. Further information about Turing pattern solutions near bifurcation points is obtained by weakly nonlinear theory. Finally, the stability of equilibrium points of the amplitude equation is discussed by weakly nonlinear theory, with the bifurcation branches of the weakly coupled system. Reference | Related Articles | Metrics | Comments（0）

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THE ANALYSIS OF STABILITY OF BINGHAM FLUIDFLOWING DOWN AN INCLINED PLANE Wang Peiguang;Wang Zhendong Applied Mathematics and Mechanics (English Edition)    1995, 16 (10): 1013-1018.   Abstract （720）      PDF（pc） （325KB）（444）       Knowledge map    Save In this paper, the stability problem of Bingham fluids flowing down an inclinedplane is studied with respect to two dimensional disturbances. The crilical Reynolodsnumber is given in ihe case of long waves, and the effect of yield stress on stability isanalysed. Reference | Related Articles | Metrics | Comments（0）

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DYNAMIC RESPONSE ANALYSIS OF PLATFORM-CYLINDER GROUP FOUNDATION DUE TO IMPACT BY WATER WAVE FLOW Fang Yingguang Applied Mathematics and Mechanics (English Edition)    1998, 19 (11): 1073-1082.   Abstract （669）      PDF（pc） （583KB）（353）       Knowledge map    Save This paper deals. with the problem of dynamic response of platform-cylinder group foumdation. Dynamic interaction of cylinder group foudation-water-soil is taken into account and the analysis of dynamic response to excitation of water wave force is given by analytic method ..The numerical examples are presented and the influence of systent’s parameters on the dynamic behaviour is discussed. Reference | Related Articles | Metrics | Comments（0）

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Fully developed forced convection through semi-elliptic ducts R. ALASSAR Applied Mathematics and Mechanics (English Edition)    2016, 37 (1): 37-44.   DOI: 10.1007/s10483-016-2020-9 Abstract （418）   HTML    PDF（pc） （263KB）（178）       Knowledge map    Save An exact solution of the problem of fully developed forced convection through semi-elliptic ducts is obtained under constant axial heat flux and peripherally uniform temperature. The solution is validated by comparing the local and average Nusselt numbers with the published approximate and asymptotic values. Reference | Related Articles | Metrics | Comments（0）

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INCREMENTAL VIRTUAL WORK EQUATION FOR GEOMETRIC NONLINEAR ANALYSIS Wang Ying-jian Applied Mathematics and Mechanics (English Edition)    1987, 8 (5): 413-417.   Abstract （525）      PDF（pc） （340KB）（557）       Knowledge map    Save In this paper, an incremental virtual work equation is derived. It is suitable for geometric nonlinear analysis in finite element method. The effect of truncation errors is considered in the incremental virtual work equation. Reference | Related Articles | Metrics | Comments（0）

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FORMULAE OF FORCE AT A POINT IN THE INTERIOR OF A HALF SPACE WITH SHEAR MODULUS LINEARLY VARIED WITH DEPTH Yun Tian-quan Applied Mathematics and Mechanics (English Edition)    1985, 6 (1): 53-59.   Abstract （497）      PDF（pc） （518KB）（743）       Knowledge map    Save According to a lemma and an assumption, this paper prexenis formulae of force at a point in the interior of a half space with Poisson’s ratio v = constant and shear modulus G linearly varied with depth. These formulae can be used as an approximate basic solution when the integral equation method is employed for the analysis of piles and other geotechnical engineering problems. Reference | Related Articles | Metrics | Comments（0）

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MOVING BOUNDARY PROBLEM FOR DIFFUSION RELEASE OF DRUG FROM A CYLINDER POLYMERIC MATRIX TAN Wen-chang;WU Wang-yi;YAN Zong-yi;WEN Gong-bi Applied Mathematics and Mechanics (English Edition)    2001, 22 (4): 379-384.   Abstract （662）      PDF（pc） （396KB）（547）       Knowledge map    Save An approximate analytical solution of moving boundary problem for diffusion release of drug from a cylinder polymeric matrix was obtained by use of refined integral method. The release kinetics has been analyzed for non-erodible matrices with perfect sink condition. The formulas of the moving boundary and the fractional drug release were given. The moving boundary and the fractional drug release have been calculated at various drug loading levels, and the calculated results were in good agreement with those of experiments. The comparison of the moving boundary in spherical, cylinder, planar matrices has been completed. An approximate formula for estimating the available release time was presented. These results are useful for the clinic experiments. This investigation provides a new theoretical tool for studying the diffusion release of drug from a cylinder polymeric matrix and designing the controlled released drug. Reference | Related Articles | Metrics | Comments（0）

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BOUNDARY AND INTERIOR LAYER BEHAVIOR FOR SINGULARLY PERTURBED VECTOR PROBLEM Zhang Xiang Applied Mathematics and Mechanics (English Edition)    1990, 11 (11): 1067-1074.   Abstract （600）      PDF（pc） （442KB）（322）       Knowledge map    Save In this paper, we consider the vector nonlinear boundary value problem:εyγ=f(x,y,z,y',ε), y(0)=A1 y(1)=B1 εzγ=f(x,y,z,z',ε), z(0)=A2 z(1)=B2where ε>0 is a small parameter,0≤x≤1 ƒ and g are continuous functions in R4 Under appropriate assumptions, by means of the differential inequalities, we demonstrate the existence and estimation, involving boundary and interior layers, of the solutions to the above problem. Reference | Related Articles | Metrics | Comments（0）

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RESEARCH ON THE COMPLICATED DYNAMICAL BEHAVIORS OF NONLINEAR ECOSYSTEMS (II) Zan Ting-qual Applied Mathematics and Mechanics (English Edition)    1989, 10 (2): 167-173.   Abstract （470）      PDF（pc） （438KB）（476）       Knowledge map    Save This paper is a further study of reference [1]. In this paper, we mainly discuss the complicated dynamical behaviors resulting from a simple one-dimensional model of nonlinear ecosystems: fixed point motion, periodic motion and chaotic motion etc., and briefly discuss the universality of the complicated dynamical behaviors, which can be described by the first and the second M. Feigenbaun. constants. At last, we discuss the "one-side lowering phenomenon" due to near unstabilization when the nonlinear ecosystem approaches bifurcation points from unbifurcation side. It is of important theoretical and practical meanings both in the development and utilization of ecological resources ar.d in the design and management of artifilial ecosystems. Reference | Related Articles | Metrics | Comments（0）

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1:2 INTERNAL RESONANCE OF COUPLED DYNAMIC SYSTEM WITH QUADRATIC AND CUBIC NONLINEARITIES CHEN Yu-shu;YANG Cai-xia;WU Zhi-qiang;CHEN Fang-qi Applied Mathematics and Mechanics (English Edition)    2001, 22 (8): 917-924.   Abstract （683）      PDF（pc） （414KB）（321）       Knowledge map    Save The 1:2 internal resonance of coupled dynamic system with quadratic and cubic nonlinearities is studied. The normal forms of this system in 1:2 internal resonance were derived by using the direct method of normal form. In the normal forms, quadratic and cubic nonlinearities were remained. Based on a new convenient transformation technique, the 4-dimension bifurcation equations were reduced to 3-dimension. A bifurcation equation with one-dimension was obtained. Then the bifurcation behaviors of a universal unfolding were studied by using the singularity theory. The method of this paper can be applied to analyze the bifurcation behavior in strong internal resonance on 4-dimension center manifolds. Reference | Related Articles | Metrics | Comments（0）

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Nonlinear stability of timber column strengthened with fiber reinforced polymer OU Yang-Yu;YANG Xiao;BAO Re-Han Applied Mathematics and Mechanics (English Edition)    2011, 32 (7): 903-916.   DOI: 10.1007/s10483-011-1468-7 Abstract （487）      PDF（pc） （381KB）（948）       Knowledge map    Save By taking into account the effect of the bi-modulus for tension and compression of the fiber reinforced polymer (FRP) sheet in the reinforcement layer, a general mathematical model for the nonlinear bending of a slender timber beam strengthened with the FRP sheet is established under the  hypothesis of the large deflection deformation of the beam. Nonlinear governing equations of the second order effect of the beam bending are derived. The nonlinear stability of a simply-supported slender timber column strengthened with the FRP sheet is then investigated. An expression of the critical load of the simply-supported FRP-strengthened timber beam is obtained. The existence of postbuckling solution of the timber column is proved theoretically, and an asymptotic analytical solution of the postbuckling state in the vicinity of the critical load is obtained using the perturbation method. Parameters are studied showing that the FRP reinforcement layer has great influence on the critical load of the timber column, and has little influence on the dimensionless postbuckling state. Reference | Related Articles | Metrics | Comments（0） Cited: Baidu(7)

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Mechanical analysis of C/C composite grids in ion optical system Shuiqiang ZHANG, Aijun LI, Yuqin ZHENG, Dongsheng ZHANG Applied Mathematics and Mechanics (English Edition)    2019, 40 (11): 1589-1600.   DOI: 10.1007/s10483-019-2527-9 Abstract （525）   HTML （14）    PDF（pc） （5546KB）（145）       Knowledge map    Save The ion thruster is an engine with high specific impulse for satellites and spacecrafts, which uses electric energy to boost the spacecraft. The ion optical system, also known as gate assemblies which consist of acceleration and screen grids, is the key component of the ion thruster. In this paper, the static mechanical properties of the C/C composite grids are evaluated based on the structural design. Representative volume element (RVE) is adopted to simplify the braded composite structure as a continuum material. The dynamical behavior of the 100 mm ion thruster optics in the launch environment (1 000g shock-load) is numerically modeled and simulated with the half-sine pulse method. The impact response of the C/C and molybdenum gate assemblies on the stress distribution and deformation is investigated. The simulated results indicate that the magnitudes of the normal displacement of the composite grids subject to the uniformly distributed load are on the same level as molybdenum grids although the normal stiffness of the composite grids is much smaller. When subject to impact loading, the stress distribution in the C/C composite grids is similar to molybdenum grids while the stress magnitude is much smaller. This finding shows that the C/C gate assemblies outperform molybdenum grids and meet the requirement of long lifetime service in space travel. Reference | Related Articles | Metrics | Comments（0）

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FREE BOUNDARY PROBLEM OF THE 2D SEEPAGE FLOW She Yinghe;Sun Ying;Guo Xiaoming Applied Mathematics and Mechanics (English Edition)    1996, 17 (6): 549-554.   Abstract （757）      PDF（pc） （342KB）（517）       Knowledge map    Save The free boundary of the seepage flow is a problem of close consideration inengineering. So far. an estimation of the wet set region usually needs a priori beforethe numerical analysis. and the configuration of the free boundary is then obtained bySuccessive approximation, The authors of this paper benefit from a new mathematical expression——The variational Inequality——to formulate the free boundary problem,which is then solved by the finite element method Instead of the conventional way of discretization, here finite element mesh is generated in the entere domain of thestudied medin and the free boundary of the seepage region can be defined directlywithout any process of iteration. The investigation gives a new effective scheme for the seepage flow analysis. Reference | Related Articles | Metrics | Comments（0）

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GENERAL ANALYTIC SOLUTION FOR ELASTIC BENDING OF REISSNER PLATES Sun Weiming;Yang Guangsong Applied Mathematics and Mechanics (English Edition)    1998, 19 (1): 85-94.   Abstract （596）      PDF（pc） （570KB）（474）       Knowledge map    Save In this paper, by developing the complex Fourier series method to solve theboundary value problem of a system of partial differential equations with constantcoefficients, for the first time a general analytic solution satisfying an arbitraryboundary condition is presented for the elastic bending of thick Reissuer plates inengineering. The solution is simple and convenient to programming. Analysis andcomputation are performed for the uniformly loaded plates under two differentsupporting conditions (four simply. supported edges or three clamped and one freeedges), the results of which are fairly satisfactory in comparison Mwth those availablefor reference. And at the some time the analytic solution has been invesligated mainlyin three aspects: a) speed of convergence. b) reliability (rationality), c) fitting ofboundary conditions. Reference | Related Articles | Metrics | Comments（0）

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Analytical modeling and vibration analysis of fiber reinforced composite hexagon honeycomb sandwich cylindrical-spherical combined shells Hui LI, Bocheng DONG, Zhijiang GAO, Jing ZHAO, Haiyang ZHANG, Xiangping WANG, Qingkai HAN Applied Mathematics and Mechanics (English Edition)    2022, 43 (9): 1307-1322.   DOI: 10.1007/s10483-022-2858-7 Abstract （1652）   HTML （29）    PDF（pc） （2616KB）（269）       Knowledge map    Save This study analyzes and predicts the vibration characteristics of fiber-reinforced composite sandwich (FRCS) cylindrical-spherical (CS) combined shells with hexagon honeycomb core (HHC) for the first time based on an analytical model developed, which makes good use of the advantage of the first-order shear deformation theory (FSDT), the multi-segment decomposition technique, the virtual spring technology, the Jacobi-Ritz approach, and the transfer function method. The equivalent material properties of HHC are firstly determined by the modified Gibson's formula, and the related energy equations are derived for the HHC-FRCS-CS combined shells, from which the fundamental frequencies, the mode shapes, and the forced vibration responses are solved. The current model is verified through the discussion of convergence and comparative analysis with the associated published literature and finite element (FE) results. The effects of geometric parameters of HHC on the dynamic property of the structure are further investigated with the verified model. It reveals that the vibration suppression capability can be greatly enhanced by reducing the ratio of HHC thickness to total thickness and the ratio of wall thickness of honeycomb cell to overall radius, and by increasing the ratio of length of honeycomb cell to overall radius and honeycomb characteristic angle of HHC. Reference | Related Articles | Metrics | Comments（0）

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MORE GENERALIZED HYBRID VARIATIONAL PRINCIPLE AND CORRESPONDING FINITE ELEMENT MODEL Chen Wan-ji Applied Mathematics and Mechanics (English Edition)    1986, 7 (5): 481-487.   Abstract （426）      PDF（pc） （400KB）（598）       Knowledge map    Save According to recent studies of the generalized variational principle by Professor Chien Weizang, the more generalized hybrid variational principle for finite element method is given, from which a new kind of the generalized hybrid element model is etablished.Using the thin plate bending element with varying thickness as an example, we compare various hybrid elements based on different generalized variational principles. Reference | Related Articles | Metrics | Comments（0）

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Elasto-plastic postbuckling of damaged orthotropic plates TIAN Yan-ping;FU Yi-ming Applied Mathematics and Mechanics (English Edition)    2008, 29 (7): 841-853.   DOI: 10.1007/s10483-008-0702-y Abstract （1497）      PDF（pc） （311KB）（815）       Knowledge map    Save Based on the elasto-plastic mechanics and continuum damage theory, a yield criterion related to spherical tensor of stress is proposed to describe the mixed hardening of damaged orthotropic materials. Its dimensionless form is isomorphic with the Mises criterion for isotropic materials. Furthermore, the incremental elasto-plastic damage constitutive equations and damage evolution equations are established. Based on the classical nonlinear plate theory, the incremental nonlinear equilibrium equations of orthotropic thin plates considering damage effect are obtained, and solved with the finite difference and iteration methods. In the numerical examples, the effects of damage evolution and initial deflection on the elasto-plastic postbuckling of orthotropic plates are discussed in detail. Related Articles | Metrics | Comments（0）