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Showing papers in "Applied Mathematics and Mechanics-english Edition in 2002"


Journal ArticleDOI
TL;DR: An exploratory discussion of an ancient Chinese algorithm, the Ying Buzu Shu, in about 2nd century BC, known as the rule of double false position in the West is given in this paper.
Abstract: An exploratory discussion of an ancient Chinese algorithm, the Ying Buzu Shu, in about 2 nd century BC, known as the rule of double false position in the West is given. In addition to pointing out that the rule of double false position is actually a translation version of the ancient Chinese algorithm, a comparison with well-known Newton iteration method is also made. If derivative is introduced, the ancient Chinese algorithm reduces to the Newton method. A modification of the ancient Chinese algorithm is also proposed, and some of applications to nonlinear oscillators are illustrated.

47 citations


Journal ArticleDOI
TL;DR: In this article, the equations of motion governing the quasi-static and dynamical behavior of a viscoelastic Timoshenko beam are derived and the effect of both transverse shear and rotational inertia on the vibration of the beam is discussed.
Abstract: The equations of motion governing the quasi-static and dynamical behavior of a viscoelastic Timoshenko beam are derived. The viscoelastic material is assumed to obey a three-dimensional fractional derivative constitutive relation. The quasi-static behavior of the viscoelastic Timoshenko beam under step loading is analyzed and the analytical solution is obtained. The influence of material parameters on the deflection is investigated. The dynamical response of the viscoelastic Timoshenko beam subjected to a periodic excitation is studied by means of mode shape functions. And the effect of both transverse shear and rotational inertia on the vibration of the beam is discussed.

44 citations


Journal ArticleDOI
TL;DR: Combining the method of constructing Green functions with operators defined piecewise, the existence result of positive solutions to a singular second order three-point boundary value problem is established.
Abstract: A fixed point theorem is used to study a singular second order three-point boundary value problem. The problem is more general. Combining the method of constructing Green functions with operators defined piecewise, the existence result of positive solutions to a singular second order three-point boundary value problem is established. The nonlinearity can be allowed to change sign.

25 citations


Journal ArticleDOI
TL;DR: In this paper, a wind tunnel investigation of response characteristics of cables with artificial rivulet is presented, where a series of cable section models of different mass and stiffness and damping ratio were designed with Artificial Rivulet.
Abstract: A wind tunnel investigation of response characteristics of cables with artificial rivulet is presented. A series of cable section models of different mass and stiffness and damping ratio were designed with artificial rivulet. They were tested in smooth flow under different wind speed and yaw angle and for different position of artificial rivulet. The measured response of cable models was then analyzed and compared with the experimental results obtained by other researchers and the existing theories for wind-induced cable vibration. The results show that the measured response of horizontal cable models with artificial rivulet could be well predicted by Den Hartog's galloping theory when wind is normal to the cable axis. For the wind with certain yaw angles, the cable models with artificial rivulet exhibit velocity-restricted response characteristics.

23 citations


Journal ArticleDOI
TL;DR: The Delta-perturbation expansion method, a kind of new perturbation technique depending upon an artificial parameter Delta was studied in this article, and the study reveals that the method exits some advantages, but also exits some limitations.
Abstract: The Delta-perturbation expansion method, a kind of new perturbation technique depending upon an artificial parameter Delta was studied. The study reveals that the method exits some advantages, but also exits some limitations. To overcome the limitations, the socalled linearized perturbation method proposed by HE Ji-huan can be powerfully applied.

22 citations


Journal ArticleDOI
TL;DR: In this article, an exponentially fitted finite difference scheme on a non-equidistant mesh is constructed for solving the singularly perturbed boundary value problem with nonlocal conditions, which exhibits boundary layer behavior for small positive values of the perturbative parameter.
Abstract: Singularly perturbed boundary value problem with nonlocal conditions is examined. The appopriate solution exhibits boundary layer behavior for small positive values of the perturbative parameter. An exponentially fitted finite difference scheme on a non-equidistant mesh is constructed for solving this problem. The uniform convergence analysis in small parameter is given. Numerical example is provided, too.

21 citations


Journal ArticleDOI
TL;DR: In this paper, the global asymptotic stability of Hopfield neural networks with time delay was investigated and a theorem and two corollaries were obtained, in which the boundedness and differentiability of fj on R in some articles were deleted.
Abstract: The global asymptotic stability for Hopfield neural networks with time delay was investigated. A theorem and two corollaries were obtained, in which the boundedness and differentiability of fj on R in some articles were deleted. Some sufficient conditions for the existence of global asymptotic stable equilibrium of the networks in this paper are better than the sufficient conditions in quoted articles.

19 citations


Journal ArticleDOI
TL;DR: In this paper, the spherical cavitated bifurcation for a hyperelastic solid sphere made of the incompressible Valanis-Landel material under boundary deadloading is examined.
Abstract: The spherical cavitated bifurcation for a hyperelastic solid sphere made of the incompressible Valanis-Landel material under boundary dead-loading is examined. The analytic solution for the bifurcation problem is obtained. The catastrophe and concentration of stresses are discussed. The stability of solutions is discussed through the energy comparison. And the growth of a pre-existing micro-void is also observed.

16 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of wall slip on the squeeze flow of a power-law fluid between two rigid spherical particles has been examined based on the Reynolds lubrication theory, and it is shown that the viscous force arising from the squeezing flow with wall slip may be resolved to the noslip solution by introducing a slip correction coefficient.
Abstract: The effect of wall slip on the squeeze flow of a power-law fluid between two rigid spherical particles has been examined based on the Reynolds lubrication theory. It is shown that the viscous force arising from the squeeze flow with wall slip may be resolved to the noslip solution by introducing a slip correction coefficient. An expression for the slip correction coefficient of force is derived which is related to the slip parameter, the flow index and the upper limit of integration. Generally, wall slip results in a reduction in the viscous force. The reduction in the viscous force increases as the flow index increases, suggesting that wall slip has a more profound effect on shear thickening material. However, such reduction decreases as the upper limit of integration increases from finite liquid bridges to fully immersed systems. The reduction in the viscous force also increases as the slip parameter increases, which is the expected behaviour.

15 citations


Journal ArticleDOI
TL;DR: In this paper, the form invariance of constrained Birkhoffian systems is defined as a kind of invariance for the constrained BGs under infinitesimal transformations, and the relation of the form-invariance and the Noether symmetry is studied.
Abstract: The form invariance of constrained Birkhoffian system is a kind of invariance of the constrained Birkhoffian equations under infinitesimal transformations. The definition and criteria of the form invariance of constrained Birkhoffian system are given, and the relation of the form invariance and the Noether symmetry is studied.

15 citations


Journal ArticleDOI
TL;DR: By the proposed procedure, the possibility distributions of responses of fuzzy structures can be generated in terms of the membership functions of the input fuzzy numbers.
Abstract: The key component of finite element analysis of structures with fuzzy parameters, which is associated with handling of some fuzzy information and arithmetic relation of fuzzy variables, was the solving of the governing equations of fuzzy finite element method. Based on a given interval representation of fuzzy numbers, some arithmetic rules of fuzzy numbers and fuzzy variables were developed in terms of the properties of interval arithmetic. According to the rules and by the theory of interval finite element method, procedures for solving the static governing equations of fuzzy finite element method of structures were presented. By the proposed procedure, the possibility distributions of responses of fuzzy structures can be generated in terms of the membership functions of the input fuzzy numbers. It is shown by a numerical example that the computational burden of the presented procedures is low and easy to implement. The effectiveness and usefulness of the presented procedures are also illustrated.

Journal ArticleDOI
TL;DR: The solitary wave solutions for the Klein-Gordon-Schrodinger Equations were obtained by using the homogeneous balance principle as discussed by the authors, which is more generalized than the result that has been proved by pure theoretical and qualitative method in literature.
Abstract: The solitary wave solutions for the Klein-Gordon-Schrodinger Equations were obtained by using the homogeneous balance principle. The form of the solutions is more generalized than the result that has been proved by pure theoretical and qualitative method in literature; namely, the form of solutions in literature is a particular case of result of the present paper.

Journal ArticleDOI
TL;DR: In this article, a cnoidal wave solution of the two dimensional RLW equation of are obtained by elliptic integral method, and some estimations the uniqueness and the stability of the periodic solution with both x, y to the Cauchy problem are proved by the priori estimations.
Abstract: A cnoidal wave solution of the two dimensional RLW equation of are obtained by elliptic integral method, and the some estimations the uniqueness and the stability of the periodic solution with both x, y to the Cauchy problem are proved by the priori estimations.

Journal ArticleDOI
TL;DR: Simulation result shows that this method is easily carried out with high precision, applicable for all kinds of symmetrical window functions and having high ability of anti-noise.
Abstract: A general method called time-shifting correcting method of phase difference on discrete spectrum is presented. That is, the second discrete-time sequence lags behind the first one with L points, then performing N-point FFT analysis on both sequences, and finally correcting spectrum by making use of the phase difference of two corresponding peak lines. The method proposed by XIE Ming et al. is just the particular case of this method in the case that L is equal to N. Simulation result shows that this method is easily carried out with high precision, applicable for all kinds of symmetrical window functions and having high ability of anti-noise.

Journal ArticleDOI
董力耘1, 薛郁1, 戴世强1, Dong Li-Yun1, Xue Yu1, Dai Shi-Qiang1 
TL;DR: An improved one-dimensional CA (Cellular Automaton) traffic model was proposed to describe the highway traffic under the periodic boundary conditions and it is found that there exists the metastability and hysteresis effect of traffic flow in the neighborhood of critical density under different initial conditions.
Abstract: An improved one-dimensional CA (Cellular Automaton) traffic model was proposed to describe the highway traffic under the periodic boundary conditions. This model was based on the idea of the car-following model, which claims that the motion of a vehicle at one time step depends on both its headway and the synchronous motion of the front vehicle, thus including indirectly the influence of its sub-neighboring vehicle. In addition, the socalled safety distance was introduced to consider the deceleration behavior of vehicles and the stochastic factor was taken into account by introducing the deceleration probability. Meanwhile, the conditional deceleration in the model gives a better description of the phenomena observed on highways. It is found that there exists the metastability and hysteresis effect of traffic flow in the neighborhood of critical density under different initial conditions. Since this model gives a reasonable depiction of the motion of a single vehicle, it is easy to be extended to the case of traffic flow under the control of traffic lights in cities.

Journal ArticleDOI
TL;DR: In this article, an approximate iteration algorithm on nonlinear governing equation was presented, and the obtained results show that, if altitude difference and span of the riverbanks are taken as 5 meters and 100 meters, respectively, the maximum gradient in the middle of the bridge exceeds 5%, much larger than maximum allowance gradient in railway design code.
Abstract: The solution and computational aspects on nonlinear deflection of Yongjiang Railway Bridge in Ningbo were investigated. An approximate iteration algorithm on nonlinear governing equation was presented, and the obtained results show that, if altitude difference and span of the riverbanks are taken as 5 meters and 100 meters, respectively, the maximum gradient in the middle of the bridge exceeds 5%, much larger than maximum allowance gradient in railway design code. Therefore, a new solution scheme for decreasing gradient of the bridge is put forward, that is, the altitude difference between two riverbanks can be decreased to about 1/10 of the initial magnitude by building roadbeds with 0.5% gradient and 1 kilometer length at two riverbanks. As a direct result, the deflection gradient of the railway bridge is much reduced and the value is between 0.5%∼0.6%.

Journal ArticleDOI
TL;DR: In this article, a method for the transient responses of axisymmetric plain strain problems of cylindrical shells subjected to dynamic loads was developed for the static plain strain problem of cylinders.
Abstract: A method is developed for the transient responses of axisymmetric plain strain problems of cylindrical shells subjected to dynamic loads. Firstly, a special function was introduced to transform the inhomogeneous boundary conditions into the homogeneous ones. Secondly, using the method of separation of variables, the quantity that the displacement subtracts the special function was expanded as the multiplication series of Bassel functions and time functions. Then by virtue of the orthogonal properties of Bessel functions, the equation with respect to the time variable was derived, of which the solution is easily obtained. The displacement solution was finally obtained by adding the two parts mentioned above. The present method can avoid the integral transform and is fit for arbitrary loads. Numerical results are presented for internally shocked isotropic and cylindrically isotropic cylindrical shells and externally shocked cylinders, as well as for an externally shocked, cylindrically isotropic cylindrical shell that is fixed at the internal surface.

Journal ArticleDOI
TL;DR: In this paper, a three dimensional steady flow field generated by transverse sonic injection into a supersonic flow was simulated by solving the Favre-averaged Navier-Stokes equations using the weighted essentially nonoscillatory (WENO) schemes and Jones-Launder k-e model.
Abstract: Three dimensional steady flowfield generated by transverse sonic injection into a supersonic flow was simulated by solving the Favre-averaged Navier-Stokes equations using the weighted essentially nonoscillatory (WENO) schemes and Jones-Launder k-e model. Results indicate that in the upstream of the square injection there exist two main recirculation regions and the primary vortex induces the horseshoe vortex region. In the downstream there is a low pressure region which conduces a pair of helical vortex.

Journal ArticleDOI
TL;DR: In this article, a classification of the bifurcations with the type of constraint was discussed and six types of transition sets were derived, in which three types are newly found and a method was proposed for analyzing the constrained bifurbation.
Abstract: Bifurcation of periodic solutions widely existed in nonlinear dynamical systems is a kind of constrained one in intrinsic quality because its amplitude is always non-negative. Classification of the bifurcations with the type of constraint was discussed. All its six types of transition sets are derived, in which three types are newly found and a method is proposed for analyzing the constrained bifurcation.

Journal ArticleDOI
TL;DR: In this paper, a vorticity-velocity method was used to study the incompressible viscous fluid flow around a circular cylinder with surface suction or blowing, and the resulting high order implicit difference equations were effeciently solved by the modified incomplete LU decomposition conjugate gradient scheme (MILU-CG).
Abstract: A vorticity-velocity method was used to study the incompressible viscous fluid flow around a circular cylinder with surface suction or blowing. The resulted high order implicit difference equations were effeciently solved by the modified incomplete LU decomposition conjugate gradient scheme (MILU-CG). The effects of surface suction or blowing’s position and strength on the vortex structures in the cylinder wake, as well as on the drag and lift forces at Reynoldes number Re=100 were investigated numerically. The results show that the suction on the shoulder of the cylinder or the blowing on the rear of the cylinder can effeciently suppress the asymmetry of the vortex wake in the transverse direction and greatly reduce the lift force; the suction on the shoulder of the cylinder, when its strength is properly chosen, can reduce the drag force significantly, too.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the formation of sand ripples is due to the instability of the laminar flow or the evolution of small-scale coherent structures in the sublayer adjacent to the wall of the open channel.
Abstract: In the flow on a mobile bed in an open channel, sand ripple often appears after the sediment begins to move. Different scholars have different views on the formation of sand ripples. This paper holds that as the ripple in general is very small, its formation is due to the instability of the laminar flow or the evolution of the small-scale coherent structures in the sublayer adjacent to the wall of the open channel. When the shear stresses caused by the disturbing waves or the coherent structure near the bed surface boundary and the water flow itself are greater than the shields stresses, responses on the bed surface appear and the sand ripple forms. If the frequency of the shear stress caused by the disturbance is close to the natural frequency of the sand grains that produced resonance, such a phenomenon is called the “detection property” of the sediment. It is at this point that the maximum resonance appears and the sand ripple develops rapidly.

Journal ArticleDOI
TL;DR: The traveling wave soliton solutions and pair soliton solution to a class of new completely integrable shallow water equation, Camassa-Holm equation are studied in this paper, where the concept of concave or convex peaked soliton and smooth soliton were introduced.
Abstract: The traveling wave soliton solutions and pair soliton solution to a class of new completely integrable shallow water equation, Camassa-Holm equation are studied. The concept of concave or convex peaked soliton and smooth soliton were introduced. And the research shows that the traveling wave solution of that equation possesses concave and convex peaked soliton and smooth soliton solutions with the peakson. Simultaneously by applying Backlund transformation the new pair soliton solutions to this class of equation are given.

Journal ArticleDOI
TL;DR: In this paper, the orientation distribution function of cylindrical particle suspensions was deduced and numerically simulated, and an application was taken in a wedge-shaped flow field, which showed that comparing with the most probable angle distribution, the distribution of the steady state doesn't vary much in range; the main difference is the anti-clockwise rotation in the right and upper field, that is, particles rotate more at the points where the velocity gradients are larger.
Abstract: The orientation distribution function of cylindrical particle suspensions was deduced and numerically simulated, and an application was taken in a wedge-shaped flow field. The relationship between the orientation distribution function and particle orientation angles was obtained. The results show that comparing with the most probable angle distribution which comes to being in short time, the distribution of the steady state doesn't vary much in range; the main difference is the anti-clockwise rotation in the right and upper field, that is, particles rotate more at the points where the velocity gradients are larger. The most probable orientations are close to the direction of local streamlines. In the direction of streamlines, with poleradius decreasing, the most probable angles increase, but the angles between their orientations and the local streamlines decrease.

Journal ArticleDOI
TL;DR: Using the matrix measure and delay differential inequality, the sufficient conditions were obtained for exponential stability of interval dynamical system with multidelay as discussed by the authors, which is an improvement and extension of the results achieved in earlier papers presented by LIAO, LIU, ZHANG, SUN, et al.
Abstract: Using the matrix measure and delay differential inequality, the sufficient conditions were obtained for exponential stability of interval dynamical system with multidelay. These conditions are an improvement and extension of the results achieved in earlier papers presented by LIAO, LIU, ZHANG, SUN, et al.

Journal ArticleDOI
TL;DR: In this paper, the authors applied the Donnell theory of shell motion to describe shell motion, and the inner and outer shells were stiffened by transverse components using deformation harmonious conditions of the interface, the effects of stiffeners were treated as reverse forces and moments on the double cylindrical shell.
Abstract: The Donnell theory of shell was applied to describe shell motion. The inner and outer shells were stiffened by transverse components. Using deformation harmonious conditions of the interface, the effects of stiffeners were treated as reverse forces and moments on the double cylindrical shell. In the acoustic field produced by vibration and sound radiation of the double shell, the structure dynamic equation, Helmholtz equation in the fluid field and the continuity conditions of the surface of fluid-structure compose the vibration equation coupled by the sound-fluid-structure. The extract of acoustic pressure comes down to the extract of coupling vibration equation. The near field acoustic pressure can be solved directly by complicated calculational methods.

Journal ArticleDOI
TL;DR: Based on the conventional arc length method, an improved arc-length method with high-efficiency is proposed in this paper, where weighted modifications with respect to the variation of structural stiffness and extra-interpolation modification by using the information of known equilibrium points are introduced to improve the incremental arc length.
Abstract: Based on the conventional arc-length method, an improved arc-length method with high-efficiency is proposed. The weighted modifications with respect to the variation of structural stiffness and extra-interpolation modification by using the information of known equilibrium points are introduced to improve the incremental arc-length. An approximate expansion method for the accumulated and expected arc-length is used to ensure the convergence at given load levels in large range of applications. Numerical results show that the improved arc-length method has well adaptability and higher efficiency in the post-buckling analysis of plates and shells structures for tracing whole load-deflection path and obtaining the convergence values at any specified load levels.

Journal ArticleDOI
TL;DR: In this article, the existence and global exponential stability of Hopfield neural networks with periodic inputs are given by using Mawhin's coincidence degree theory and Liapunov's function method without assuming the boundedness and differentiability of nonlinear activation functions.
Abstract: Without assuming the boundedness and differentiability of the nonlinear activation functions, the new sufficient conditions of the existence and the global exponential stability of periodic solutions for Hopfield neural network with periodic inputs are given by using Mawhin's coincidence degree theory and Liapunov's function method.

Journal ArticleDOI
TL;DR: The Birkhoff system is a generalization of the Hamiltonian system and generalized canonical transformations are studied in this paper, where the generalized canonical transformation is extended into the Birkhofian system using the Kailey transformation.
Abstract: The Birkhoff systems are the generalization of the Hamiltonian systems Generalized canonical transformations are studied The symplectic algorithm of the Hamiltonian systems is extended into that of the Birkhoffian systems Symplectic differential scheme of autonomous Birkhoffian systems was structured and discussed by introducing the Kailey Transformation

Journal ArticleDOI
TL;DR: In this article, the principal resonance of Van der Pol-Duffing oscillator to combined deterministic and random parametric excitations is investigated, and the behavior, stability and bifurcation of steady state response are studied.
Abstract: The principal resonance of Van der Pol-Duffing oscillator to combined deterministic and random parametric excitations is investigated. The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The behavior, stability and bifurcation of steady state response were studied. Jumps were shown to occur under some conditions. The effects of damping, detuning, bandwidth, and magnitudes of deterministic and random excitations are analyzed. The theoretical analysis were verified by numerical results.

Journal ArticleDOI
TL;DR: In this paper, the macroscopic steady creep behavior of short fiber reinforcement matrix composites under uniaxial stress states was investigated and a statistical model was presented based on the numerical results of the unit cell models.
Abstract: The aim of the paper is to discover the general creep mechanisms for the short fiber reinforcement matrix composites (MMCs) under uniaxial stress states and to build a relationship between the macroscopic steady creep behavior and the material micro geometric parameters. The unit cell models were used to calculate the macroscopic creep behavior with different micro geometric parameters of fibers on different loading directions. The influence of the geometric parameters of the fibers and loading directions on the macroscopic creep behavior had been obtained, and described quantitatively. The matrix/fiber interface had been considered by a third layer, matrix/fiber interlayer, in the unit cells with different creep properties and thickness. Based on the numerical results of the unit cell models, a statistic model had been presented for the plane randomly-distributed-fiber MMCs. The fiber breakage had been taken into account in the statistic model for it starts experimentally early in the creep life. With the distribution of the geometric parameters of the fibers, the results of the statistic model agree well with the experiments. With the statistic model, the influence of the geometric parameters and the breakage of the fibers as well as the properties and thickness of the interlayer on the macroscopic steady creep rate have been discussed.