Showing papers in "Applied Mathematics and Mechanics-english Edition in 1998"
TL;DR: In this paper, the basic ideas of a new analytic technique, namely the Homotopy Analysis Method (HAM), are described, and the validity of the HAM is independent on whether or not there exist small parameters in considered nonlinear equations.
Abstract: In this paper, the basic ideas of a new analytic technique, namely the Homotopy Analysis Method (HAM), are described. Different from perturbation methods, the validity of the HAM is independent on whether or not there exist small parameters in considered nonlinear equations. Therefore, it provides us with a powerful analytic tool for strongly nonlinear problems. A typical nonlinear problem is used as an example to verify the validity and the great potential of the HAM.
186 citations
TL;DR: In this paper, numerical simulations have been performed in time-developing plane mixing layers of the viscoelastic second-order fluids with pseudo-spectral method for roll-up, pairing and merging of large eldies.
Abstract: Numerical simulations have been performed in time-developing plane mixing layers of the viscoelastic second-order fluids with pseudo-spectral method. Roll-up, pairing and merging of large eldies were examined at high Reynolds numbers and low Deborah numbers. The effect of viscoelastics on the evolution of the large coherent structure was shown by making a comparison between the second-order and Newtonian fluids at the same Reynolds numbers.
52 citations
TL;DR: In this article, an approach is proposed for taking calculations of high order differentials of scaling functions in wavelet theory in order to apply the wavelet Galerkin FEM to numerical analysis of those boundary-value problems with order higher than 2.
Abstract: In this paper, an approach is proposed for taking calculations of high order differentials of scaling functions in wavelet theory in order to apply the wavelet Galerkin FEM to numerical analysis of those boundary-value problems with order higher than 2. After that, it is realized that the wavalet Galerkin FEM is used to solve mechanical problems such as bending of beams and plates. The numerical results show that this method has good precision.
42 citations
TL;DR: In this article, a class of mixed nonlinear variational-like inequalities in reflexive Banach space is studied and some existence uniqueness theorems of solutions for the mixed NN-like inequality are proved.
Abstract: In this paper, the author studies a class of mixed nonlinear variational-like inequalities in reflexive Banach space. By applying a minimax inequality obtained by the author, some existence uniqueness theorems of solutions for the mixed nonlinear variational-like inequalities are proved. Next, by applying the auxiliary problem technique, the author suggests an innovative iterative algorithm to compute the approximate solutions of the mixed nonlinear variational-like inequalities. Finally, the convergence criteria is also discussed.
31 citations
TL;DR: In this article, generalized Duhamel's integral and deflection impulse response function of the beam make it easy for us to obtain final solution of moving line load problem and also present definition of moving dynamic coefficient which reflects moving effect.
Abstract: Based on the principle of linear superposition, this paper proves generalized Duhamel's integral which reverses moving dynamical load problem to fixed dynamical load problem. Laplace transform and Fourier transform are used to solve patial differential equation of infinite beam. The generalized Duhamel's integral and deflection impulse response function of the beam make it easy for us to obtain final solution of moving line load problem. Deep analyses indicate that the extreme value of dynamic response always lies in the center of the line load and travels with moving load at the same speed. Additionally, the authors also present definition of moving dynamic coefficient which reflects moving effect.
27 citations
TL;DR: In this paper, the Backlund transformations for Whitham-broer-kaup equations (WBK) were derived by using a new method and Mathematica, and connections between WBK equation, heat equation and Burgers equation were found, which were used to obtain three families of solutions for WBK equations, one of which is the family of solitary wave solutions.
Abstract: By using a new method and Mathematica, the Backlund transformations for Whitham-Broer-Kaup equations (WBK) are derived. The connections between WBK equation, heat equation and Burgers equation are found, which are used to obtain three families of solutions for WBK equations, one of which is the family of solitary wave solutions.
26 citations
TL;DR: In this paper, the state space exact linearization method is used to control the Lorenz system with a controllable Rayleigh number, and the nonlinear feedback is utilized to design the transformation changing the original chaotic system into a linear controllably one so that the control is realized.
Abstract: Controlling chaos in the Lorenz system with a controllable Rayleigh number is investigated by the state space exact linearization method. Based on proving the exact linearizability, the nonlinear feedback is utilized to design the transformation changing the original chaotic system into a linear controllable one so that the control is realized. Numerical examples of control are presented.
24 citations
TL;DR: In this article, sufficient conditions are obtained for the global asymptotic stability of the equilibrium of neural networks with interneuronal transmission delays of the type described in this paper.
Abstract: In this paper, some sufficient conditions are obtained for the global asymptotic stability of the equilibrium of neural networks with interneuronal transmission delays of the type
$$x'_i (t) = - b_i x_i (t) + \sum\limits_{j = 1}^n {\omega _{\ddot y} f_j (x_j (t - \tau _j )) + p_i (t > 0;i = 1,2, \cdots ,n)} $$
19 citations
TL;DR: In this paper, a new approach to Backlund transformations of nonlinear evolution equations is presented, and the results obtained by this procedure are completely the same as that by Painleve truncating expansion.
Abstract: In this paper, a new approach to Backlund transformations of nonlinear evolution equations is presented. The results obtained by this procedure are completely the same as that by Painleve truncating expansion.
17 citations
TL;DR: In this paper, an equation of solid-liquid coupling vibration of pipe conveying fluid is deduced on the basis of Hamilton principle and an asymmetrical solid- liquid coupling damp matrix and a symmetrical solid liquid coupling stiffness matrix are obtained.
Abstract: On the basis of Hamilton principle, the equation of solid-liquid coupling vibration of pipe conveying fluid is deduced. An asymmetrical solid-liquid coupling damp matrix and a symmetrical solid-liquid coupling stiffness matrix are obtained. UsingQR method, pipe's nature frequencies are calculated. The curves of the first four orders of natural frequency-flow velocity of pipe waw given. The influence of flowing velocity, pressure, solid-liquid coupling damp and solid-liquid coupling stiffness on natural frequency are discussed respectively. The dynamic respondence of the pipes for stepload with different flow velocity are calculated by Newmark method. It is found that, with the flow velocity increased, the nature frequency of the pipes reduced, increased, reduced again and so on.
16 citations
TL;DR: In this article, a definition of the modes of a nonlinear autonomous system was developed by using the geometry theory of invariant manifolds that include stable manifold theorem, center maifold theorm and sub-center manifold theorem.
Abstract: A definition of the modes of a nonlinear autonomous system was developed. The existence conditions and orbits' nature of modes are given by using the geometry theory of invariant manifolds that include stable manifold theorem, center maifold theorm and sub-center manifold theorem. The Taylor series expansion was used in order to approach the sub-manifolds of the modes and obtain the motions of the mods on the manifolds. Two examples were given to demonstrate the applications.
TL;DR: The OOGY method is the most important method of controlling chaos as mentioned in this paper, it stabilizes a hyperbolic periodic orbit by making small perturbations for a system parameter.
Abstract: OGY method is the most important method of controlling chaos. It stabilizes a hyperbolic periodic orbit by making small perturbations for a system parameter. This paper improves the method of choosing parameter, and gives a mathematics proof of it.
TL;DR: In this paper, the authors introduce nonlinear freqyency, using Floquet theory and referring to the characteristics of the solution when it passes through the transition boundaries, all kinds of bifurcation modes and their transition boundaries of the Duffing equation with two periodic excitations as well as the possible ways to chaos are studied.
Abstract: By introducing nonlinear freqyency, using Floquet theory and referring to the characteristics of the solution when it passes through the transition boundaries, all kinds of bifurcation modes and their transition boundaries of Duffing equation with two periodic excitations as well as the possible ways to chaos are studied in this paper.
TL;DR: In this article, the theory of rotational relativistic mechanics is discussed, and a theory of relativist analytical mechanics of the rotational systems is constructed, and furthermore, the Hamilton principle and three kinds of D'Alembert principles are given.
Abstract: The theory of rotational relativistic mechanics is discussed and the theory of relativistic analytical mechanics of the rotational systems is constructed. The relativistic generalized kinetic energy function for the rotational systems\(T_r^* = \sum\limits_{i = 1}^n {I_{oi} \Gamma _i^2 (1 - \sqrt {1 - \dot \theta _i^2 /} \Gamma _i^2 )} \) and the generalized acceleration energy function\(S_r^* = \frac{1}{2}\sum\limits_{i = 1}^n {I_i \left[ {\frac{{(\theta _i \cdot\dot \theta _i )^2 }}{{\Gamma _i^2 - \dot \theta _i^2 }} + \dot \theta _i^2 } \right]} \) are constructed, and furthermore, the Hamilton principle and three kinds of D'Alembert principles are given. For the systems with holonomic constraints, the relativistic Lagrange equation, Nielsen equation, Appell equation and Hamilton canonical equation of the rotational systems are constructed; For the systems with nonholonomic constraints, the relativistic Routh equation, Chaplygin equation, Nielsen equation and Appell equation of the rotational systems are constructed; the relativistic Noether conservation law of the rotational systems are given too.
TL;DR: The response of a nonlinear vibration system may be of three types, namely, periodic, quasiperiodic or chaotic, when the parameters of the system are changed as mentioned in this paper.
Abstract: The response of a nonlinear vibration system may be of three types, namely, periodic, quasiperiodic or chaotic, when the parameters of the system are changed. The periodic motions can be identified by Poincare map, and harmonic wavelet transform (HWT) can distinguish quasiperiod from chaos, so the existing domains of different types of motions of the system can be revealed in the parametric space with the method of HWT joining with Poincar'e map.
TL;DR: In this article, a weakly convex graph for set-valued mappings is introduced and studied, and the best approximation and fixed point theorems are obtained by using the concept, some new coincidence.
Abstract: In this paper, a new concept of weakly convex graph for set-valued mappings is introduced and studied. By using the concept, some new coincidence, the best approximation and fixed point theorems are obtained.
TL;DR: In this article, the Green's functions of the plane problem in transversely isotropic piezoelectric media with an elliptic hole are obtained in terms of exact electric boundary conditions at the rim of the hole.
Abstract: Based on the complex potential method, the Green's functions of the plane problem in transversely isotropic piezoelectric media with an elliptic hole are obtained in terms of exact electric boundary conditions at the rim of the hole. When the elliptic hole degenerates into a crack, the fundamental solutions for the field intensity factors are given. The general solutions for concentrated and distributed loads applied on the surface of the hole or crack are produced through the superposition of the fundamental solutions. With the aid of these solutions, some erroneous results provided previously in other works are pointed out. More important is that these solutions can be used as the fundamental solutions of boundary element method to solve more practical problems in piezoelectric media.
TL;DR: In this article, the generalized Hahn-Banach theorem was proved for K-convex multifunction and K-sublinear multifunction in partially ordered locally convex topological vector space.
Abstract: We have proved generalized Hahn-Banach theorem by using the concept of efficient for K-convex multifunction and K-sublinear multifunction in partially ordered locally convex topological vector space.
TL;DR: In this article, the influence of convection and diffusion on the contamination between batches in multi-products pipeline transport is studied in detail, and the results of numerical computation explain the forming and developing of contamination very well.
Abstract: Contamination between batches in multi-products pipeline transport is studied. The influences of convection and diffusion on the contamination are studied in detail. Diffusion equations, which are mainly controlled by convection, are developed under turbulent pipe flow. The diffusion equation, is separated into a pure convection equation and a pure diffusion equation which are solved by characteristics method and finite difference method respectively to obtain numerical solutions. The results of numerical computation explain the forming and developing of contamination very well.
TL;DR: In this article, the spline wavelet basis was used to construct the approximate inertial manifold, and the behavior of perturbed perodic KdV equation was studied by using the splines.
Abstract: In the paper by using the spline wavelet basis to construct the approximate inertial manifold, we study the longtime behavior of perturbed perodic KdV equation.
TL;DR: In this paper, a surrogate data method of phase-randomized is proposed to identify the random or chaotic nature of the data obtained in dynamic analysis, which can increase the extent of accuracy of the results.
Abstract: In this paper surrogate data method of phase-randomized is proposed to identify the random or chaotic nature of the data obtained in dynamic analysis. The calculating results validate the phase-randomized method to be useful as it can increase the extent of accuracy of the results. And the calculating results show that threshold values of the random timeseries and nonlinear chaotic timeseries have marked difference.
TL;DR: In this article, an idea of "stiffness patition" is proposed to deal with the puzzle that the in-plane normal response is coupled with the shear response of the laminates.
Abstract: The study on property degradation of damaged composite laminates is extended to anisotropic laminates with matrix cracking. In (I) of the paper, an idea of “stiffness patition” is proposed to deal with the puzzle that the in-plane normal response is coupled with the shear response of the laminates. For (θm/90n), laminates containing transversely cracked layers under general in-plane loading, the constitutive relations are derived and the effective stiffnesses are expressed as the function of crack density.
TL;DR: In this article, a topological degree for a class of mappings of the form F=L+S where L is closed densely defined maximal monotones operator and S is a nonlinear multivalued map of class (S+) with respect to the domain of L is given.
Abstract: This paper is to generalize the results of Zhang and Chen[1]. We construct a topological degree for a class of mappings of the form F=L+S where L is closed densely defined maximal monotones operator and S is a nonlinear multivalued map of class (S+) with respect to the domain of L.
TL;DR: In this article, the character of stress increment which causes the rotation of principal stress axes is analyzed and the general stress increment is decomposed into two parts: coaxial part and rotational part.
Abstract: In the light of matrix theory, the character of stress increment which causes the rotation of principal stress axes is analysed and the general stress increment is decomposed into two parts: coaxial part and rotational part. Based on these, the complex three dimensional (3-D) problem involving the rotation of principal stress axes is simplified to the combination of the 3-D coaxial model and the theory about pure rotation of principal stress axes that is only around one principal stress axes. The difficulty of analysis is reduced significantly. The concrete calculating method of general 3-D problem is provided and other applications are also presented.
TL;DR: In this paper, the hyperbolic Lagrangian equation and the Hamilton-Jacobi equation were derived from the invariants of four-dimensional space-time intervals and the Hyperbolic Lorentz transformations.
Abstract: Hyperbolic complex numbers correspond with Minkowski geometry. The hyperbolic Lagrangian equation and the Hamilton-Jacobi equation will be derived from the invariants of four-dimensional space-time intervals and hyperbolic Lorentz transformations.
TL;DR: The article gives a semi-discrete method for solving high-dimension wave equation which is converted by means of discretization into I-D wave equation system which is well-posed and the speed of convergence is high.
Abstract: The article gives a semi-discrete method for solving high-dimension wave equation. By the method, high-dimension wave equation is converted by means of discretization into I-D wave equation system which is well-posed. The convergence of the semidiscrete method is given. The numerical calculating results show that the speed of convergence is high.
TL;DR: In this article, the generalized cell mapping (GCM) method is used to study multiple-attractor coexisting system with parameter uncertainties and the effects that the uncertain parameters has on the global properties of the system are presented.
Abstract: In this paper the generalized cell mapping (GCM) method is used to study multiple-attractor coexisting system with parameter uncertainties. The effects that the uncertain parameters has on the global properties of the system are presented. And It is obtained that the attractor with much smaller value of protect thickness, will disappear firstly with the degree of the uncertainty of parameter increasing.
TL;DR: In this article, a three-porous medium model for transvascular exchange and extravascular transport of fluid and macromolecules in a spherical solid tumor is developed, where the microvasculature, lymphatics, and tissue space are each treated as a porous medium with the flow of blood, lymph, and interstitial fluid obeying Darcy's law and Starling's assumption.
Abstract: A three-porous-medium model for transvascular exchange and extravascular transport of fluid and macromolecules in a spherical solid tumor is developed. The microvasculature, lymphatics, and tissue space are each treated as a porous medium with the flow of blood, lymph, and interstitial fluid obeying Darcy's law and Starling's assumption. In this part, the role of interstitial pressure and fluid convection are studied. The analytical solutions are obtained for the isolated tumor and the normal-tissue-surrounded tumor respectively. The calculated interstitial pressure projue are consistent with the experimental observation that the elevated interstitial pressure is a major barrier in the penetration of macromolecular drug into tumors. The factors which may reduce the interstitial pressure are analyzed in details.
TL;DR: In this article, the active and passive hybrid control of a thin plate with Local Active Constrained damping layer (LACL) is studied. And the results show that the hybrid control method is a better one for vibration control of the plate.
Abstract: This paper concerns in the active and passive hybrid control of vibration of the thin plate with Local Active Constrained damping Layer (LACL). The governing equations of system are formulated based on the constitutive equations of elastic, viscoelastic, piezoelectric materials. Galerkin method and GHM method are employed to transform partial differential equations into ordinary ones with a lower dimension. LQR method of classical control theory is used in simulating calculation. Numeral results show that the active and passive hybrid control manner obtained in this paper is a better one for vibration control of the plate.
TL;DR: In this paper, the modified method of multiple scales is applied to study the bending problems for circular thin plate with large deflection under the hinged and simply supported edge conditions, and series solutions are constructed, the boundary layer effects are analysed and their asymptotics are proved.
Abstract: In this paper, the modified method of multiple scales is applied to study the bending problems for circular thin plate with large deflection under the hinged and simply supported edge conditions. The series solutions are constructed, the boundary layer effects are analysed and their asymptotics are proved.