Showing papers in "Applied Mathematics and Mechanics-english Edition in 2003"
TL;DR: In this paper, the Hencky transformation was extended and a exact solution of large deformation of circular membrane under the concentrated force has been obtained, making use of the basic equation of large deformations of circular membranes under a concentrated force and its boundary conditions, the problems of nonlinear boundary condition were solved.
Abstract: Making use of basic equation of large deformation of circular membrane under the concentrated force and its boundary conditions and Hencky transformation, the problems of nonlinear boundary condition were solved. The Hencky transformation was extended and a exact solution of large deformation of circular membrane under the concentrated force has been obtained.
30 citations
TL;DR: In this paper, the thermal postbuckling responses of elastic beams, with immovably simply supported ends and subjected to a transversely non-uniformly distributed temperature rising, were investigated.
Abstract: Based on the nonlinear geometric theory of axially extensible beams and by using the shooting method, the thermal post-buckling responses of an elastic beams, with immovably simply supported ends and subjected to a transversely non-uniformly distributed temperature rising, were investigated. Especially, the influences of the transverse temperature change on the thermal post-buckling deformations were examined and the corresponding characteristic curves were plotted. The numerical results show that the equilibrium paths of the beam are similar to what of an initially deformed beam because of the thermal bending moment produced in the beam by the transverse temperature change.
20 citations
TL;DR: In this article, the influence of labyrinth seal on the stability of unbalanced rotor system was presented, where the Muszynska model of seal force and shooting method were used to investigate synchronous solution of the dynamic equation of rotor system.
Abstract: The influence of labyrinth seal on the stability of unbalanced rotor system was presented. Under the periodic excitation of rotor unbalance, the whirling vibration of rotor is synchronous if the rotation speed is below stability threshold, whereas the vibration becomes severe and asynchronous which is defined as unstable if the rotation speed exceeds threshold. The Muszynska model of seal force and shooting method were used to investigate synchronous solution of the dynamic equation of rotor system. Then, based on Floquet theory the stability of synchronous solution and unstable dynamic characteristic of system were analyzed.
20 citations
TL;DR: In this paper, a new numerical method for the fractional integral that only stores part history data is presented, and its discretization error is estimated, and the method can be used to solve the integro-differential equation including fractional integral integral or fractional derivative in a long history.
Abstract: A new numerical method for the fractional integral that only stores part history data is presented, and its discretization error is estimated. The method can be used solve the integro-differential equation including fractional integral or fractional derivative in a long history. The difficulty of storing all history data is overcome and the error can be controlled. As application, motion equations governing the dynamical behavior of a viscoelastic Timoshenko beam with fractional derivative constitutive relation are given. The dynamical response of the beam subjected to a periodic excitation is studied by using the separation variables method. Then the new numerical method is used to solve a class of weakly singular Volterra integro-differential equations which are applied to describe the dynamical behavior of viscoelastic beams with fractional derivative constitutive relations. The analytical and unmerical results are compared. It is found that they are very close.
19 citations
TL;DR: In this paper, a lowest order finite difference scheme based on mixed finite element method for non-stationary natural convection problem was derived, where the numerical solution of velocity, pressure, and temperature can be found together, and a numerical example to simulate the close square cavity is given.
Abstract: The non-stationary natural convection problem is studied. A lowest order finite difference scheme based on mixed finite element method for non-stationary natural convection problem, by the spatial variations discreted with finite element method and time with finite difference scheme was derived, where the numerical solution of velocity, pressure, and temperature can be found together, and a numerical example to simulate the close square cavity is given, which is of practical importance.
18 citations
TL;DR: A new discrete approximation to the convection term of the covection-diffusion equation was constructed in Saul's type difference scheme, then the alternating segment Crank-Nicolson (ASC-N) method was developed as discussed by the authors.
Abstract: A new discrete approximation to the convection term of the covection-diffusion equation was constructed in Saul' yev type difference scheme, then the alternating segment Crank-Nicolson (ASC-N) method for solving the convection-diffusion equation with variable coefficient was developed. The ASC-N method is unconditionally stable. Numerical experiment shows that this method has the obvious property of parallelism and accuracy. The method can he used directly on parallel computers.
18 citations
TL;DR: In this paper, a mathematical model of an impacting-rub rotor system with bending-torsion coupling was established, and compared with the model without bending-torion coupling through the modern nonlinear dynamic theory.
Abstract: A mathematical model of an impacting- rub rotor system with bending-torsion coupling was established. It was compared with the model without bending-torsion coupling through the modern nonlinear dynamic theory. It is observed that periodical, chaotic, period adding phenomena in them and the two models have a similar bifurcation process in their bifurcation figures. But the influence of bending-torsion on the dynmaic characteristics of the system is not neglected. The results have considerable meanings to analyze and improve the characteristics of an impacting-rub rotor system.
17 citations
TL;DR: In this article, the conditions for coexistence of single impact periodic orbits are derived, and in particular, it is investigated in details how to assure that no other impacts will happen in an evolution period of a single-impact periodic motion.
Abstract: A method is presented to seek for coexisting periodic orbits which may be stable or unstable in piecewise-linear vibro-impacting systems. The conditions for coexistence of single impact periodic orbits are derived, and in particular, it is investigated in details how to assure that no other impacts will happen in an evolution period of a single impact periodic motion. Furthermore, some criteria for nonexistence of single impact periodic orbits with specific periods are also established. Finally, the stability of coexisting periodic orbits is discussed, and the corresponding computation formula is given. Examples of numerical simulation are in good agreement with the theoretic analysis.
16 citations
TL;DR: In this paper, the analytical solution of a simply supported piezoelectric beam subjected to a uniformly distributed loading has been studied using the inverse method, and the polynomials of stress function and induction function are given.
Abstract: Using the inverse method, the analytical solution of a simply supported piezoelectric beam subjected to a uniformly distributed loading has been studied. First, the polynomials of stress function and induction function are given. Then, considering the gradient properties of the elastic parameter and the potential functon as well as the piezoelectric parameter, the analytical solution of a simply supported beam subjected to a uniformly distributed loading is obtained and discussed.
16 citations
TL;DR: In this article, the existence theorems of maximal elements for a family of GB-majorized mappings in a product space of G-convex spaces, some coincidence theorem, Fan-Browder type fixed point theorem and some existence theoresms of solutions for a system of minimax inequalities are proved under noncompact setting of Gconcave spaces.
Abstract: By applying existence theorems of maximal elements for a family of GB-majorized mappings in a product space of G-convex spaces, some coincidence theorem, Fan-Browder type fixed point theorem and some existence theorems of solutions for a system of minimax inequalities are proved under noncompact setting of G-convex spaces. These theorems improve and generalize many important known results in literature.
16 citations
TL;DR: In this paper, the output of chaotic transition system was sampled at a given sampling rate, then the sampled output was used by a feedbacks subsystem to construct a control signal for controlling chaotic transition systems to the origin.
Abstract: The method for controlling chaotic transition system was investigated using sampled-data. The output of chaotic transition system was sampled at a given sampling rate, then the sampled output was used by a feedbacks subsystem to construct a control signal for controlling chaotic transition system to the origin. Numerical simulations are presented to show the effectiveness and feasibility of the developed controller.
TL;DR: In this paper, a brief survey of fractional calculus and fractional differential forms was given, and the fractional exterior transition to curvilinear coordinate at the origin was discussed.
Abstract: A brief survey of fractional calculus and fractional differential forms was firstly given The fractional exterior transition to curvilinear coordinate at the origin were discussed and the two coordinate transformations for the fractional differentials for three-dimensional Cartesian coordinates to spherical and cylindrical coordinates are obtained, respectively In particular, for v=m=1, the usual exterior transformations, between the spherical coordinate and Cartesian coordinate, as well as the cylindrical coordinate and Cartesian coordinate, are found respectively, from fractional exterior transformation
TL;DR: In this article, the coupling interaction between the surface-wave mode and internal wave mode must be taken into account for the cases of large density difference between two layers, the source approaching to the pynocline and the total Froude number Fr close to the critical number Fr2.
Abstract: Based on the potential flow theory of water waves, the interaction mechanism between the free-surface and internal waves generated by a moving point source in the lower layer of a two-layer fluid was studied. By virtue of the method of Green's function, the properties of the divergence field at the free surface were obtained, which plays an important role in the SAR (Synthetic Aperture Radar) image. It is shown that the coupling interaction between the surface-wave mode and internal-wave mode must be taken into account for the cases of large density difference between two layers, the source approaching to the pynocline and the total Froude number Fr close to the critical number Fr2. The theoretical analysis is qualitatively consistent with the experimental results presented by Ma Hui-yang.
TL;DR: Based on the Kelvin viscoelastic differential constitutive law and the motion equation of the axially moving belt, the nonlinear dynamic model of the visco-elastic axial moving belt was established as mentioned in this paper.
Abstract: Based on the Kelvin viscoelastic differential constitutive law and the motion equation of the axially moving belt, the nonlinear dynamic model of the viscoelastic axial moving belt was established. And then it was reduced to be a linear differential system which the analytical solutions with a constant transport velocity and with a harmonically varying transport velocity were obtained by applying Lie group transformations. According to the nonlinear dynamic model, the effects of material parameters and the steady-state velocity and the perturbed axial velocity of the belt on the dynamic responses of the belts were investigated by the research of digital simulation. The result shows: 1) the nonlinear vibration frequency of the belt will become small when the relocity of the belt increases. 2) Increasing the value of viscosity or decreasing the value of elasticity leads to a deceasing in vibration frequencies. 3) The most effects of the transverse amplitudes come from the frequency of the perturbed velocity when the belt moves with harmonic velocity.
TL;DR: In this paper, a general algorithm is applied to the regularization of nearly singular integrals in the boundary element method of planar potential problems, and quadratic elements are used in addition to linear ones.
Abstract: A general algorithm is applied to the regularization of nearly singular integrals in the boundary element method of planar potential problems. For linear elements, the strongly singular and hypersingular integrals of the interior points very close to boundary were categorized into two forms. The factor leading to the singularity was transformed out of the integral representations with integration by parts, so non-singular regularized formulas were presented for the two forms of integrals. Furthermore, quadratic elements are used in addition to linear ones. The quadratic element very close to the internal point can be divided into two linear ones, so that the algorithm is still valid. Numerical examples demonstrate the effectiveness and accuracy of this algorithm. Especially for problems with curved boundaries, the combination of quadratic elements and linear elements can give more accurate results.
TL;DR: In this article, a complete system of basic balance laws and equations for micropolar continuum theory is presented based on the restudies of existing polar continuum theories and the new coupled balance laws of linear momentum, angular momentum and energy are reestablished.
Abstract: Based on the restudies of existing polar continuum theories rather complete systems of basic balance laws and equations for micropolar continuum theory are presented. In these new systems not only the additional angular momentum, surface moment and body moment produced by the linear momentum, surface force and body force, respectively, but also the additional velocity produced by the angular velocity are considered. The new coupled balance laws of linear momentum, angular momentum and energy are reestablished. From them the new coupled local and nonlocal balance equations are naturally derived. Via contrast it can be clearly seen that the new results are believed to be rather general and complete.
TL;DR: In this paper, the Hilbert problem of complex potentials for three material regions was reduced to a functional equation in the complex potential of the interphase layer, resulting in an explicit series solution.
Abstract: The interaction of a screw dislocation in the interphase layer with the circular inhomogeneity and matrix was dealt with. An efficient method for multiply connected regions was developed by combining the sectionally subholomorphic function theory, Schwarz symmetric principle and Cauchy integral technique. The Hilbert problem of the complex potentials for three material regions was reduced to a functional equation in the complex potential of the interphase layer, resulting in an explicit series solution. By using the present solution the interaction energy and force acting dislocation were evaluated and discussed.
Journal Article•
TL;DR: In this article, the spectrum distribution of the second order generalized distributed parameter system was discussed via functional analysis and operator theory in Hilbert space, and the solutions of the problem and the constructive expression of the solutions are given by the generalized inverse one of bounded linear operator.
Abstract: Spectrum distribution of the second order generalized distributed parameter system was discussed via the functional analysis and operator theory in Hilbert space.The solutions of the problem and the constructive expression of the solutions are given by the generalized inverse one of bounded linear operator.This is theoretically important for studying the stabilization and asymptotic stability of the second order generalized distributed parameter system.
Journal Article•
TL;DR: In this paper, a nonlinear dynamic model of the viscoelastic axial moving belt was established and the analytical solutions with a constant transport velocity and with a harmonically varying transport velocity were obtained by applying Lie group transformations.
Abstract: Based on the Kelvin viscoelastic differential constitutive law and the motion equation of the axially moving belt,the nonlinear dynamic model of the viscoelastic axial moving belt was established.And then it was reduced to be a linear differential system which the analytical solutions with a constant transport velocity and with a harmonically varying transport velocity were obtained by applying Lie group transformations.According to the nonlinear dynamic model,the effects of material parameters and the steady_state velocity and the perturbed axial velocity of the belt on the dynaic responses of the belts were investigated by the research of digital simulation.The result shows:1) The nonlinear vibration frequency of the belt will become small when the velocity of the belt increases.2) Increasing the value of viscosity or decreasing the value of elasticity leads to a deceasing in vibration frequencies.3) The most effects of the transverse amplitudes come from the frequency of the perturbed velocity when the belt moves with harmonic velocity.
TL;DR: All mathematic description about the RVFP has the closing operation for fuzzy probability, as a result, the foundation of perfecting fuzzy probability operation method is laid.
Abstract: Mathematic description about the second kind fuzzy random variable namely the random variable with crisp event—fuzzy probability was studied. Based on the interval probability and using the fuzzy resolution theorem, the feasible condition about a probability fuzzy number set was given go a step further the definition and characters of random variable with fuzzy probability (RVFP) and the fuzzy distribution function and fuzzy probability distribution sequence of the RVFP were put forward. The fuzzy probability resolution theorem with the closing operation of fuzzy probability was given and proved. The definition and characters of mathematical expectation and variance of the RVFP were studied also. All mathematic description about the RVFP has the closing operation for fuzzy probability, as a result, the foundation of perfecting fuzzy probability operation method is laid.
TL;DR: It is shown that for the hybrid probabilistic and fuzzy reliability problems, the probability of failure should be suitably taken as a fuzzy variable in order to indicate the real safety of system objectively.
Abstract: Traditionally, the calculation of reliability of fuzzy random structures is based on the well-known formulation of probability of fuzzy events But sometimes the results of this formulation will not indicating the real state of safety of fuzzy-random structures Based on the possibility theory, a computational procedure for the reliability analysis of fuzzy failure problems and random-fuzzy failure problems of mechanical structures that contain fuzzy variables were presented A procedure for the analysis of structural reliability of problems of fuzzy failure criterion was also proposed The failure possibility of fuzzy structures and possibility distribution of the probability of failure of fuzzy-random structures can be given by the proposed methods It is shown that for the hybrid probabilistic and fuzzy reliability problems, the probability of failure should be suitably taken as a fuzzy variable in order to indicate the real safety of system objectively Two examples illustrate the validity and rationality of the proposed methods
TL;DR: In this paper, the balance laws of momentum, angular momentum and energy for micromorphic continuum mechanics and couple stress theory were derived via direct transitions and reductions from the coupled conservation law of energy.
Abstract: The purpose is to reestablish the balance laws of momentum, angular momentum and energy and to derive the corresponding local and nonlocal balance equations for micromorphic continuum mechanics and couple stress theory. The desired results for micromorphic continuum mechanics and couple stress theory are naturally obtained via direct transitions and reductions from the coupled conservation law of energy for micropolar continuum theory, respectively. The basic balance laws and equations for micromorphic continuum mechanics and couple stress theory are constituted by combining these results derived here and the traditional conservation laws and equations of mass and microinertia and the entropy inequality. The incomplete degrees of the former related continuum theories are clarified. Finally, some special cases are conveniently derived.
TL;DR: In this article, a new family of set-valued mappings from a topological space into generalized convex spaces was introduced and studied by using the continuous partition of unity theorem and Brouwer fixed point theorem.
Abstract: A new family of set-valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set-valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems improve, unify and generalize many important results in recent literature.
TL;DR: In this paper, a series of switched processes generalized M (Mandelbrot) sets for complex index number were constructed, and the construction characteristics of the generalized M sets were expounded according to the analysis of the algorithm constructing the switched process generalized m sets.
Abstract: According to the switched complex mapping proposed by the author, the method constructing the switched processes generalized M (Mandelbrot) sets was elaborated, and a series of the switched processes generalized M sets for complex index number were constructed. The construction characteristics of the generalized M sets were expounded according to the analysis of the algorithm constructing the generalized M sets. On the basis of what has already been achieved, the trajectories of a starting point in the complex C-plane under the switched mapping were researched into. The results show that the switched processes generalized M sets have the fractal feature, the construction characteristics of the switched processes generalized M sets are dependent on the complex index number w and the switched variable r0, and the reason which results in the discontinuity of the switched processes generalized M sets is the discontinuity of choice of the principal range of the phase angle.
TL;DR: In this paper, the nonlinear boundary value problem of a corrugated diaphragm was reduced to nonlinear integral equations by applying the method of Green's function, and a so-called interpolated parameter important to prevent divergence was introduced into the iterative format.
Abstract: By using the simplified Reissner's equation of axisymmetric shells of revolution, the nonlinear bending of a corrugated annular plate with a large boundary corrugation and a nondeformable rigid body at the center under compound load are investigated. The nonlinear boundary value problem of the corrugated diaphragm reduces to the nonlinear integral equations by applying the method of Green's function. To solve the integral equations, a so-called interpolated parameter important to prevent divergence is introduced into the iterative format. Computation shows that when loads are small, any value of interpolated parameter can assure the convergence of iteration. Interpolated parameter equal or almost equal to 1 yields a faster convergence rate; when loads are large, interpolated parameter cannot be taken too large in order to assure convergence The characteristic curves of the corrugated diaphragm for different load combinations are given. The obtained characteristic curves are available for reference to design. It can be concluded that the deflection is larger when the diaphragm is acted by both uniform load and concentrated load than when it is acted only by uniform load. The solution method can be applied to corrugated shells of arbitrary diametral sections.
TL;DR: According to the large amplitude equation of the circular plate on nonlinear elastic foundation, elastic resisting force has linear item, cubic nonlinear item and resisting bend elastic item. as mentioned in this paper The critical curves of the chaotic region and phase figure under some foundation parameters are obtained with the method of digital artificial.
Abstract: According to the large amplitude equation of the circular plate on nonlinear elastic foundation, elastic resisting force has linear item, cubic nonlinear item and resisting bend elastic item. A nonlinear vibration equation is obtained with the method of Galerkin under the condition of fixed boundary. Floquet exponent at equilibrium point is obtained without external excitation. Its stability and condition of possible bifurcation is analysed. Possible chaotic vibration is analysed and studied with the method of Melnikov with external excitation. The critical curves of the chaotic region and phase figure under some foundation parameters are obtained with the method of digital artificial.
TL;DR: In this paper, a new method developed from orbital element description of single satellite, named relative orbital element method (ROEM) was introduced, with clear physics conception and wide application range, overcomes the limitation of C-W's equation, and the periodic solution is a natural conclusion.
Abstract: Recently, the research of dynamics and control of the satellite formation flying has been attracting a great deal of attentions of the researchers. The theory of the research was mainly based on Clohessy-Wiltshire's (C-W's) equations, which describe the relative motion between two satellites. But according to some special examples and qualitative analysis, neither the initial parameters nor the period of the solution of C-W's equations accord with the actual situation, and the conservation of energy is no longer held. A new method developed from orbital element description of single satellite, named relative orbital element method (ROEM), was introduced. This new method, with clear physics conception and wide application range, overcomes the limitation of C-W's equation, and the periodic solution is a natural conclusion. The simplified equation of the relative motion is obtained when the eccentricity of the main satellite is small. Finally, the results of the two methods (C-W's equation and ROEM) are compared and the limitations of C-W's equations are pointed out and explained.
TL;DR: A class of nonlinear nonlocal for singularly perturbed Robin initial boundary value problems for reaction diffusion equations is considered in this article, under suitable conditions, the outer solution of the original problem is obtained, secondly, using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed, and using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary values problems are studied and educing some relational inequalities the existence and uniqueness of solution.
Abstract: A class of nonlinear nonlocal for singularly perturbed Robin initial boundary value problems for reaction diffusion equations is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed, finally, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems are studied and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation is discussed.
TL;DR: The Chebyshev pseudospectral approximation of the homogenous initial boundary value problem for a class of multi-dimensional generalized symmetric regularized long wave (SRLW) equations is considered and the convergence of the approximation solution and the optimum error of approximation solution are obtained.
Abstract: The Chebyshev pseudospectral approximation of the homogenous initial boundary value problem for a class of multi-dimensional generalized symmetric regularized long wave (SRLW) equations is considered. The fully discrete Chebyshev pseudospectral scheme is constructed. The convergence of the approximation solution and the optimum error of approximation solution are obtained.
TL;DR: The vascular stress-strain relationship under equilibrium state was analyzed and the circumferential and axial elastic moduli were deduced that are expressed while the arterial strains around the equilibrium state are relatively small, so that the equations of vessel wall motion under the pulsatile pressure could be established here.
Abstract: Blood flow in artery was treated as the flow under equilibrium state (the steady flow under mean pressure) combined with the periodically small pulsatile flow. Using vascular strain energy function advanced by Fung, the vascular stress-strain relationship under equilibrium state was analyzed and the circumferential and axial elastic moduli were deduced that are expressed while the arterial strains around the equilibrium state are relatively small, so that the equations of vessel wall motion under the pulsatile pressure could be established here. Through solving both the vessel equations and the linear Navier-Stokes equations, the analytic expressions of the blood flow velocities and the vascular displacements were obtained. The influence of the difference between vascular circumferential and axial elasticities on pulsatile blood flow and vascular motion was discussed in details.