应用数学和力学

2004 Vol. 25, No. 4

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Nonlinear Dynamical Stability Analysis of the Circular Three-Dimensional Frame

WANG Xin-zhi, WANG Gang, ZHAO Yan-ying, YEH Kai-yuan

2004, 25(4): 331-336.

Abstract(2480) PDF(691)

Abstract:
The three dimensional frame is simplified into flat plate by the method of quasi-plate. The nonlinear relationships between the surface strain and the ntidst plane displacement are established According to the thin plate nonlinex dynantical theory,the nonlinear dynantical equations of threedimensional frame in the orthogonal coordinates system are obtained Then the equatiorn are translated into the axial symmetry nonlinear dynamical equations in the polar coordinates system. Some dimensionless quantities different from the plate of uniform thickness are introduced under the boundxy conditions of fixed edges,then these fundamental equations are simplified with these dimensionless quantities. A cubic nonlinear vibration equation is obtained with the method of Galerkin. The stability and bifurcation of the circular three-dimernional frame are steadied under the condition of without outer motivation. The contingent chaotic vibration of the three-dimensional frame is studied with the method of Melnikov. Some phase figures of contingent chaotic vibration are plotted with digital artifivial method.

Inhomogeneous Initial Boundary Value Problem for Generalized Ginzburg-Landau Equations

YANG Ling-e, GUO Bo-ling, XU Hai-xiang

2004, 25(4): 337-344.

Abstract(2747) PDF(678)

Abstract:
The existence of global weak solution for a class of generalized Ginzburg-Landau equations with an inhomogeneous boundary condition was studied Some integral indentities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced,by which a priori estimates of the square none on boundary of normal derivative and the square norm of partial derivatives were obtaned Then the existence of global weak solution for an inhomogeneous initial boundary value problem of Ginzburg-Landau equations was proved by the method of approximation technique and a priori estimates and making lirrit.

Generalized Variational Principles of the Viscoelastic Body With Voids and Their Applications

SHENG Dong-fa, CHENG Chang-jun, FU Ming-fu

2004, 25(4): 345-353.

Abstract(2896) PDF(670)

Abstract:
From the Boltzmann's constitutive law of viscoelastic materials and the linear theory of elastic materials with voids,a constitutive model of generalized force fields for viscoelastic solids with voids was given.By using the variational integral method,the convolution-type functional was given and the corresponding generalized variational principles and potential energy principle of viscoelastic solids with voids were presented It can be shown that the variational principles correspond to the did ferential equations and the initial and boundary conditions of viscoela stic body with voids. As an applicanon,a generalized variational prindple of viscoelastic Timoshenko beams with damage was obtained which corresponds to the differential equations of generalized motion and the initial and boundary conditions of beams. The variational principles provide a way for solving problems of viscoelastic solids with voids.

Coupling Vibration of Vehicle-Bridge System

CHEN Yan, HUANG Xiao-qing, MA You-fa

2004, 25(4): 354-358.

Abstract(3071) PDF(856)

Abstract:
By applying the sinusoidal wave mode to simulate the rugged surface of bridge deck,accounting for vehicle-bridge interaction and using Euler-Bernoulli beam theory,a coupling vibration model of vehicle-bridge system was developed. The modd was solved by mode analyzing method and Range-Kutta method,and the dynamic resporne and the resonance curve of the bridge were obtained It is found that there are two resonance regions,one represents the main resonance while the other the minor resonance,in the resonance curve. The influence due to the rugged surface,the vibration made of bridge,and the interaction between vehicle and bridge on vibration of the system were discussed. Numerical results show that the influence due to these parameters is so significant that the effeet of roughness of the bridge deck and the mode shape of the bridge can't be ignored andthe vehide velodty should be kept away from the critical speed of the vehicle.

Global Analysis of Some Epidemic Models With General Contact Rate and Constant Immigration

LI Jian-quan, ZHANG Juan, MA Zhi-en

2004, 25(4): 359-367.

Abstract(2971) PDF(810)

Abstract:
An epidemic models of SIR type and SIRS type with general contact rate and corntant immigration of each class were discussed by means of theory of limit system a1d suitable Iiapunov funcdons. In the absence of input of infectious individuals,the threshold of existence of endemic equifibrium is found. For the disease-free equilibrium and the endemic equilibrium of corresponding SIR model,the suffident and necessary conditiorn of global asymptotical stabifities are all obtained For corresponding SIRS model,the sufficient conditions of global asymptotical stabilitiese of the disease-free equifibrium and the endemic equilibrium are obtained In the existence of input of infectious individuals,the models have no disease-free equilibrium. For corresponding SIR model,the endemic equilibrium is globally asymptotically stable;for corresponding SIRS model,the sufficient conditions of global asymptotical stabifitv of the endemic equilibrium are obtained.

Numerical Analysis of Delamintation Growth for Stiffened Composite Laminated Plates

BAI Rui-xiang, CHEN Hao-ran

2004, 25(4): 368-378.

Abstract(3204) PDF(751)

Abstract:
A study of postbudding and delamination propagation behavior in delaminated stiffened composite plies is presented. A methodology is proposed for simulating the multi-failure responses,such as initial and postbuckling,delamination onset and propagation,etc. A finite element analysis was conducted on the bass of the Mindlin first order shear effect theory and the von-Kûrmûn nonlinear deformation assumption The total energy release rate used as the criteria of delamination growth was estimatedwith virtual aback closure technique (VCGT). A self-adaptive grid moving technology was adopted to model the delalrunation growth prooess. Moreover,the contact effect along delaminafion front was also considered during the numerical simulation process.By some nurrerical examples,the influence of distribution a1d location of stiffener,configuration and size of the delamination,boundary condition and contact effect upon the delamination growth behavior of the stiffened composite plates were investigated The method and numerical condusion provided should be of great value to engineers dealing with composite structures.

Research on the Companion Solution for a Thin Plate in the Meshless Local Boundary Integral Equation Method

LONG Shu-yao, XIONG Yuan-bo

2004, 25(4): 379-384.

Abstract(2686) PDF(768)

Abstract:
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(EFGVI),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.

Lie Group Integration for Constrained Generalized Hamiltonian System With Dissipation by Projection Method

ZHANG Su-ying, DENG Zi-chen

2004, 25(4): 385-390.

Abstract(2343) PDF(703)

Abstract:
For the constrained generalized Hamiltonian system with dissipation,by introducing Lagrange multiplier and using projection technique,the Lie group integration method was presented,which can preserve the inherent structure of dynamic system and the constraint-invariant.Firstly,the constrained generalized Hamiltonian system with dissipative was converted to the non-constraint generalized Hamiltonian system,then Lie group integration algorithm for the non-constraint generalized Harrultonian system was discussed,finally the projection method for generalized Hamiltonian system with constraint was given It is found that the constraint invariant is ensured by projection tedtnique,and after introducing Lagrange multiplier the Lie group character of the dynamic system can't be deshroyed while projecting to the constraint manifold The discussion is restricted to the case of bolonomic constraint.A presented numerical example shows the effectiveness of the method.

Thermoelastically Coupled Axisymmetric Nonlinear Vibration of Shallow Spherical and Conical Shells

WANG Yong-gang, DAI Shi-liang

2004, 25(4): 391-399.

Abstract(2893) PDF(587)

Abstract:
The problem of axisymmetric nonlinear vibration for shallow thin spherical and conical shells when temperature and strain fields are coupled is studied Based on the la be deflection theories of von-kûrnûn and the theory of thermoelasticity,the whole governing equations and their simplified type are derived The time-spatial variables xe separated by Galerlari's technique,thus reducing the governing equations to a system of time-dependent nonlinear ordinary differential equation.By means of regular perturbation method and multiple-scales method,the first order approximate analytical solution for chxacterislic relation of frequency vs amplitude pararreters along with the decay rate of ampfitude are obtained,and the effects of different geomdric parameters and coupling factors as well as boundary conditions on thermoelaslically coupled nonlinear vibration behaviors are discussed.

Method on Estimation of Drug's Penetrated Parameters

LIU Yu-hong, ZENG Yan-jun, XU Jing-feng, ZHANG Mei

2004, 25(4): 400-404.

Abstract(2024) PDF(839)

Abstract:
Transdermal drug delivery system(TDDS) is a new method for drug delivery.The analysis of plenty of experiments in vitro can lead to a suitable mathematical model for the description of the process of the drug's penetration through the skin,together with the important parameters that are related to the characters of the drugs.After the research work of the experiments data,a suitable nonlinear regression model was selected.Using this model,the most important parameter-penetrated coefficient of 20 drugs was computed.In the result one can find,this work supports the theory that the skin can be regarded as singular membrane.

Analysis of a Partially Debonded Elliptic Inhomogeneity in Piezoelectric Materials

ZHONG Zheng

2004, 25(4): 405-416.

Abstract(2600) PDF(690)

Abstract:
A generalized solution was obtained for the partially debonded elliptic inhomogeneity problem in piezoelectric materials under antiplane shear and inplane electric loading using the complex variable method.It was assumed that the interfacial debonding induced an electrically impermeable crack at the interface.The principle of conformal transformation and analytical continuation were employed to reduce the formulation into two Riemann-Hilbert problems.This enabled the determination of the complex potentials in the inhomogeneity and the matrix by means of series of expressions.The resulting solution was then used to obtain the electroelastic fields and the energy release rate involving the debonding at the inhomogeneity-matrix interface.The validity and versatility of the current general solution have been demonstrated through some specific examples such as the problems of perfectly bonded elliptic inhomogeneity,totally debonded elliptic inhomogeneity,partially debonded rigid and conducting elliptic inhomogeneity,and partially debonded circular inhomogeneity.

Antiplane Problem of Circular Arc Interfacial Rigid Line Inclusions

LIU You-wen, FANG Qi-hong, WANG Ming-bin

2004, 25(4): 417-424.

Abstract(2876) PDF(630)

Abstract:
The antiplane problem of circular arc rigid line inclusions under antiplane concentrated force and longitudinal shear loading was dealt with.By using Riemann-Schwarz's symmetry principle integrated with the singularity analysis of complex functions,the general solution of the problem and the closed form solutions for some important practical problems were presented.The stress distribution in the immediate vicinity of circular arc rigid line end was examined in detail.The results show that the singular stress fields near the rigid inclusion tip possess a square-root singularity similar to that for the corresponding crack problem under antiplane shear loading,but no oscillatory character. Furthermore,the stresses are found to depend on geometrical dimension,loading conditions and materials parameters.Some practical results concluded are in agreement with the previous solutions.

Muhammet Yürüsoy

2004, 25(4): 425-432.

Abstract(2600) PDF(667)

Abstract:
The two dimensional equations of motions for the slowly flowing and heat transfer in second grade fluid are written in Cartesian coordinates neglecting the inertial terms.When the inertia terms are simply omitted from the equations of motions the resulting solutions are valid approximately for Re<<1.This fact can also be deduced from the dimensionless form of the momentum and energy equations.By employing Lie group analysis,the symmetries of the equations are calculated.The Lie algebra consists of four finite parameter and one infinite parameter Lie group transformations,one being the scaling symmetry and the others being translations.Two different types of solutions are found using the symmetries.Using translations in x and y coordinates,an exponential type of exact solution is presented.For the scaling symmetry,the outcoming ordinary differential equations are more involved and only a series type of approximate solution is presented.Finally,some boundary value problems are discussed.

Optimal Dynamical Balance Harvesting for a Class of Renewable Resources System

HE Ze-rong, WANG Mian-se, WANG Feng

2004, 25(4): 433-440.

Abstract(2482) PDF(585)

Abstract:
An optimal utilization problem for a class of renewable resources system is investigated. Firstly,a control problem was proposed by introducing a new utility function which depends on the harvesting effort and the stock of resources.Secondly,the existence of optimal solution for the problem was discussed.Then,using a maximum principle for infinite horizon problem,a nonlinear four-dimensional differential equations system was attained.After a detailed analysis of the unique positive equilibrium solution,the existence of limit cycles for the system is demonstrated.Next a reduced system on the central manifold is carefully derived,which assures the stability of limit cycles.Finally significance of the results in bioeconomics is explained.