应用数学和力学

2005 Vol. 26, No. 3

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Nonlinear Natural Frequency of Shallow Conical Shiells With Variable Thickness

WANG Xin-zhi, HAN Ming-jun, ZHAO Yong-gang, YEH Kai-yuan

2005, 26(3): 253-258.

Abstract(2896) PDF(620)

Abstract:
The nonlinear dynamical variation equation and compatible equation of the shallow conical shell with variable thickness are obtained by the theory of nonlinear dynamical variation equation and compatible equation of the circular thin plate with variable thickness. Assuming the thin film tension is composed of two items. The compatible equation is transformed into two independent equations. Selecting the maximum amplitude in the center of the shallow conical shells with variable thickness as the perturbation parameter, the variation equation and the differential equation are transformed into linear expression by theory of perturbation variation method. The nonlinear natural frequency of shallow conical shells with circular bottom and variable thickness under the fixed boundary conditions is solved; in the first approximate equation, the linear natural frequency of shallow conical shells with variable thickness is obtained, in the third approximate equation, the nonlinear natural frequency of it is obtained. The figures of the characteristic curves of the natural frequency varying with stationary loads, large amplitude, and variable thickness coefficient are plotted. A valuable reference is given for dynamic engineering.

Exponential Attractor for the Generalized Symmetric Regularized Long Wave Equation With Damping Term

SHANG Ya-dong, GUO Bo-ling

2005, 26(3): 259-266.

Abstract(2464) PDF(923)

Abstract:
The global fast dynamics for the generalized symmetric regularized long wave equation with damping term is considered. The squeezing property of the nonlinear semi-group associated with this equation and the existence of exponential attractor are proved. The upper bounds of its fractal dimension are also estimated.

Scaling Exponents in Fully Developed Asymmetric Channel Flow

JIANG Jian-bo, QIU Xiang, LU Zhi-ming, LIU Yu-lu

2005, 26(3): 267-273.

Abstract(2432) PDF(632)

Abstract:
Wavelet analysis is applied to study the global and local scaling exponents in fully developed asymmetric channel flow. Global exponents are calculated by orthogonal wavelets and Extended Scaling Similarity(ESS). The results show that the flow in an asymmetric channel flow exhibits different characteristics of intermittence from that in a symmetric flow. It is also shown that the intermittence property of the streamwise fluctuations is different from that of vertical fluctuations, and the intermittence does not decay with the increase of the distance from the wall. In addition, the Continuous Wavelet Transform(CWT) method is found to be unreliable to calculate the local scaling components. Finally, it is pointed out that the existence and the significance of negative local scaling components need further study.

Investigation of the Dynamic Buckling of Doublewalled Carbon Nanotube Subjected to Axial Periodic Disturbing Forces

SHA Feng-huan, ZHAO Long-mao, YANG Gui-tong

2005, 26(3): 274-280.

Abstract(2576) PDF(538)

Abstract:
The dynamic response of a double-walled carbon nanotube embedded in elastic medium subjected to periodic disturbing forces is investigated. Investigation of the dynamic buckling of a double-walled carbon nanotube develops continuum model. The effect of the van der Waals forces between two tubes and the surrounding elastic medium for axial dynamic buckling are considered. The buckling model subjected to periodic disturbing forces and the critical axial strain and the critical frequencies are given. It is found that the critical axial strain of the embedded multi-walled carbon nanotube due to the intertube van der Waals forces is lower than that of an embedded single-walled carbon nanotube. The van der Waals forces and the surrounding elastic medium affect region of dynamic instability. The van der Waals forces increase the critical frequencies of a double-walled carbon nanotube. The effect of the surrounding elastic medium for the critical frequencies is small.

Effects of Tensor Closure Models and 3-D Orientation on the Stability of Fiber Suspensions in a Channel Flow

YOU Zhen-jiang, LIN Jian-zhong

2005, 26(3): 281-286.

Abstract(2823) PDF(542)

Abstract:
Three different kinds of closure model of fiber orientation tensors were applied to simulate numerically the hydrodynamic stability of fiber suspensions in a channel flow. The effects of closure models and three-dimensional (3-D) orientation distribution of fibers on the results of stability analysis were examined. It is found that the relationship of the behavior in hydrodynamic stability and the parameter of the fiber given by all the three models are the same. However, the attenuation of flow instability is most distinct using 3-D hybrid model because the orientation of the fiber departures from the flow direction, and least apparent using its 2-D counterpart for that the fibers show a tendency towards alignment with the flow direction in this case.

Renewal of Basic Laws and Principlesfor Polar Continuum Theories (Ⅷ)——Principle of Total Work and Energy

DAI Tian-min

2005, 26(3): 287-292.

Abstract(2517) PDF(835)

Abstract:
Theoretical incompleteness of the existing conservation laws of energy for polar continuum mechanics is further clarified. For completeness, the principles of total work and energy and of total work and energy of incremental rate type are postulated. Viatotal variations of the former and the latter of them, the principles of virtual displacement and microrotation & stress and couple stress as well as virtual velocity and angular velocity & stress rate and couple stress rate are immediately obtained, respectively. From these principles all balance equations and boundary conditions for micropolar mechanics are naturally and simultaneously deduced. The essential differences between the nontraditional results obtained in this paper and the existing conservation laws of energy are expounded.

Effect of Damage on Nonlinear Dynamic Properties of Viscoelastic Rectangular Plates

ZHENG Yu-fang, FU Yi-ming

2005, 26(3): 293-299.

Abstract(2492) PDF(671)

Abstract:
The nonlinear dynamic behaviors of viscoelastic rectangular plates including the damage effects under the action of a transverse periodic load were studied. Using the von Karman equations, Boltzmann superposition principle and continuum damage mechanics, the nonlinear dynamic equations in terms of the midplane displacements for the viscoelastic thin plates with damage effect were derived. By adopting the finite difference method and Newmark method, these equations were solved. The results were compared with the available data. In the numerical calculations, the effects of the external loading parameters and geometric dimensions of the plate on the nonlinear dynamic responses of the plate were discussed. Research results show that the nonlinear dynamic response of the structure will change remarkably when the damage effect is considered.

Global Dynamics of Delayed Bidirectional Associative Memory (BAM) Neural Networks

ZHOU Jin, LIU Zeng-rong, XIANG Lan

2005, 26(3): 300-308.

Abstract(2813) PDF(947)

Abstract:
Without assuming the smoothness, monotonicity and boundedness of the activation functions, some novel criteria on the existence and global exponential stability of equilibrium point for delayed bidirectional associative memory (BAM) neural networks are established by applying the Liapunov functional methods and matrix-algebraic techniques. It is shown that the new conditions presented in terms of a nonsingular M matrix described by the networks parameters, the connection matrix and the Lipschitz constant of the activation functions, are not only simple and practical, but also easier to check and less conservative than those imposed by similar results in recent literature.

Analytical Solutions for Elastostatic Problems of Particle- and Fiber-Reinforced Composites With Inhomogeneous Interphases

DUAN Hui-ling, WANG Jian-xiang, HUANG Zhu-ping, HUANG Hong-bo

2005, 26(3): 309-315.

Abstract(2713) PDF(783)

Abstract:
By transforming the governing equations for displacement components into Riccati equations, analytical solutions for displacements, strains and stresses for RVEs of particle- and fiber-reinforced composites containing inhomogeneous interphases were obtained. The analytical solutions derived here are new and general for power-law variations of the elastic moduli of the inhomogeneous interphases. Given a power exponent, analytical expressions for the bulk moduli of the composites with inhomogeneous interphases can be obtained. By changing the power exponent and the coefficients of the power terms, the solutions derived here can be applied to inhomogeneous interphases with many different property profiles. The results show that the modulus variation and the thickness of the inhomogeneous interphase have great effect on the bulk moduli of the composites. The particle will exhibit a sort of "size effect", if there is an interphase.

Performance Modeling and Analyis of Blood Flow in Elastic Arteries

Anil Kumar, C. L. Varshney, G. C. Sharma

2005, 26(3): 316-324.

Abstract(3250) PDF(1014)

Abstract:
Two different non-Newtonian models for blood flow are considered, first a simple power law model displaying shear thinning viscosity, and second a generalized Maxwell model displaying both shear thinning viscosity and oscillating flow viscous-elasticity. These models are used along with a Newtonian model to study sinusoidal flow of blood in rigid and elastic strainght arteries in the presence of magnetic field. The elasticity of blood does not appear to influence its flow behavior under physiological conditions in the large arteries, purely viscous shear thinning model should be quite realistic for simulating blood flow under these conditions. On using the power law model with high shear rate for sinusoidal flow simulation in elastic arteries, the mean and amplitude of the flow rate were found to be lower for a power law fluid compared to Newtonian fluid for the same pressure gradient. The governing equations have been solved by Crand-Niclson scheme. The results are interpreted in the context of blood in the elastic arteries keeping the magnetic effects in view. For physiological flow simulation in the aorta, an increase in mean wall shear stress, but a reduction in peak wall shear stress were observed for power law model compared to a Newtonian fluid model for matched flow rate wave form. Blood flow in the presence of transverse magnetic field in an elastic artery is investigated and the influence of factors such as morphology and surface irregularity is evaluated.

Study on Coupling Model of Seepage-Field and Stress-Field for RCCD

GU Chong-shi, SU Huai-zhi, ZHOU Hong

2005, 26(3): 325-332.

Abstract(2240) PDF(721)

Abstract:
Based on the construction interfaces in RCCD, the methods were proposed to calculate the influence thickness of construction interfaces and the corresponding physical mechanics parameters. The principle on establishing the coupling model of seepage-field and stress-field for RCCD was presented. A 3-D FEM program was developed. Study shows that such parameters as the thickness of construction interfaces, the elastic ratio and the Poisson's ratio obtained by tests and theoretical analysis are more reasonable, the coupling model of seepage-field and stress-field for RCCD may indicate the coupling effect between the two fields scientifically, and the developed 3-D FEM program can reflect the effect of the construction interfaces more adequately. According to the study, many scientific opinions are given both to analyze the influence of the construction interfaces to the dam's characteristicinteraction between the stress-field and the seepage-field.

Adaptive Interval Wavelet Precise Integration Method for Partial Differential Equations

MEI Shu-li, LU Qi-shao, ZHANG Sen-wen, JIN Li

2005, 26(3): 333-340.

Abstract(2860) PDF(1364)

Abstract:
The quasi-shannon interval wavelet is constructed based on the interpolation wavelet theory, and an adaptive precise integration method, which is based on extrapolation method is presented for nonlinear ODEs. And then, an adaptive interval wavelet precise integration method (AIWPIM) for nonlinear PDEs is proposed. The numerical results show that the computational precision of AIWPIM is higher than that of the method constructed by combining the wavelet and the 4th Runge-Kutta method, and the computational amounts of these two methods are almost equal. For convenience, the Burgers equation is taken as an example in introducing this method, which is also valid for more general cases.

Global Asymptotic Stability Conditions of Delayed Neural Networks

ZHOU Dong-ming, CAO Jin-de, ZHANG Li-ming

2005, 26(3): 341-348.

Abstract(2655) PDF(939)

Abstract:
Utilizing the Liapunov functional method and combining the inequality of matrices technique to analyze the existence of a unique equilibrium point and the global asymptotic stability for delayed cellular neural networks (DCNNs), a new sufficient criterion ensuring the global stability of DCNNs is obtained. Our criteria provide some parameters to appropriately compensate for the tradeoff between the matrix definite condition on feedback matrix and delayed feedback matrix. The criteria can easily be used to design and verify globally stable networks. Furthermore, the condition presented here is independent of the delay parameter and is less restrictive than that given in the references.

Forming Michell Truss in Therr-Dimensions by Finite Element Method

ZHOU Ke-min, LI Jun-feng

2005, 26(3): 349-355.

Abstract(3375) PDF(978)

Abstract:
The finite element method to form Michell truss in three-dimensions is presented. The orthotropic composite with fiber-reinforcement is employed as the material model to simulate Michell truss. The orientation and densities of fibers at nodes are taken as basic design variables. The stresses and strains at nodes are calculated by finite element method. An iteration scheme is suggested to adjust the orientations of fibers to be along the orientations of principal stresses, and the densities of fibers according to the strains in the orientations of fibers. The strain field satisfying Michell criteria and truss-like continuum are achieved after several iterations. Lastly, the Michell truss is showed by continuous lines, which are formed according to the orientations of fibers at nodes. Several examples are used to demonstrate the efficiency of the presented approach.

Hamiltonian Symplectic Semi-Analytical Method and Its Application in Inhomogeneous Electromagnetic Waveguides

SUN Yan, XIE Jun

2005, 26(3): 356-362.

Abstract(2654) PDF(597)

Abstract:
Dual vectors are applied in Hamilton system of applied mechanics. Electric and magnetic field vectors are the dual vectors in electromagnetic field. The Hamilton system method is introduced into the analysis of electromagnetism waveguide with inhomogeneous materials. The transverse electric and magnetic fields are regarded as the dual. The basic equations are solved in Hamilton system and symplectic geometry. With the Hamilton variational principle, the symplectic semianalytical equations are derived and preserve their symplectic structures. The given numerical example demonstrates the solution of LSE mode in a dielectric waveguide.

New Variational Inequality Formulation for Seepage Problems With Free Surfaces

ZHENG Hong, LIU De-fu, LEE C. F., THAM L. G.

2005, 26(3): 363-371.

Abstract(2410) PDF(758)

Abstract:
A new variational inequality formulation for seepage problems with free surfaces was presented, in which a boundary condition of Signorini's type was prescribed over the potential seepage surfaces. This made the singularity of seepage points eliminated and the location of seepage points determined. Compared to other variational formulations, the proposed formulation owns better numerical stability.

Interactions Between Two Sedimenting Particles With Different Sizes

SHAO Xue-ming, LIU Yang, YU Zhao-sheng

2005, 26(3): 372-378.

Abstract(2418) PDF(687)

Abstract:
An improved implementation of Distributed Lagrange multiplier/fictitious domain method was presented and used to simulate the interactions between two circular particles sedimenting in a two-dimensional channel. The simulation results were verified by comparison with experiments. The results show that the interactions between two particles with different sizes can be described as drafting, kissing, tumbling and separating. Only for small diameter ratio, the two particles will interact undergoing repeated DKT process. Otherwise, the two particles will separate after their tumbling. The results also show that, during the interaction process, the motion of the small particle is strongly affected while the large particle is affected slightly.