应用数学和力学

2005 Vol. 26, No. 2

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Homoclinic Orbits of the Davey-Stewartson Equations

ZHANG Jun, GUO Bo-ling, SHEN Shou-feng

2005, 26(2): 127-129.

Abstract(2588) PDF(756)

Abstract:
The homoclinic solutions problem of the Davey-Stewartson (DS) Equations were studied.By using the Hirota's bilinear method,the homoclinic orbits of the Davey-Stewartson Equations were obtained through the dependent variable transformation.The homoclinic orbits of the Davey-Stewartson Equations were discussed.

Nonlinear Complex Dynamic Phenomena of the Perturbed Metallic Bar Considering Dissipating Effect

ZHAO Guang-hui, ZHANG Nian-mei, YANG Gui-tong

2005, 26(2): 130-136.

Abstract(2518) PDF(625)

Abstract:
Considering Peierls-Nabarro effect,one-dimensional finite metallic bar subjected with periodic field was researched under Neumann boundary condition.Dynamics of this system was described with displacement by perturbed sine-Gordon type equation.Finite difference scheme with fourth-order central differences in space and second-order central differences in time was used to simulate dynamic responses of this system.For the metallic bar with specified sizes and physical features,effect of amplitude of external driving on dynamic behavior of the bar was investigated under initial breather condition.Four kinds of typical dynamic behaviors are shown:x-independent simple harmonic motion;harmonic motion with single wave;quasi-periodic motion with single wave;temporal chaotic motion with single spatial mode.Poincar map and power spectrum are used to determine dynamic features.

Intracellular Solitary Pulse Calcium Waves in Frog Sympathetic Neurons

SHI Xiao-min, DAI Shi-qiang

2005, 26(2): 137-144.

Abstract(2662) PDF(497)

Abstract:
In certain extracellular environments,there would appear a kind of solitary pulse calcium waves in Rana pipiens sympathetic neurons,propagating inwards along the radial direction from the plasma membrane.To gain a deeper insight into the waves,a model describing intracellular calcium waves in frog sympathetic neurons was established.In the piecewise linear approximation,the present model is identical to the Sneyd model.Thus,with Sneyd's method,analytical expressions for the wave speed and profiles of 1D solitary pulse wave were obtained.A wave speed of 21.5μm/s was deduced,which agrees rather well with experimental data.

Dynamic Behavior of Two Unequal Parallel Permeable Interface Cracks in a Piezoelectric Layer Bonded to Two Half Piezoelectric Materials Planes

SUN Jian-liang, ZHOU Zhen-gong, WANG Biao

2005, 26(2): 145-154.

Abstract(2792) PDF(479)

Abstract:
The dynamic behavior of two unequal parallel permeable interface cracks in a piezoelectric layer bonded to two half-piezoelectric material planes subjected to harmonic anti-plane shear waves is investigated.By using the Fourier transform,the problem can be solved with the help of two pairs of dual integral equations in which the unknown variables were the jumps of the displacements across the crack surfaces.Numerical results are presented graphically to show the effects of the geometric parameters,the frequency of the incident wave on the dynamic stress intensity factors and the electric displacement intensity factors.Especially,the present problem can be returned to static problem of two parallel permeable interface cracks.Compared with the solutions of impermeable crack surface condition,it is found that the electric displacement intensity factors for the permeable crack surface conditions are much smaller.

Generalized Homogeneous Functions and the Two-Body Problem

C. Biasi, S. M. S. Godoy

2005, 26(2): 155-162.

Abstract(2198) PDF(490)

Abstract:
A generalization of the homogeneous function concept is studied.An application is done with a solution of the two-body problem.

Denoising Method Based on Singular Spectrum Analysis and Its Applications in Calculation of Maximal Liapunov Exponent

LIU Yuan-feng, ZHAO Mei

2005, 26(2): 163-168.

Abstract(2524) PDF(1080)

Abstract:
An algorithm based on the data-adaptive filtering characteristics of singular spectrum analy sis (SSA) is proposed to denoise chaotic data.Firstly,the empirical orthogonal functions (EOFs) and principal components (PCs) of the signal were calculated,reconstruct the signal using the EOFs and PCs,and choose the optimal reconstructing order based on sigular spectrum to obtain the denoised signal.The noise of the signal can influence the calculating precision of maximal Liapunov exponents.The proposed denoising algorithm was applied to the maximal Liapunov exponents calculations of two chaotic system,Henon map and Logistic map.Some numerical results show that this denoising algo rithm could improve the calculating precision of maximal Liapunov exponent.

Qualitative Study of Cavitated Bifurcation for a Class of Incompressible Generalized neo-Hookean Spheres

YUAN Xue-gang, ZHU Zheng-you

2005, 26(2): 169-177.

Abstract(2220) PDF(471)

Abstract:
The problem of spherical cavitated bifurcation was examined for a class of incompressible generalized neo-Hookean materials,in which the materials may be viewed as the homogeneous incompressible isotropic neo-Hookean material with radial perturbations.The condition of void nucleation for this problem was obtained.In contrast to the situation for a homogeneous isotropic neo-Hookean sphere,it is shown that not only there exists a secondary turning bifurcation point on the cavitated bifurcation solution which bifurcates locally to the left from trivial solution,and also the critical load is smaller than that for the material with no perturbations,as the parameters belong to some regions.It is proved that the cavitated bifurcation equation is equivalent to a class of normal forms with singlesided constraints near the critical point by using singularity theory.The stability of solutions and the actual stable equilibrium state were discussed respectively by using the minimal potential energy principle.

Splitting of the Spectral Domain Electrical Dyadic Green’s Function in Chiral Media

QIN Zhi-an, QIN Rui, CHEN Yan, SHENG De-yuan

2005, 26(2): 178-182.

Abstract(2698) PDF(637)

Abstract:
A new method of formulating dyadic Green's functions in lossless,reciprocal and unbounded chiral medium was presented.Based on Helmholtz theorem and the non-divergence and irrotational splitting of dyadic Dirac delta-function was this method,the electrical vector dyadic Green's function equation was first decomposed into the non-divergence electrical vector dyadic Green's function equation and irrotational electrical vector dyadic Green's function equation,and then Fourier's transformation was used to derive the expressions of the non-divergence and irrotational component of the spectral domain electrical dyadic Green's function in chiral media.It can avoid having to use the wavefield decomposition method and dyadic Green's function eigenfunction expansion technique that this method is used to derive the dyadic Green's functions in chiral media.

Nonlinear Stability for Eady’s Model

LIU Yong-ming, QIU Ling-cun

2005, 26(2): 183-186.

Abstract(3001) PDF(680)

Abstract:
Poincar type integral inequality plays an important role in the study of nonlinear stability (in the sense of Arnold's second theorem) for three-dimensional quasi-geostophic flow.The nonlinear stability of Eady's model is one of the most important cases in the application of the method.But the best nonlinear stability criterion obtained so far and the linear stability criterion are not coincident.The two criteria coincide only when the period of the channel is infinite.To fill this gap,the enhanced Poincar inequality was obtained by considering the additional conservation law of momentum and by rigorous estimate of integral inequality.So the new nonlinear stability criterion was obtained,which shows that for Eady's model in the periodic channel,the linear stable implies the nonlinear stable.

Form Invariance and Lie Symmetry of Variable Mass Nonholonomic Mechanical System

FANG Jian-hui, CHEN Pei-sheng, ZHANG Jun

2005, 26(2): 187-192.

Abstract(3021) PDF(700)

Abstract:
The form invariance and Lie symmetry of a variable mass nonholonomic mechanical system is studied.The definition and the criterion and the conserved quantity of form invariance and Lie symmetry for the variable mass nonholonomic mechanical system are given.The relation between the form invariance and Lie symmetry is obtained.An example is given to illustrate the application of the result.

Bifurcation in a Two-Dimensional Neural Network Model With Delay

WEI Jun-jie, ZHANG Chun-rui, LI Xiu-ling

2005, 26(2): 193-200.

Abstract(2740) PDF(592)

Abstract:
A kind of 2-dimensional neural network model with delay is considered.By analyzing the distribution of the roots of the characteristic equation associated with the model,a bifurcation diagram was drawn in an appropriate parameter plane.It is found that a line is a pitchfork bifurcation curve.Further more,the stability of each fixed point and existence of Hopf bifurcation were obtained.Finally,the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions were determined by using the normal form method and centre manifold theory.

Investigation on Gradient-Dependent Nonlocal Constitutive Models for Elasto-Plasticity Coupled With Damage

SHEN Xin-pu, SHEN Guo-xiao, CHEN Li-xin, YANG Lu

2005, 26(2): 201-214.

Abstract(2609) PDF(943)

Abstract:
Firstly,typical gradient-dependent nonlocal inelastic models were briefly reviewed.Secondly,based on the principle of-gradient-dependent energy dissipation,a gradient-dependent constitutive model for plasticity coupled with isotropic damage was presented in the framework of continuum thermodynamics.Numerical scheme for calculation of Laplacian term of damage field with the numerical results obtained by FEM calculation was proposed.Equations have been presented on the basis of Taylor series for both 2-dimensional and 3-dimensional cases respectively.Numerical results have indicated the validity of the proposed gradient-dependent model and corresponding numerical scheme.

Green’s Functions of Internal Electrodes Between Two Dissimilar Piezoelectric Media

GAO Cun-fa, Herbert Balke

2005, 26(2): 215-221.

Abstract(2189) PDF(464)

Abstract:
The generalized 2D problem of a half-infinite interfacial electrode layer between two arbitrary piezoelectric half-spaces is studied.Based on the Stroh formalism,exact expressions for the Green's functions of a line force,a line charge and a line electric dipole applied at an arbitrary pointnear the electrode edge,were presented,respectively.The corresponding solutions for the intensity factors of fields were also obtained in an explicit form.These results can be used as the foundational solutions in boundary element method (BEM) to solve more complicated fracture problems of piezoelectric composites.

Perturbational Finite Volume Method for the Solution of 2-D Navier-Stokes Equations on Unstructured and Structured Colocated Meshes

GAO Zhi, DAI Min-guo, LI Gui-bo, BAI Wei

2005, 26(2): 222-230.

Abstract(2923) PDF(578)

Abstract:
Based on the first order upwind and second order central type of finite volume (UFV and CFV) scheme,upwind and central type of perturbation finite volume (UPFV and CPFV) schemes of the Navier-Stokes equations were developed.In PFV method,the mass fluxes of across the cell faces of the control volume (CV) were expanded into power series of the grid spacing and the coefficients of the power series were determined by means of the conservation equation itself.The UPFV and CPFV scheme respectively uses the same nodes and expressions as those of the normal first-order upwind and second-order central scheme,which is apt to programming.The results of numerical experiments about the flow in a lid-driven cavity and the problem of transport of a scalar quantity in a known velocity field show that compared to the first order UFV and second order CFV schemes,upwind PFV scheme is higher accuracy and resolution,especially better robustness.The numerical computation to flow in a lid-driven cavity shows that the underrelaxation factor can be arbitrarily selected ranging from 0.3 to 0.8 and convergence perform excellent with Reynolds number variation from 10²to 10⁴.

Numerical Analysis of Fluid Flow and Added Mass Induced by Vibration of Structure

SU Li, LI Shu-juan, TANG Guo-an

2005, 26(2): 231-238.

Abstract(2845) PDF(618)

Abstract:
The fluid flow induced by light-density,low-stiffness structures was treated as inviscid,incompressible irrotational and steady plane flow.On the basis of the dipole configuration method,a singularity distribution method of distributing sources/sinks and dipoles on interfaces of the structure and fluid was developed to solve the problem of fluid flow induced by the vibration of common structures,such as columns and columns with fins,deduce the expression of kinetic energy of the fluid flow,and obtain the added mass finally.The calculational instances with analytical solutions prove the reliability of this method.

A Novel Ellipsoidal Acoustic Infinite Element

YANG Rui-liang, WANG Hong-zhen

2005, 26(2): 239-245.

Abstract(2235) PDF(598)

Abstract:
A novel ellipsoidal acoustic infinite element is proposed.It is based a new pressure representation,which can describe and solve the ellipsoidal acoustic field more exactly.The shape functions of this novel acoustic infinite element are similar to the Burnett.s method,while the weight functions are defined as the product of the complex conjugates of the shaped functions and an additional weighting factor.The code of this method is cheap to generate as for 1-D element because only 1-D integral needs to be numerical.Coupling with the standard finite element,this method provides a capability for very efficiently modeling acoustic fields surrounding structures of virtually any practical shape.This novel method was deduced in brief and the conclusion was kept in detail.To test the feasibility of this novel method efficiently,in the examples the infinite elements were considered,excluding the finite elements relative.This novel ellipsoidal acoustic infinite element can deduce the analytic solution of an oscillating sphere.The example of a prolate spheroid shows that the novel infinite element is superior to the boundary element and other acoustic infinite elements.Analytical and numericalresults of these examples show that this novel method is feasible.

A Method of Online Damage Identification for Structures Based on Ambient Vibration

YAO Zhi-yuan, WANG Feng-quan, ZHAO Chun-sheng

2005, 26(2): 246-252.

Abstract(2532) PDF(624)

Abstract:
A method of damage identification for engineering structures based on ambient vibration is put forward,in which output data are used only.Firstly,it was identification of the statistic parameters to associate with the exterior excitation for undamaged structures.Then it was detection and location of the structural damages for damaged structures.The ambient identification method includes a theoretical model and numerical method.The numerical experiment results show the method is precise and effective.This method may be used in health monitoring for bridges and architectures.