应用数学和力学

1999 Vol. 20, No. 12

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Engineering Mechanics and Materials Research in the Information Technology Age

Ken P Chong, Daniel C Davis

1999, 20(12): 1211-1214.

Abstract(1814) PDF(605)

Abstract:
In this paper,importance of information technology research and development for economic growth and prosperity is presented.Major missio of the research for fundamental science and engineering base is discussed.Critical points of the mechanics and materials research in the 21th Century are proposed.

Mann and Ishikawa Iterative Approximation of Solutions for m-Accretive Operator Equations

Zhang Shisheng

1999, 20(12): 1215-1223.

Abstract(1687) PDF(684)

Abstract:
The purpose of the paper is to study the Mann and Ishikawa iterative approximation of solutions for m-accretive operator equations in Banach spaces.The results presented in this paper extend and improve some authors.recent results.

Subharmonic and Ultra-Subharmonic Response of Nonlinear Elastic Beams Subjected to Harmonic Excitation

Zhang Nianmei, Yang Guitong

1999, 20(12): 1224-1228.

Abstract(2128) PDF(559)

Abstract:
In this paper the dynamics response of beams subjected to transverse harmonic excitation is studied.The nonlinearity of constitutive relations of the beam material is considered.When the buckled beams compressed by axial forces are subjected to transverse period perturbation,the harmonic bifurcates into subharmonic and ultra-subharmonic sequences.The critical conditions for subharmonic and ultra-subharmonic orbits are determined by use of Melnikov method.

Controlling Chaotic Oscillations of Viscoelastic Plates by the Linearization via Output Feedback

Chen Liqun, Cheng Changjun

1999, 20(12): 1229-1234.

Abstract(2183) PDF(621)

Abstract:
Controlling chaotic oscillations of viscoelastic plates is investigated in this paper.Based on the exact linearization method in nonlinear system control theory,a nonlinear feedback control law is presented for a class of non-affine control systems.The mathematical model describing motion of nonlinear viscoelastic plates is established,and it is simplified by the Galerkin method.The phase space portrait and the power spectrum are employed to demonstrate chaos in the system.The deflection is treated as an output,and is controlled to given periodic goals.

Finite Element Analysis of Wave Propagation in Fluid-Saturated Porous Media

Yan Bo, Liu Zhanfang, Zhang Xiangwei

1999, 20(12): 1235-1244.

Abstract(2213) PDF(646)

Abstract:
With the porous media model based on mixture theory,a finite element formulation for dynamic transient analysis of fluid-saturated two-phase porous media is presented.Time integration of the equation,deduced with penalty method,can be performed by using implicit or explicit method. One-dimensional wave propagation in column under step loading and impulsive loading are analyzed with the developed finite element program.The obtained curves of displacements,velocities,effective stresses and pore pressures against time demonstrate the existence of wave propagation phenomena,which coincide with the theoretical results.

Effect of the Distributary of Nasal Meatuses on Olfaction

Tan Wenchang, Wu Wangyi, Yan Zongyi, Wen Gongbi

1999, 20(12): 1245-1251.

Abstract(1842) PDF(773)

Abstract:
Considering the effect of distributary of the interior meatus and middle meatus on olfaction,an unsteady two-dimensional model of olfaction has been developed with describing the mean cross-sectional velocity of odorant flow in the common meatus as a function of axis coordinate.The analytical solution is obtained,and it reveals the relation among the physiological parameters of the model.The obtained results are in agreement with those of experiments.This investigation is valuable for a research for the mechanism of olfaction.

Double-Moment of Spacial Curved Bars With Closed Thin-Wall Cross Section

Zhu Yuchun, Zhang Peiyuan, Yan Bo

1999, 20(12): 1252-1258.

Abstract(2082) PDF(1150)

Abstract:
In this paper,the double-moment of thin-wall cross section spacial curved bars of anisotropic materials is discussed,and a general solving method for this type of problems as well as the concrete double-moment formula of planary curved bars subjected to action of vertical loads are given out.

A Mixture Differential Quadrature Method for Solving Two-Dimensional Incompressible Navier-Stokes Equations

Sun Jian'an, Zhu Zhengyou

1999, 20(12): 1259-1266.

Abstract(2459) PDF(758)

Abstract:
Differential quadrature method(DQM)is able to obtain highly accurate numerical solutions of differential equations just using a few grid points.But using purely differential quadrature method, good numerical solutions of two-dimensional incompressible Navier-Stokes equations can be obtained only for low Reynolds number flow and numerical solutions will not be convergent for high Reynolds number flow.For this reason,in this paper a combinative predicting-correcting numerical scheme for solving two-dimensional incompressible Navier-Stokes equations is presented by mixing upwind difference method into differential quadrature one.Using this scheme and pseudo-time-dependent algorithm,numerical solutions of high Reynolds number flow are obtained with only a few grid points.For example,1:1 and 1:2 driven cavity flows are calculated and good numerical solutions are obtained.

Generalized Flow Analysis of Non-Newtonian Visco-Elastic Fluids Flow Through Fractal Reservoir

Tong Dengke, Chen Qinlei

1999, 20(12): 1267-1274.

Abstract(2394) PDF(503)

Abstract:
In this paper,fractal geometry theory is used to combine with the seepage flow mechanics to establish the relaxation models of non-Newtonian visco-elastic fluids flow in fractal reservoirs.A method to scale the fractal properties of a fractal reservoir by a double parameters(d_f,d_s)and to describe the generalized flow characteristics of visco-elastic fluid by four parameters(d_f,d_s,λ_v,λ_p) are presented.Exact solutions and asymptotic solutions have been obtained by using Laplace-Weber and Laplace-orthogonal transforms with both infinite and finite reservoirs.The pressure transient behavior of non-Newtonian visco-elastic fluids flow through a fractal reservoir are studied by using the numerical Laplace transform inversion and asymptotic solutions.The law of pressure change for various fractal parameter is obtained.

A Damage Function Used for Prediction of Low Cyclic Fatigue Life

Jiang Fengchun, Liu Ruitang, Liu Diankui

1999, 20(12): 1275-1280.

Abstract(2184) PDF(695)

Abstract:
In this paper,the cyclic plastic strain energy is acted as damage variable and its mathematical model of transient response is established.The nonlinear fatigue damage function is given by means of the damage mechanical method.The formula used for prediction of low cyclic fatigue life is obtained from this damage function which takes into account the cyclic relativity of cyclic plastic strain energy.The low cyclic fatigue life predicted by this formula is in correspondence with the experimental result.

A Method of Following the Unstable Path Between Two Saddle-Node Bifurcation Points in Nonlinear Dynamic System

Zhang Jiazhong, Hua Jun, Xu Qingyu

1999, 20(12): 1281-1285.

Abstract(2527) PDF(571)

Abstract:
A computation algorithm based on the Poincar Mapping in combination with Pseudo-Arc Length Continuation Method is presented for calculating the unstable response with saddle-node bifurcation,and the singularity,which occurs using the general continuation method combined with Poincar Mapping to follow the path,is also proved. A normalization equation can be introduced to avoid the singularity in the process of iteration, and a new iteration algorithm will be presented too.There will be two directions in which the path can be continued at each point,but only one can be used,the method of determining the direction will be presented in the paper.It can be concluded that this method is effective in analysis of non-linear dynamic system with saddle-node bifurcations.

Modeling and Bifurcation Analysis of the Centre Rigid-Body Mounted on an External Timoshenko Beam

Xiao Shifu, Chen Bin

1999, 20(12): 1286-1290.

Abstract(2072) PDF(575)

Abstract:
For the system of the centre rigid-body mounted on an external cantilever beam,the equilibrium solution of the steadily rotating beam is stable if the effect of its shearing stress(i.e.the beam belongs to the Euler-Bernoulli type)is not considered.But for the deep beam,it is necessary to consider the effect of the shearing stress(i.e.the beam belongs to the Timoshenko type).In this case,the tension buckling of the equilibrium solution of the steadily rotating beam may occur.In the present work,using the general Hamilton Variation Principle,a nonlinear dynamic model of the rigid- flexible system with a centre rigid-body mounted on an external Timoshenko beam is established.The bifurcation regular of the steadily rotating Timoshenko beam is investigated by using numerical methods.Furthermore,the critical rotating velocity is also obtained.

A Complete Expression of the Asymptotic Solution of Differential Equation With Three-Turning Points

Zhang Juling, Zhu Wenli

1999, 20(12): 1291-1300.

Abstract(2188) PDF(546)

Abstract:
In this paper,a second order linear ordinary differential equation with three-turning points is studied.This equation is as follows and λ is a large parameter,but . By using JL function,the complete expression of the formal uniformly valid asymptotic solutions of the equation near turning point is obtained.

On the Asymptotical Behaviour of Solutions of a Class of Nonlinear Control Systems

Teng Zhidong

1999, 20(12): 1301-1308.

Abstract(2316) PDF(585)

Abstract:
In this paper the asymptotical behaviour solutions of a class of nonlinear control systems are studied.By establishing infinite integrals along solutions of the system and drawing support from a LaSalle's invariance principle of integral form,criteria of dichotomy and global asymptotical behaviour of solutions are obtained.This work is an improvement and further extension of research methods and results of A. S. Aisagaliev.

A Study of the Static and Global Bifurcations for Duffing Equation

Cao Qingjie, Zhang Tiande, Li Jiuping

1999, 20(12): 1309-1316.

Abstract(2283) PDF(1159)

Abstract:
In this paper,the static and global bifurcations of the forced Duffing equation have been studied by means of the averaged system.Bifurcation condition has been obtained in the whole parametric space.The change of the phase plane structure has been investigated.