应用数学和力学

2000 Vol. 21, No. 9

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Nonlinear Stability of Truncated Shallow Conical Sandwich Shell With Variable Thickness

XU Jia-chu, WANG Cheng, LIU Ren-huai

2000, 21(9): 881-889.

Abstract(2288) PDF(566)

Abstract:
The theory of nonlinear stability for a truncated shallow conical shell with variable thickness under the action of uniform pressure was presented.The fundamental equations and boundary conditions were derived by means of calculus of variations.An analytic solution for the critical buckling pressure of the shell with a hyperbolically varying thichness is obtained by use of modified iteration method.The results of numerical calculations are presented in diagrams,which show the influence of geometrical and physical parameters on the buckling behavior.

Stability and Chaotic Motion in Columns of Nonlinear Viscoelastic Material

CHEN Li-qun, CHENG Chang-jun

2000, 21(9): 890-896.

Abstract(2820) PDF(607)

Abstract:
The dynamical stability of a homogeneous,simple supported column,subjected to a periodic axial force,is investigated.The viscoelastic material is assumed to obey the Leaderman nonlinear constitutive ralation.The equation of motion was derived as a nonlinear integro-partial-differential equation,and was simplified into a nonlinear integro-differential equation by the Galerkin method. The averaging method was employed to carry out the stability analysis.Numerical results are presented to compare with the analytical ones.Numerical results also indicate that chaotic motion appears.

Dynamical Behavior of Nonlinear Viscoelastic Beams

CHEN Li-qun, CHENG Chang-jun

2000, 21(9): 897-902.

Abstract(2674) PDF(1211)

Abstract:
The integro-partial-differential equation that governs the dynamical behavior of homogeneous viscoelastic beams was established.The material of the beams obeys the Leaderman nonlinear constitutive relation.In the case of two simply supported ends,the mathematical model was simplified into an integro-differential equation after a 2-order truncation by the Galerkin method.Then the equation is further reduced to an ordinary differential equation which is convenient to carry out numerical experiments.Finally,the dynamical behavior of 1-order and 2-order truncation are numerically compared.

Noncompact Infinite of Optimization and Equilibria of Constrained Games in Generalized Convex Spaces

DING Xie-ping

2000, 21(9): 903-908.

Abstract(2325) PDF(576)

Abstract:
By applying a new existence theorem of quasi-equilibrium problems due to the author, some existence theorems of solutions for noncompact infinite optimization problems and noncompact constrained game problems are proved in generalized convex spaces without linear structure.These theorems improve and generalize a number of important results in recent literature.

Anomalous Dynamics Response of Nonlinear Elastic Bar

ZHANG Nian-mei, HAN Qiang, YANG Gui-tong, XU Bing-ye

2000, 21(9): 909-915.

Abstract(2347) PDF(539)

Abstract:
The dynamics behavior of tension bar with periodic tension velocity was presented. Melinkov method was used to study the dynamic system.The results show that material nonlinear may result in anomalo us dynamics response.The subharmonic bifurcation and chaos may occur in the determined system when the tension velocity exceeds the critical value.

Extended Self-Similar Scaling Law of Multi-Scale Eddy Structure in Wall Turbulence

JIANG Nan, WANG Zhen-dong, SHU Wei

2000, 21(9): 916-924.

Abstract(1885) PDF(597)

Abstract:
The longitudinal fluctuating velocity of a turbulent boundary layer was measured in a water channel at a moderate Reynolds number.The extended self-similar scaling law of structure function proposed by Benzi was verified.The longitudinal fluctuating velocity in the turbulent boundary layer was decomposed into many multi-scale eddy structures by wavelet transform.The extended self-similar scaling law of structure function for each scale eddy velocity was investigated.The conclusions are 1)The statistical properties of turbulence could be self-similar not only at high Reynolds number,but also at moderate and low Reynolds number,and they could be characterized by the same set of scaling exponents ζ₁(n)=n/3 and ζ₂(n)=n/3 of the fully developed regime.2)The range of scales where the extended self-similarity valid is much larger than the inertial range and extends far deep into the dissipation range with the same set of scaling exponents.3)The extended self-similarity is applicable not only for homogeneous turbulence,but also for shear turbulence such as turbulent boundary layers.

Imperfect Bifurcation of Systems With Slowly Varying Parameters and Application to Duffing’s Equation

HUA Cun-cai, LU Qi-shao

2000, 21(9): 925-932.

Abstract(2185) PDF(552)

Abstract:
A new method a proposed for essentially studying the imperfect bifurcation problem of nonlinear systems with a slowly varying parameter.By establishing some theorems on the solution approximated by that of the linearized system,the delayed bifurcation transition and jump phenomena of the time-dependent equation were analyzed.V-function was used to predict the bifurcation transition value.Applying the new method to analyze the Duffing's equation,some new results about bifurcation as well as that about the sensitivity of the solutions with respect to initial values and parameters are obtained.

Electromagnetric Tomography (EMT):Theoretical Analysis of the Forward Problem

XIONG Han-liang, XU Ling-an

2000, 21(9): 933-941.

Abstract(2790) PDF(686)

Abstract:
Inductance-based electromagnetic tomography(EMT)is a novel industrial process tomographic technique.Exact expressions of the magnetic field distribution in a two-dimensional object space were derived by analytically solving the forward problem for a particular two-component flow. The physical mechanisms within the sensor and the detectability limits of the EMT technique were quantitatively analyzed.Direct mathematical expressions for the field sensitivity and the sensitivity maps were established.To a certain extent,mathematical and theoretical bases are given for quantitative design of the sensor,detectability analysis of the EMT technique and image reconstruction of two-compontnt processes based on the linear back-projection algorithm.

A Class of Parabolic Hemivariational Inequalities

LIU Zhen-hai

2000, 21(9): 942-948.

Abstract(2113) PDF(690)

Abstract:
Quasilinear parabolic hemivariational inequalities as a generalization to nonconvex functions of the parabolic variational inequalities are discussed.This extension is strongly motivated by various problems in mechanics.By use of the notion of the generalized gradient of Clarke and the theory of pseudomonotone operators,it is proved there exists at least one soluton.

Decentralized Stabilization of Large-Scale Linear Interconnected Systems with Time-Varying Delays

YU Zhao-xu, SUN Ji-tao

2000, 21(9): 949-953.

Abstract(2017) PDF(713)

Abstract:
The decentralized stabilization conditions for large-scale linear interconnection systems with time-varying delays were established by using some different decomposition cases of interconnection matrices,and a method for designing the decentralized local memoryless state feedback controllers was proposed.All of the considered delays are continous function,and satisfy some conditions.

The Effects of Blood Viscoelasticity on the Pulse Wave in Arteries

YAO Da-kang, YAN Yu-bing, LIU Zhao-rong

2000, 21(9): 954-960.

Abstract(2419) PDF(1048)

Abstract:
Based on Womersley's theory,the frequency equation satisfied by a complex wave velocity of a pulse wave in arteries was generalized to viscoelastic blood,a general formula of the complex wave velocity with regard to both linearly viscoelastic arteries and linearly viscolelastic blood was obtained,and the effects of the viscoelastic property of blood on the phase velocity and the wave attenuation of the pulse wave using the formula systematically was discussed.It is concluded that the influence of the blood elasticity on the wave propagation of a pulse wave in arteries is weaker than that of the arterial viscosity and may be neglected in larger arteries.

An Application of Theoretical Solutions About Cylindrical Shells With Small Openings

SONG Tian-shu, LIU Dian-kui

2000, 21(9): 961-965.

Abstract(2330) PDF(848)

Abstract:
Stress concentrations about thin cylindrical shells with small openings are reconsidered from a new angle.There is a sort of special internal relation between theoretical solutions about cylindrical shells with large openings and one with small openings.Using this relation,the extent of applying the theory about small openings to engineering practice is estimated again,thus an idea of how to use this theory and a new appraisal of the application of theoretical solutions about cylindrical shells with small openings to engineering practice are given.

A Class of Two-Level Explicit Difference Schemes for Solving Three Dimensional Heat Conduction Equation

ZENG Wen-ping

2000, 21(9): 966-972.

Abstract(2699) PDF(1055)

Abstract:
A class of two-level explicit difference schemes are presented for solving three-dimensional heat conduction equation.When the order of truncation error is O(Δt+(Δx)²),the stability condition is mesh ratio r=Δt/(Δx)²=Δt/(Δy)²=Δt/(Δz)²≤1/2, which is better than that of a all the other explicit difference schemes.And when the order of truncation error is O((Δt)²+(Δx)⁴),the stability condition is r≤1/6,which contains the known results.

A Note on Stochastic Optimal Control of Reflected Diffusions With Jumps

DING Deng

2000, 21(9): 973-983.

Abstract(2843) PDF(733)

Abstract:
Stochastic optimal control problems for a class of reflected diffusion with Poisson jumps in a half-space are considered.The nonlinear Nisio.s semigro up for such optimal control problems was constructed.A Hamilton-Jaco bi-Bellman equation with the Ne umann boundary condition associated with this semigroup was o btained.Then,visco sity solutions of this equation were defined and discussed,and various uniqueness of this equation was also considered.Finally,the value function in such optimal control problems is shown to be a viscosity solution of this equation.

Bending Theories for Beams and Plates With Single Generalized Displacement

GONG Ke

2000, 21(9): 984-990.

Abstract(2468) PDF(981)

Abstract:
Classical bending theories for beams and plates can not be used for short,stubby beams and thick plates since transverse shearing effect is excluded,and ordinary theories with multiple generalized displacements can not be used for long,slender beams and thin plates since the innate relation between rotation angle and deflection is ignored.These two types of theories are not consistent due to the contradiction of dependence and independence of the rotation angle.Based on several basic assumptions,a new type of theories which not only include the transverse shearing effect is presented, but also the relation between rotation angle and deflection is obtained.Analytical solutions of several simple beams are given.It has been testified by numerical examples that the new theories can be used for either long,slender beams and thin plates or short,stubby beams and thick plates.