应用数学和力学

Numerical Study of Local Boundary Layer Receptivity to Freestream Vortical Disturbances

ZHANG Yong-ming, ZHOU Heng

2005, 26(5): 505-211.

Abstract(2745) PDF(854)

Abstract:
Method of direct numerical simulation was used for the investigation of the local receptivity of a 2-D boundary layer of a flat plate to harmonic vortical disturbances in the freestream. Under the interaction of the vortical disturbances in the freestream and the roughness element on the wall, Tollmein-Schlichting (T-S) waves were generated and detected in the boundary layer, thus confirming that the wavelength conversion mechanism and the local receptivity exist. Numerical simulations were performed to obtain the relations between the amplitude of the generated T-S wave and the amplitude of freestream disturbance, the roughness height, and the width of rectangular roughness elements, which agree with those obtained from experiments. Then the range of validity of the linear receptivity formula, which was determined by these relations, also agrees with that determined by experimental results.

Precise Integral Algorithm Based Solution for Transient Inverse Heat Conduction Problems With Multi-Variables

WANG Yi-bo, YANG Hai-tian, WU Rui-feng

2005, 26(5): 512-518.

Abstract(2981) PDF(616)

Abstract:
By modeling direct transient heat conduction problems via finite element method (FEM) and precise integral algorithm, a new approach is presented to solve transient inverse heat conduction problems with multi-variables. Firstly, the spatial space and temporal domain are discretized by FEM and precise integral algorithm respectively. Then, the high accuracy semi-analytical solution of direct problem can be got. Finally, based on the solution, the computing model of inverse problem and expression of sensitivity analysis are established. Single variable and variables combined identifications including thermal parameters, boundary conditions and source-related terms etc. are given to validate the approach proposed in 1-D and 2-D cases. The effects of noise data and initial guess on the results are investigated. The numerical examples show the effectiveness of this approach.

Generalized Vector Quasi-Equilibrium Problems in Locally G-Convex Spaces

DING Xie-ping

2005, 26(5): 519-526.

Abstract(2401) PDF(752)

Abstract:
Some classes of generalized vector quasi-equilibrium problems (in short, GVQEP) are introduced and studied in locally G-convex spaces which includes most of generalized vector equilibrium problems, generalized vector variational inequality problems, quasi-equilibrium problems and quasi-variational inequality problems as special cases. First, an equilibrium existence theorem for one person games is proved in locally G-convex spaces. As applications, some new existence theorems of solutions for the GVQEP are established in noncompact locally G-convex spaces. These results and argument methods are new and completely different from that in recent literature.

Model and Method of Well Test Analysis for Wells With Vertical Fracture

GUO Da-li, ZENG Xiao-hui, ZHAO Jin-zhou, LIU Ci-qun4

2005, 26(5): 527-533.

Abstract(2459) PDF(718)

Abstract:
Based on the flow mechanism of hydraulic fractured wells, through integrating linear-flow model and effective well-radius model, a new model of well test analysis for wells with vertical fracture was established. In the model, wellbore storage, the damage in the wall of fracture and all kinds of boundary conditions are considered. The model is concise in form, has intact curves and computes fast, which may meet the demand of real-time computation and fast responded well test interpretation. A new method to determine effective well radius was presented, and the correlation between e-f fective well radius and the fracture length, fracture conductivity, skin factor of fracture was given. Matching flow rate or pressure tested, the optimization model that identified formation and fracture parameters was set up. The automatic matching method was presented by synthetically using step by step linear least square method and sequential quadratic programming. At last, the application was also discussed. Application shows that all of these results can analyze and evaluate the fracturing treatment quality scientifically and rationally, instruct and modify the design of fracturing and improve fracturing design level.

Vibrating-Uplift Rocking Motion of Caisson Breakwaters Under Various Breaking Wave Impact Forces

WANG Yuan-zhan, ZHOU Zhi-rong, YANG Hai-dong

2005, 26(5): 534-540.

Abstract(3953) PDF(607)

Abstract:
Overturning is one of principal failure types of caisson breakwaters and is an essential content of stability examination in caisson breakwater design. The mass-spring-dashpot model of caisson-foundation system is used to simulate the vibrating-uplift rocking motion of caisson under various types of breaking wave impact forces, i. e., single peak impact force, double peak impact force, and shock-damping oscillation impact force. The effects of various breaking wave types and the uplift rocking motion on dynamic response behaviors of caisson breakwaters are investigated. It is shown that the dynamic responses of a caisson are significantly different under different types of breaking wave impact forces even when the amplitudes of impact forces are equal. Though the rotation of a caisson is larger due to the uplift rocking motion, the displacement, the sliding force and the overturning moment of the caisson are significantly reduced. It provides the theoretical base for the design idea that the uplift rocking motion of caisson is allowed in design.

Laminar Dissipative Flow in a Porous Channel Bounded by Isothermal Parallel Plates

Kamel Hooman, Mofid Gorji-Bandpy

2005, 26(5): 541-546.

Abstract(2764) PDF(549)

Abstract:
The effects of viscous dissipation on thermal entrance heat transfer in a parallel plate channel filled with a saturated porous medium, is investigated analytically on the basis of a Darcy model. The case of isothermal boundary is treated. The local and the bulk temperature distribution along with the Nusselt number in the thermal entrance region were found. The fully developed Nusselt number, independent of the Brinkman number, is found to be 6. It is observed that neglecting the effects of viscous dissipation would lead to the wellknown case of internal flows, with Nusselt number equal to 4.93. A finite difference numerical solution is also utilized. It is seen that the results of these two methods-analytical and numerical are in good agreement.

Model of Centrifugal Effect and Attitude Maneuver Stability of a Coupled Rigid-Flexible System

LI Zhi-bin, WANG Zhao-lin, WANG Tian-shu, LIU Ning

2005, 26(5): 547-555.

Abstract(2594) PDF(587)

Abstract:
The influences of nonlinear centrifugal force to large overall attitude motion of coupled rigid-flexible system was investigated. First the nonlinear model of the coupled rigid-flexible system was deduced from the idea of "centrifugal potential field", and then the dynamic effects of the nonlinear centrifugal force to system attitude motion were analyzed by approximate calculation; At last, the Liapunov function based on energy norm was selected, in the condition that only the measured values of attitude and attitude speed are available, and it is proved that the PD feedback control law can ensure the attitude stability during large angle maneuver.

Boundary Integral Formula of the Elastic Problems in Circle Plane

DONG Zheng-zhu, LI Shun-cai, YU De-hao

2005, 26(5): 556-560.

Abstract(2582) PDF(863)

Abstract:
By bianalytic functions, the boundary integral formula of the stress function for the elastic problem in a circle plane is developed. But this integral formula includes a strongly singular integral and can not be directly calculated. After the stress function is expounded to Fourier series, making use of some formulas in generalized functions to the convolutions, the boundary integral formula which doesn't include strongly singular integral is derived further. Then the stress function can be got simply by the integration of the values of the stress function and its derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function for the elastic problem is convenient.

A Dynamic Model for Rocket Launcher With Coupled Rigid and Flexible Motion

ZHANG Ding-guo, XIAO Jian-qiang

2005, 26(5): 561-568.

Abstract(2824) PDF(682)

Abstract:
The dynamics of a coupled rigid-flexible rocket launcher is reported. The coupled rigid-flexible rocket launcher is divided into two subsystems, one is a system of rigid bodies, the other a flexible launch tube which can undergo large overall motions spatially. First, the mathematical models for these two subsystems were established respectively. Then the dynamic model for the whole system was obtained by considering the coupling effect between these two subsystems. The approach reported, which divides a complex system into several simple subsystems first and then obtains the dynamic model for the whole system via combining the existing dynamic models for simple subsystems, can make the modeling procedure efficient and convenient.

Damage Progressive Model of Compression of Composite Laminates After Low Velocity Impact

CHENG Xiao-quan, LI Zheng-neng

2005, 26(5): 569-576.

Abstract(3096) PDF(1180)

Abstract:
Compressive properties of composite laminates after low velocity impact are one of the most serious circumstances that must be taken into account in damage tolerance design of composite structures. In order to investigate compressive properties of composite laminates after low velocity impact, three dimensional dynamic finite element method (FEM) was used to simulate low-velocity impact damage of 2 kinds of composite laminates firstly. Damage distributions and projective damage areas of the laminates were predicted under two impact energy levels. The analyzed damage after im pact was considered to be the initial damage of the laminates under compressive loads. Then three di mensional static FEM was used to simulate the compressive failure process and to calculate residual compressive strengths of the impact damaged laminates. It is achieved to simulate the whole process from initial low-velocity impact damage to final compressive failure of composite laminates. Compared with experimental results, it shows that the numerical predicting results agree with the test results fairly well.

Investigation on Kane Dynamic Equations Based on Screw Theory for Open-Chain Manipulators

LIU Wu-fa, GONG Zhen-bang, WANG Qin-que

2005, 26(5): 577-584.

Abstract(2618) PDF(1268)

Abstract:
First, screw theory, product of exponential formulas and Jacobian matrix are introduced. Then definitions are given about active force wrench, inertial force wrench, partial velocity twist, generalized active force, and generalized inertial force according to screw theory. After that Kane dynamic equations based on screw theory for open-chain manipulators have been derived. Later on how to compute the partial velocity twist by geometrical method is illustrated. Finally the correctness of conclusions is verified by example.

Applications of Nonlinear Optimization Method to the Numerical Studies of Atmospheric and Oceanic Sciences

DUAN Wan-suo, MU Mu

2005, 26(5): 585-594.

Abstract(2679) PDF(1304)

Abstract:
Linear singular vect or and linear singular value can only describe the evolution of sufficiently small perturbations during the period in which the tangent linear model is valid. With this in mind, the applications of nonlinear optimization methods to the atmospheric and oceanic sciences are introduced, which include nonlinear singular vector (NSV) and nonlinear singular value (NSVA), conditional nonlinear optimal perturbation (CNOP), and their applications to the studies of predictability in numerical weather and climate prediction. The results suggest that the nonlinear characteristics of the motions of atmosphere and oceans can be explored by NSV and CNOP. Also attentions are paid to the introduction of the classification of predictability problems, which are related to the maximum predictable time, the maximum prediction error, and the maximum allowing error of initial value and the parameters. All the information has the background of application to the evaluation of products of numerical weather and climate prediction. Furthermore the nonlinear optimization methods of the sensitivity analysis with numerical model are also introduced, which can give a quantitative assessment whether a numerical model is able to simulate the observations and find the initial field that yield the optimal simulation. Finally, the difficulties in the lack of ripe algorithms are also discussed, which leave future work to both computational mathematics and scientists in geophysics.

Adaptive Generalized Predictive Control of Switched Systems

WANG Yi-jing, WANG Long

2005, 26(5): 595-601.

Abstract(2686) PDF(834)

Abstract:
The problem of adaptive generalized predictive control which consists of output prediction errors for a class of switched systems is studied. The switching law is determined by the output predictive errors of a finite number of subsystems. For the single subsystem and multiple subsystems cases, it is proved that the given direct algorithm of generalized predictive control guarantees the global convergence of the system. This algorithm overcomes the inherent drawbacks of the slow convergence and large transient errors for the conventional adaptive control.

Nonlinear Evolution of the Wave on the Small-Amplitude Uneven Sloping Bed

BAI Yu-chuan, XU Hai-jue, LU Dong-qiang

2005, 26(5): 602-608.

Abstract(2366) PDF(597)

Abstract:
There are different forms of the beds on the natural sandy coast, on which the propagation process of the wave is a typical nonlinear one. Based on this, the nonlinear propagation process of the wave on the small-amplitude uneven sloping bed is analyzed by using the perturbation method. The results of the analytic expression are compared with the correlative experimental data, which shows that the practical situation can be reflected in the evolution of the estabilished model of the wave.

Application of Wavelet Theory in Research on Weight Function of Meshless Method

ZHANG Hong, ZHANG Xuan-bing, GE Xiu-run

2005, 26(5): 609-613.

Abstract(2689) PDF(651)

Abstract:
Multiresolution analysis of wavelet theory can give an effective way to describe the information at various levels of approximations or different resolutions, based on spline wavelet analysis, so weight function is orthonormally projected onto a sequence of closed spline subspaces, and is viewed at various levels of approximations or different resolutions. Now, the useful new way to research weight function is found, and the numerical result is given.

Geometrical Nonlinear Waves in Finite Deformation Elastic Rods

GUO Jian-gang, ZHOU Li-jun, ZHANG Shan-yuan

2005, 26(5): 614-620.

Abstract(2903) PDF(730)

Abstract:
By usinge Hamilton-type variation principle in non-conservation system, the nonlinear equation of wave motion of a elastic thin rod was derived according to Lagrange description of finite deformation theory. The dissipation caused due to viscous effect and the dispersion introduced by transverse inertia were taken into consideration so that steady traveling wave solution can be obtained. Using multi-scale method the nonlinear equation is reduced to a KdV-Burgers equation which corresponds with saddle-spiral heteroclinic orbit on phase plane. Its solution is called the oscillating-solitary wave or saddle-spiral shock wave. If viscous effect or transverse inertia is neglected, the equation is degraded to classical KdV or Burgers equation. The former implies a propagating solitary wave with homoclinic on phase plane, the latter means shock wave and heteroclinic orbit.

Research on an Orthogonal Relationship for Orthotropic Elasticity

LUO Jian-hui, LIU Guang-dong

2005, 26(5): 621-624.

Abstract(2466) PDF(718)

Abstract:
The new orthogonal relationship is generalized for orthotropic elasticity of three-dimensions. The thought of how dual vectors are constructed in a new orthogonal relationship for theory of elasticity is generalized into orthotropic problems. A new dual vector is presented by the dual vector of the symplectic systematic methodology for elasticity that is over again sorted. A dual differential equation is directly obtained by using a mixed variables method. A dual differential matrix to be derived possesses a peculiarity of which principal diagonal sub-matrixes are zero matrixes. As a result of the peculiarity of the dual differential matrix, two independently and symmetrically orthogonal sub-relationships are discovered for orthotropic elasticity of three-dimensions. The dual differential equation is solved by a method of separation of variable. Based on the integral form of orthotropic elasticity a new orthogonal relationship is proved by using some identical equations. The new orthogonal relationship not only includes the symplectic orthogonal relationship but is also simpler. The physical significance of the new orthogonal relationship is the symmetry representation about an axis z for solutions of the dual equation. The symplectic orthogonal relationship is a generalized relationship but it may be appeared in a strong form with narrow sense in certain condition. This theoretical achievement will provide new effective tools for the research on analytical and finite element solutions to orthotropic elasticity of three-dimensions.

Study on the Structure of Singular Points of Laminar Flame System

WANG Xiu-e, YIN Xian-jun

2005, 26(5): 625-630.

Abstract(2142) PDF(622)

Abstract:
Under some certain assumptions, the physical model of the air combustion system was simplified to a laminar flame system. The mathematical model of the laminar flame system, which was built according to thermodynamics theory and the corresponding conservative laws, was studied. With the aid of qualitative theory and method of ordinary differential equations, the location of singular points on the Rayleigh curves is determined, the qualitative structure and the stability of the singular points of the laminar flame system, which are located in the areas of deflagration and detonation, are given for different parameter values and uses of combustion. The phase portraits of the laminar flame system in the reaction-stagnation enthalpy and combustion velocity-stagnation enthalpy planes are shown in the corresponding figures.

2005 Vol. 26, No. 5