应用数学和力学

2006 Vol. 27, No. 1

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Mesh Free Method Based on Local Cartesian Frame

LIU Gao-lian, LI Xiao-wei

2006, 27(1): 1-5.

Abstract(2497) PDF(550)

Abstract:
A new mesh free method proposed by the authors was presented in which the derivatives at each node were constructed using whole derivative formulas through the nodes selected around the node using local Cartesian frame in an autonomous manner,so that without any element it could be considered as a completely mesh free method.The method had been tested with a numerical example,and reliable solution was obtained with high accuracy and efficiency.

Prediction Techniques of Chaotic Time Series and Its Applications at Low Noise Level

MA Jun-hai, WANG Zhi-qiang, CHEN Yu-shu

2006, 27(1): 6-12.

Abstract(2402) PDF(576)

Abstract:
Not only the noise reduction methods of chaotic time series with noise and its reconstruction techniques were studied,but also prediction techniques of chaotic time series and its applications were discussed based on chaotic data noise reduction.First the phase space of chaotic time series was decomposed to range space and null noise space'secondly original chaotic time series was reconstrucled in range space.Lastly on the basis of the above,the order of the nonlinear model was established and the nonlinear model was made use of to predict some research.The result indicates that the nonlinear model has very strong ability of approximation function,and Chaos prediction method has certain tutorial significance to the practical problems.

Eigenvalue Problem of a Large Scale Indefinite Gyroscopic Dynamic System

SUI Yong-feng, ZHONG Wan-xie

2006, 27(1): 13-20.

Abstract(2326) PDF(741)

Abstract:
Gyroscopic dynamic system can be introduced to Hamiltonian system.Based on an adjoint symplectic subspace iteration method of Hamiltonian gyroscopic system,an adjoint symplectic subspace iteration method of indefinite Hamiltonian function gyroscopic system is proposed to solve the eigenvalue problem of indefinite Hamiltonian function gyroscopic system.The character that the eigenvalues of Hamiltonian gyroscopic system are only pure imaginary or zero is used.The eigenvalues that Hamiltonian fuction is negative can be separated so that the eigenvalue problem of positive definite Hamiltonian function system is presented,and an adjoint symplectic subspace iteration method of positive definite Hamiltonian function system is used to solve the separated eigenvalue problem. Therefore,the eigenvalue problem of indefinite Hamiltonian function gyroscopic system is solved,two numerical examples are given to demonstrate that the eigensolutions converge exactly.

Finite Difference Method for Simulatting Transverse Vibrations of an Axially Moving Viscoelatic String

ZHAO Wei-jia, CHEN Li-qun, Jean W Zu

2006, 27(1): 21-27.

Abstract(2722) PDF(655)

Abstract:
Finite difference method is presented to simulate transverse vibrations of an axially moving string.The equation of motion is derived first.By discretizing the governing equation and the equation of stress_strain relation at different frictional knots,two linear sparse finite difference equation systems are obtained.The two resulting difference schemes can be calculated alternatively,which make the computation much more efficient.The numerical method makes the nonlinear model easier to deal with and of truncation errors.It also shows stability for small initial values,so it can be used in analyzing the nonlinear vibration of viscoelastic moving string effectively.Numerical examples are presented to demonstrate the efficiency and the stability of the algorithm,and dynamic analysis of a viscoelastic string is given by using the numerical results.

Weight Function for Stress Intensity Factors in Rotating Thick-Walled Cylinder

CHEN Ai-jun, ZENG Wen-ji

2006, 27(1): 28-34.

Abstract(2712) PDF(641)

Abstract:
The equation of stress intensity factors of internally pressurized thick_walled cylinder was used as the reference case'sIF equation of rotating thick_walled cylinder containing a radial crack along the internal bore was presented in weight function method.The weight function formulas were worked out and can be used for all kinds of depth of cracks,rotating speed,material,size of thick_ walled cylinder to calculate the stress intensity factors.The results indicated the validity and effectiveness of these formulas.Meanwhile,the rules of the stress intensity factors in rotating thick_walled cylinder with the change of crack depths and the ratio of outer radius to inner radius were studied. The studies are valuable to engineering application.

Eigenfrequency Analysis of Cable Structures With Inclined Cables

William Paulsen, Greg Slayton

2006, 27(1): 35-46.

Abstract(2968) PDF(485)

Abstract:
The approximate eigenfrequencies for the in_plane vibrations of a cable structure consisting of inclined cables,together with point masses at various points were computed.It was discovered that the classical transfer matrix method was inadequate for this task,and hence the larger exterior matrices to determine the eigenfequency equation were used.Then predictions of the dynamics of the general cable structure based on the asymptotic estimates of the exterior matries were made.

A Symplectic Algorithm for the Dynamics of a Rigid Body

LU Ying-jie, REN Ge-xue

2006, 27(1): 47-52.

Abstract(3507) PDF(1487)

Abstract:
For the dynamics of a rigid body with a fixed point based on quaternion and the corresponding generalized momenta,a displacement_based symplectic integration scheme for differential_algebraic equations is proposed and applied to the Lagrange's equations based on dependent generalized momenta.Numerical experiments show that the algorithm possesses such characters as high precision and preserving system invariants.More importantly,the generalized momenta based Lagrange's equations show unique advantages over the traditional Lagrange's equations in symplectic integrations.

Rule of Transient Phreatic Flow Subjected to Vertical and Horizontal Seepage

TAO Yue-zan, XI Dao-ying

2006, 27(1): 53-59.

Abstract(2632) PDF(739)

Abstract:
In a semi_infinite aquifer bounded by a channel,a transient flow model is constructed for phreatic water subjected to vertical and horizontal seepage.Based on the first linearized Boussinesq equation,the analytical solution of the model is obtained by Laplace transform.Having proven the transformation between the analytical solution and some relevant classic formulas,suitable condition for each of these formulas is demonstrated.According to the analytical solution,the variation of transient flow process caused by the variables,such as vertical infiltration intensity,fluctuation range of river stage,aquifer parameters such as transmissivity and specific yield,and the distance from calculating point to channel boundary,is analyzed quantitatively one by one.Lagging effect will happen to the time,when phreatic water gets its maximum fluctuation velocity,response to the varying of the variables stated above.The condition for some variables that can form equivalent lagging effect is demonstrated.Corresponding to the mathematical characteristics of the analytical solution,the physical implication and the fluctuation rule of groundwater level are discussed.

Droplet Collision and Coalescence Model

LI Qiang, CAI Ti-min, HE Guo-qiang, HU Chun-bo

2006, 27(1): 60-66.

Abstract(2720) PDF(819)

Abstract:
A new droplet collision and coalescence model was presented,a quick_sort method for locating collision partners was also devised and based on theoretical and experimental results,further advancement was made to the droplet collision outcome.The advantages of the two implementations of SPH method were used to limit the collision of droplets to a given number of nearest droplets and define the probability of coalescence,numerical simulations were carried out for model validation. Results show that the model presented is mesh_independent and less time consuming,it can not only maintain the system momentum conservation perfectly,but not susceptible to initial droplet size distri bution as well.

Unconventional Hamilton-Type Variational Principles For Dynamics of Reissner Sandwich Plate

HUANG Wei-jiang, LUO En, SHE Hui

2006, 27(1): 67-74.

Abstract(2659) PDF(880)

Abstract:
According to the basic idea of classical yin_yang complementarity and modern dual_complementarity,in a simple and unified way proposed by Luo(1987),some unconventional Hamilton_type variational principles for dynamics of Reissner sandwich plate can be established systematically.The unconventional Hamilton_type variation principle can fully characterize the initial_boundary_value problem of this dynamics.An important integral relation is given,which can be considered as the generalized principle of virtual work in mechanics.Based on this relation,it is possible not only to obtain the principle of virtual work,in dynamics of Reissner sandwich plate,but also to derive systematically the complementary functionals for five_field,two_field and one_field unconventional Hamilton_type variational principles by the generalized Legendre transformations.Furthermore,with this approach,the intrinsic relationship among the various principles can be explained clearly.

Vertical Vibration Analysis of Axisymmetric Saturated Soil

CAI Yuan-qiang, XU Chang-jie, ZHENG Zao-feng, WU Da-zhi

2006, 27(1): 75-81.

Abstract(2401) PDF(620)

Abstract:
Based on Biot's dynamic consolidation equations,by means of Laplace_Hankel transform technology,the integral solutions of stress and displacement in saturated soil with subjacent rock_stratum under axisymmetric arbitrary excitations were derived.Influence of the reflected wave generated by the boundary was revealed.Numerical results indicate that the vibration frequency has some effect on the vertical displacement of saturated soil.The vertical displacement at the surface of saturated soil lags in phase with the load.Furthermore,the dynamic permeability coefficient of saturated soil has significant effect on the vertical displacement at the initial stage of load applied,but when the load becomes stable,the effect is inapparent.

Wave Interactions in Suliciu Model for Dynaimc Phase Transitions

TANG Shao-qiang, QIAN Jing, XIAO Jun

2006, 27(1): 82-88.

Abstract(2285) PDF(501)

Abstract:
Elementary waves in Suliciu model for dynamic phase transitions are obtained through traveling wave analysis.For any given initial data with two pieces of constant states,the Riemann solutions are constructed as a combination of elementary waves.When the initial profile contains three pieces of constant states,the solution may be constructed from the Riemann solutions,with each two adjacent states connected by elementary waves.A new Riemann problem forms when these two waves collide.Through the exploration of these Riemann problems,the outcome of wave interactions may be classified in a suitable parametric space.

Fault Diagnosis of Rotating Machinery Using Knowledge-Based Fuzzy Neural Network

LI Ru-qiang, CHEN Jin, WU Xing

2006, 27(1): 89-97.

Abstract(2830) PDF(697)

Abstract:
A novel knowledge_based fuzzy neural network(KBFNN)for fault diagnosis is presented. Crude rules were extracted and the corresponding dependent factors and antecedent coverage factors were calculated firstly from the diagnostic sample based on rough sets theory.Then the number of rules was used to construct partially the structure of a fuzzy neural network and those factors were implemented as initial weights,with fuzzy output parameters being optimized by genetic algorithm. Such fuzzy neural network was called KBFNN.This KBFNN was utilized to identify typical faults of rotating machinery.Diagnostic results show that it has those merits of shorter training time and higher right diagnostic level compared to general fuzzy neural networks.

Boundary Control of MKdV-Burgers Equation

TIAN Li-xin, ZHAO Zhi-feng, WANG Jing-feng

2006, 27(1): 98-104.

Abstract(2482) PDF(753)

Abstract:
The boundary control of MKdV_Burgers equation was considered by feedback control on the domain[0,1].The existence of the solution of MKdV_Burgers equation with the feedback control law was proved.On the base,priori estimates for the solution was given.At last,the existence of the weak solution of MKdV_Burgers equation was proved and global_exponential and asymptotic stability of the solution of MKdV_Burgers equation was given.

Preliminary Probe Into the Optimization on Propulsion in Short Distance Competitive Swimming

WANG Xin-feng, WANG Lian-ze

2006, 27(1): 105-111.

Abstract(2710) PDF(721)

Abstract:
Based on the modeling of dynamics and energy conversion in competitive swimming,the optimal control theory was used to make an optimization analysis of the distance traveled in a given time.Using the records of the 27th Olympics and the results from previous research,an optimal solu tion of propulsion was derived using some hypotheses and constraints.Correspondingly,the optimal tactic for velocity and energy was put forward which was in agreement with the practice.

Poincaré Inequalities in Weighted Sobolev Spaces

WANG Wan-yi, SUN Jiong, ZHENG Zhi-ming

2006, 27(1): 112-118.

Abstract(3209) PDF(1002)

Abstract:
The weighted Poincar inequalities in weighted Sobolev spaces were discussed and some necessary and sufficient conditions for them to hold were given.

Dynamic Analysis of Flexible Body With Definite Moving Attitude

YANG Yuan-ming, ZHANG Wei, SONG Tian-xia, CHEN Chuan-yao

2006, 27(1): 119-126.

Abstract(2490) PDF(539)

Abstract:
The nonlinear dynamic control equation of a flexible multi-body system with definite moving attitude is discussed.The motion of the aircraft in space is regarded as known and the influence of the flexible structural members in the aircraft on the motion and attitude of the aircraft is analyzed.By means of a hypothetical mode,the deformation of flexible members is regarded as composed of the line element vibration in the axial direction of rectangular coordinates in space.According to Kane's method in dynamics,a dynamic equation is established,which contains the structural stiffness matrix that represents the elastic deformation and the geometric stiffness matrix that represents the nonlinear deformation of the deformed body.Through simplification the dynamic equation of the influence of the planar flexible body with a windsurfboard structure on the spacecraft motion is obtained.The numerical solution for this kind of equation can be realized by a computer.