应用数学和力学

2002 Vol. 23, No. 10

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A Numerical Method on Estimation of Stable Regions of Rotor Systems Supported on Lubricated Bearings

ZHENG Hui-ping, CHEN Yu-shu

2002, 23(10): 991-996.

Abstract(2121) PDF(889)

Abstract:
The stability degree of periodic solution of nonlinear nonautonomous system was defined by means of the Floquet theory. A method evaluating the stability degree of periodic solution based on transient response was presented by the aid of the concept of dynamic systems or flows. The critical value of a system was determined by the condition i. e. its stability degree equals zero. Stable regions of rotor systems with balanced and unbalanced disk supported on lubricated bearings were calculated. The study shows that stable region decreases with the increase of speed for a balanced rotor system and decreases with the increase of unbalance for an unbalanced rotor system. Stable regions of periodic solutions are less than that of equilibrium points under the same systematic conditions.

Singular Analysis of Bifurcation of Nonlinear Normal Modes for a Class of Systems With Dual Internal Resonances

LI Xin-ye, CHEN Yu-shu, WU Zhi-qiang

2002, 23(10): 997-1007.

Abstract(2399) PDF(764)

Abstract:
The nonlinear normal modes(NNMs) associated with internal resonance can be classified into two kinds:uncoupled and coupled. The bifurcation problem of the coupled NNM of systems with 1:2:5 dual internal resonance is in two variables. The singular analysis of it is presented after separating the two variables by taking advantage of Maple algebra,and some new bifurcation patterns are found. Different from the NNMs of systems with single internal resonance,the number of the NNMs of systems with dual internal resonance may be more or less than the number of the degrees of freedom. At last,it is pointed out that bifurcation problems in two variables can be conveniently solved by separating variables as well as using coupling equations.

A Symbolic Computation Method to Decide the Completeness of the Solutions to the System of Linear Partial Differential Equations

ZHANG Hong-qing, XIE Fu-ding, LU Bin

2002, 23(10): 1008-1012.

Abstract(2306) PDF(1093)

Abstract:
A symbolic computation method to decide whether the solutions to the system of linear partial differential equation is complete via using differential algebra and characteristic set is presented. This is a mechanization method,and it can be carried out on the computer in the Maple environment.

Wavelet Approximate Inertial Manifold and Numerical Solution of Burgers' Equation

TIAN Li-xin, XU Bo-qiang, LIU Zeng-rong

2002, 23(10): 1013-1024.

Abstract(2178) PDF(539)

Abstract:
The existence of approximate inertial manifold using wavelet to Burgers. equation,and numerical solution under multiresolution analysis with the low modes were studied. It is shown that the Burgers. equation has a good localization property of the numerical solution distinguishably.

General Solution of the Overall Bending of Flexible Circular Ring Shells With Moderately Slender Ratio and Applications to the Bellows(Ⅲ)- Calculation for C-Shaped Bellows

ZHU Wei-ping, HUANG Qian

2002, 23(10): 1025-1034.

Abstract(2384) PDF(505)

Abstract:
This is one of the applications of Part(Ⅰ),in which the angular stiffness,the lateral stiffness and the corresponding stress distributions of C-shaped bellows were calculated. The bellows was divided into protruding sections and concave sections for the use of the general solution(Ⅰ),but the continuity of the stress resultants and the deformations at each joint of the sections were entirely satisfied. The present results were compared with those of the other theories and experiments,and are also tested by the numerically integral method. It is shown that the governing equation and the general solution(Ⅰ) are very effective.

General Solution of the Overall Bending of Flexible Circular Ring Shells With Moderately Slender Ratio and Applications to the Bellows(Ⅳ)- Calculation for U-Shaped Bellows

ZHU Wei-ping, HUANG Qian

2002, 23(10): 1035-1040.

Abstract(2021) PDF(724)

Abstract:
This is one of the applications of Part(Ⅰ),in which the angular stiffness,and the corresponding stress distributions of U-shaped bellows were discussed. The bellows was divided into protruding sections,concave sections and ring plates for the calculation that the general solution(Ⅰ) with its reduced form to ring plates were used respectively,but the continuity of the surface stresses and the meridian rotations at each joint of the sections were entirely satisfied. The present results were compared with those of the slender ring shell solution proposed earlier by the authors,the standards of the Expansion Joint Manufacturers Association(EJMA),the experiment and the finite element method. It is shown that the governing equation and the general solution(Ⅰ) are very effective.

Nonoscillation Results for a Class of Third Order Nonlinear Differential Equations

Pakize Temtek, Aydn Tiryaki

2002, 23(10): 1041-1046.

Abstract(2162) PDF(644)

Abstract:
Sufficient conditions for the nonoscillatory solutions of a class of third order nonline ardifferential equations are presented. The results obtained generalize some criteria given by Parhi. In some special cases,some of these results contain weaker conditions.

Response Characteristics of Wind Excited Cables With Artificial Rivulet

GU Ming, LIU Ci-jun, XU You-lin, XIANG Hai-fan

2002, 23(10): 1047-1054.

Abstract(1980) PDF(879)

Abstract:
A wind tunnel investigation of response characteristics of cables with artificial rivulet is presented. A series of cable section models of different mass and stiffness and damping ratio were designed with artificial rivulet. They were tested in smooth flow under different wind speed and yaw angle and for different position of artificial rivulet. The measured response of cable models was then analyzed and compared with the experimental results obtained by other researchers and the existing theories for wind-induced cable vibration. The results show that the measured response of horizontal cable models with artificial rivulet could be well predicted by Den Hartog's galloping theory when wind is normal to the cable axis. For the wind with certain yaw angles,the cable models with artificial rivulet exhibit velocity-restricted response characteristics.

Generalized Fatigue Constant Life Curve and Two-Dimensional Probability Distribution of Fatigue Limit

XIONG Jun-jiang, WU Zhe, GAO Zhen-tong

2002, 23(10): 1055-1060.

Abstract(2548) PDF(823)

Abstract:
According to the traditional fatigue constant life curve,the concept and the universal expression of the generalized fatigue constant life curve were proposed. Then,on the basis of the optimization method of the correlation coefficient,the parameter estimation formulas were induced and the generalized fatigue constant life curve with the reliability level p was given. From P-Sa-Sm curve,the two-dimensional probability distribution of the fatigue limit was derived. After then,three set of tests of LY11CZ corresponding to the different average stress were carried out in terms of the two-dimensional up-down method. Finally,the methods are used to analyze the test results,and it is found that the analyzed results with the high precision may be obtained.

A Nonlinear Galerkin Mixed Element Method and a Posteriori Error Estimator for the Stationary Navier-Stokes Equations

LUO Zhen-dong, ZHU Jiang

2002, 23(10): 1061-1072.

Abstract(2664) PDF(721)

Abstract:
A nonlinear Galerkin mixed element(NGME) method and a posteriori error estimator based on the method are established for the stationary Navier-Stokes equations. The esistence and error estimates of the NGME solution are first discussed,and then a posteriori error estimator based on the NGME method is derived.

Convergence of Simplified and Stabilized Mixed Element Formats Based on Bubble Function for the Stokes Problem

LUO Zhen-dong, ZHU Jiang

2002, 23(10): 1073-1079.

Abstract(1966) PDF(720)

Abstract:
Two simplified and stabilized mixed element formats for the Stokes problem are derived by bubble function,and their convergence,i. e.,error analysis,are proved. These formats can save more freedom degrees than other usual formats.

The Lie Symmetries and Conserved Quantities of Variable-Mass Nonholonomic System of Non-Chetaev's Type in Phase Space

FANG Jian-hui, ZHAO Song-qing, JIAO Zhi-yong

2002, 23(10): 1080-1084.

Abstract(2829) PDF(688)

Abstract:
The Lie symmetries and the conserved quantities of a variable mass nonholonomic system of non-Chetaev's type are studied by introducing the infinitesimal transformations of groups in phase space. By using the invariance of the differential equations of motion under the infinitesmal transformations of groups,the determining equations and the restriction equations of the Lie symmetries of the system are established,and the structure equations and the conserved quantities are obtained. An example is given to illustrate the application of the result.

Velocity Field in Ship Waves on the Viscous Fluid

LIU Min-jia, TAO Ming-de

2002, 23(10): 1085-1092.

Abstract(2430) PDF(766)

Abstract:
From the Navier-Stokers equations,the integral expressions of the free-surface elevation and the velocity field in ship waves of a moving waterborne body are obtained. Next,Lighthill's two- stage scheme is employed to change the above-mentioned integral expressions to algebraic expressions. Compared with the results obtained when the seawater is idealized to an inviscid fluid,the singularities are dispelled or weakened,and the accuracy of the digit information of ship waves is improved.

Research of the Periodic Motion and Stability of Two-Degree-of-Freedom Nonlinear Oscillating Systems

LIU Jun

2002, 23(10): 1093-1100.

Abstract(2657) PDF(733)

Abstract:
The periodic motion and stability for a class of two-degree-of-freedom nonlinear oscilating systems are studied by using the method of Liapunov function. The sufficient conditions which guarantee the existence,uniqueness and asymptotic stability of the periodic solutions are obtained.