应用数学和力学

Control of a Hyperchaotic Discrete System

CHEN Li-qun, LIU Zeng-rong

2001, 22(7): 661-665.

Abstract(2036) PDF(482)

Abstract:
The Control of a hyperchaotic discrete system is investigated. A time-varying feedback control law is established on the base of local linearization. The Liapunov direct method is applied to estimate the neighborhood in which the control law can be effectively used. Numerical examples are presented to demonstrate the applications of the control law to solve the problem of stabilizing unstable periodic orbits and the problem of tracking an arbitrarily given periodic orbit.

Nonlinear Bending Theory of Diagonal Square Pyramid Reticulated Shallow Shells

XIAO Tan, LIU Ren-huai

2001, 22(7): 666-672.

Abstract(2066) PDF(582)

Abstract:
Double-deck reticulated shells are a main form of large space structures. One of the shells is the diagonal square pyramid reticulated shallow shell, whose its upper and lower faces bear most of the load but its core is comparatively flexible. According to its geometrical and mechanical characteristics, the diagonal square pyramid reticulated shallow shell is treated as a shallow sandwich shell on the basis of three basic assumptions. Its constitutive relations are analyzed from the point of view of energy and internal force equivalence. Basic equations of the geometrically nonlinear bending theory of the diagonal square pyramid reticulated shallow shell are established by means of the virtual work principle.

A New Method for Solution of 3D Elastic-Plastic Frictional Contact Problems

ZHANG Hong-wu, ZHONG Wan-xie, GU Yuan-xian

2001, 22(7): 673-681.

Abstract(2428) PDF(792)

Abstract:
The solution of 3D elastic-plastic frictional contact problems belongs to the unspecified boundary problems where the interaction between two kinds of nonlinearities should occur. Considering the difficulties for the solution of 3D frictional contact problems, the key part is the determination of the tangential slip states at the contact points, and a great amount of computing work is needed for a high accuracy result. A new method based on a combination of programming and iteration methods, which are respectively known as two main kinds of methods for contact analysis, was put forward to deal with 3D elastic-plastic contact problems. Numerical results demonstrate the efficiency of the algorithm illustrated here.

Investigation of the Scattering of Harmonic Elastic Waves by Two Collinear Symmetric Cracks Using the Non-Local Theory

ZHOU Zhen-gong, WANG Biao

2001, 22(7): 682-690.

Abstract(2378) PDF(628)

Abstract:
The scattering of harmonic waves by two collinear symmetric cracks is studied using the non-local theory. A one-dimensional non-local kernel was used to replace a two-dimensional one for the dynamic problem to obtain the stress occurring at the crack tips. The Fourier transform was applied and a mixed boundary value problem was formulated. Then a set of triple integral equations was solved by using Schmidt's method. This method is more exact and more reasonable than Eringen's for solving this problem. Contrary to the classical elasticity solution, it is found that no stress singularity is present at the crack tip. The non-local dynamic elastic solutions yield a finite hoop stress at the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the lattice parameter and the circular frequency of incident wave.

The Eigentensors of an Arbitrary Second Order Tensor and Their Quality Analyses

HUANG Yong-nian

2001, 22(7): 691-694.

Abstract(2255) PDF(1375)

Abstract:
A notation of the eigentensors of an arbitrary second order tensor had been introduced by HUANG Yong-nian(1992). By using this notation an explicit solution of homogeneous linear ordinary differential equations with constant coefficients had been given. Recently, it is found that these eigen tensors are dyads. By using these dyads the tensor calculations can be simplified greatly.

A Method for Topological Optimization of Structures with Discrete Variables under Dynamic Stress and Displacement Constraints

SHI Lian-shuan, SUN Huan-chun, FENG En-min

2001, 22(7): 695-700.

Abstract(2419) PDF(825)

Abstract:
A method for topological optimization of structures with discrete variables subjected to dynamic stress and displacement constraints is presented. By using the quasi-static method, the structure optimization problem under dynamic stress and displacement constraints is converted into one subjected to static stress and displacement constraints. The comprehensive algorithm for topological optimization of structures with discrete variables is used to find the optimum solution.

New Explicit and Exact Travelling Wave Solutions for a Class of Nonlinear Evolution Equations

XIA Tie-cheng, ZHANG Hong-qing, YAN Zhen-ya

2001, 22(7): 701-705.

Abstract(2565) PDF(701)

Abstract:
With the help of Mathematica, many travelling wave solutions for a class of nonlinear evolution equations u_tt+au_xx+bu+cu²+du³=0 are obtained by using hyperbola function method and Wuelimation method, which include new travelling wave solutions, periodicl solutions and kink soliton solutions. Some equations such as Duffing equation, sin-Gordon equation, φ⁴ and Klein-Gordon equation are particular cases of the evolution equations. The method can also be applied to other nonlinear equations.

The Analysis for the Airflow Exciting-Vibration Force of Control Stage of Steam Turbine

CHAI Shan, ZHANG Yao-ming, MA Hao, QU Qing-wen, ZHAO You-qun

2001, 22(7): 706-712.

Abstract(2120) PDF(677)

Abstract:
Based on the hydrodynamics, the airflow exciting-vibration force of control stage of steam turbine is studied by using the momentum theorem. A formulation for calculating the air exciting-vibration force of the control stage of steam turbine is deduced first by using theoretical analysis method and taking all the design factors of vane and nozzles into consideration. Moreover the exciting-vibration forces in different load cases are discussed respectively.

The Application of a Modified Normal Form Approach

ZHANG Wei-yi, Koncay Huseyin, YE Min

2001, 22(7): 713-718.

Abstract(2199) PDF(503)

Abstract:
The modified normal form approach presented by ZHANG Wei-yi, K Huseyin and CHEN Yu-shu is further extended and a different procedure is introduced which lends itself readily to symbolic calculations, like MAPLE. This provides a number of significant advantages over the previous approach, and facilitates the associated calculations. To illustrate the new approach, three examples are presented.

Diffusion Characters of the Orbits in the Asteroid Motion

ZHOU Li-yong, SUN Yi-sui, ZHOU Ji-lin

2001, 22(7): 719-728.

Abstract(2039) PDF(571)

Abstract:
A symplectic mapping is studied carefully. The exponential diffusion law in developed chaotic region and algebraic law in mixed region were observed. An area was found where the diffusion follows a logarithmic law. It is shown in the vicinity of an island, the logarithm of the escape time decreases linearily as the initial position moves away from the island. But when approaching close to the island, the escape time goes up very quickly, consistent with the superexponential stability of the invariant curve. When applied to the motion of asteroid, this mapping's fixed points and their stabilities give an explanation of the distribution of asteroids. The diffusion velocities in 4:3, 3:2 and 2:1 jovian resonances are also investigated.

Affine Transformation in Random Iterated Function Systems

XIONG Yong, SHI Ding-hua

2001, 22(7): 729-734.

Abstract(2152) PDF(1162)

Abstract:
Random iterated function systems (IFSs) is discussed, which is one of the methods for fractal drawing. A certain figure can be reconstructed by a random IFS. One approach is presented to determine a new random IFS, that the figure reconstructed by the new random IFS is the image of the origin figure reconstructed by old IFS under a given affin transformation. Two particular examples are used to show this approach.

NGP_G-Stability of Linear Multistep Methods for Systems of Generalized Neutral Delay Differential Equations

CONG Yu-hao

2001, 22(7): 735-742.

Abstract(2308) PDF(618)

Abstract:
The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was analysed for the solution of the generalized system of linear neutral test equations. After the establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, it is shown that a linear multistep method is NGP_G-stable if and only if it is A-stable.

Parameter Iteration Method for Solving Nonlinear Problem

LIN Jiang-guo

2001, 22(7): 743-748.

Abstract(2351) PDF(501)

Abstract:
The parameter iteration method was developed for solving the nonlinear problem in this paper. The results of several examples show that even the first iteration solution has very good accuracy.

Qualitative Analysis for a Class of Second Order Nonlinear System with Delay

PENG Qi-lin

2001, 22(7): 749-752.

Abstract(2434) PDF(646)

Abstract:
The second order nonlinear system with delay x"(t)+f(x(t),x'(t))+g(x(t),x'(t))ψ(x(t-τ))=p(t) being considered. Four theorems on the stability of zero solution, the boundedness of the solutions, the existence of the periodic solutions, the existence and uniqueness of the stationary oscilation are obtained by means of the Liapunov's second method. The conclusion in the literatures are generalized.

Reductive Perturbation Method of Super KdV Equations

LÜ Ke-pu, SUN Jian-an, DUAN Wen-shan, ZHAO Jin-bao

2001, 22(7): 753-757.

Abstract(2537) PDF(571)

Abstract:
By using reductive perturbation method, super KdV equations are changed into ordinary KdV equations, small amplitude perturbation solutions are obtained.

Comments on AMSAA-BISE Reliability Growth Model

MEI Wen-hua, GUO Yue-e, YANG Yi-xian

2001, 22(7): 758-762.

Abstract(2627) PDF(576)

Abstract:
From 1986 to 1991, based on AMSAA model, ZHOU Yuan-quan and WENG Zhao-xi presented AMSAA-BISE model to estimate reliability growth for multiple systems development, for the case that more than one system of the same type is put into reliability growth test, once a Type B failure mode is seen during test, corrective action will be taken to all systems. It is shown that there is something wrong with AMSAA-BISE model. According to AMSAA-BISE model, the maximum likelihood estimation of MTBF for multiple systems reliability growth test is much larger than that according to AMSAA model for a single system; The more systems is put into test, the larger the estimation of MTBF. An example is given, and an approximate method is presented.

Research on AMSAA-BISE Model--an Answer to MEI Wen-hua

ZHOU Yuan-quan

2001, 22(7): 763-767.

Abstract(2579) PDF(664)

Abstract:
The AMSAA-BISE model is derived from another approach. This certainly shows the correctness of the AMSAA-BISE model, and indicates the incorrectness of the approximate model given in this paper. The engineering example illustrating these conclusions is given. Merits and demerits of AMSAA and AMSAA-BISE model are discussed.

Comments on AMSAA-BISE Reliability Growth Model(Ⅱ)

MEI Wen-hua, GUO Yue-e

2001, 22(7): 768-770.

Abstract(2206) PDF(703)

Abstract:
The AMSAA-BISE model is derived from another approach. This certainly shows the correctness of the AMSAA-BISE model, and indicates the incorrectness of the approximate model given in this paper. The engineering example illustrating these conclusions is given. Merits and demerits of AMSAA and AMSAA-BISE model are discussed.

2001, 22(7): 771-772.

Abstract(1859) PDF(393)

Abstract:

2001 Vol. 22, No. 7