应用数学和力学

PSE as Applied to Problems of Secondary Instability in Supersonic Boundary Layers

ZHANG Yong-ming, ZHOU Heng

2008, 29(1): 1-7.

Abstract(2631) PDF(589)

Abstract:
Parabolized stability equations (PSE) approach is used to investigate problems of secondary instability in supersonic boundary layers. The results show that the mechanism of secondary instability does work, whether the 2-D fundamental disturbance is of the first mode or second mode T-S wave. The variation of the growth rates of the 3-D sub-harmonic wave against its span-wise wave number and the amplitude of the 2-D fundamental wave is found to be similar to those found in incompressible boundary layers. But even as the amplitude of the 2-D wave is as large as the order 2%, the maximum growth rate of the 3-D sub-harmonic is still much smaller than the growth rate of the most unstable second mode 2-D T-S wave. Consequently, secondary instability is unlikely the main cause leading to transition in supersonic boundary layers.

Modal Analysis of Coupled Vibration of Belt Drive Systems

LI Xiao-jun, CHEN Li-qun

2008, 29(1): 8-12.

Abstract(2488) PDF(605)

Abstract:
The modal method is applied to analyze coupled vibration of belt drive systems. A belt drive system is a hybrid system consisting of continuous belts modeled as strings as well as discrete pulleys and a tensioner arm. The characteristic equation of the system was derived from the governing equation. Numerical results demenstrate the effects of the transport speed and the initial tension on natural frequencies.

Numerical Simulation of Quasi-Streamwise Hairpin-Like Vortex Generation in a Turbulent Boundary Layer

ZHANG Nan, LU Li-peng, DUAN Zhen-zhen, YUAN Xiang-jiang

2008, 29(1): 13-20.

Abstract(3646) PDF(792)

Abstract:

Some Integral Inequalities on Time Scales

Adnan Tuna, Servet Kutukcu

2008, 29(1): 21-26.

Abstract(2120) PDF(664)

Abstract:
The reverse Hêlder type inequality and Hêlder inequality in two dimensional case on time scales were studied. Many integral inequalities by using Hêlder inequalities on time scales were also obtained which give Hardy. sinequalities as spacial cases.

Nonlinear Turbulence Models That Predict Strong Curvature Effects

XU Jing-lei, MA Hui-yang, HUANG Yu-ning

2008, 29(1): 27-37.

Abstract(2900) PDF(868)

Abstract:
The curvature effects on the structure of turbulence were analyzed qualitatively. Numerical simulations of a turbulent U-duct flow with a number of turbulence models in order to assess their overall performance were conducted. The models evaluated are some typical linear eddy viscosity turbulence models, nonlinear eddy viscosity turbulence models (NLEVM) (quadratic and cubic), a quadratic explicit algebraic stress model (EASM) and a Reynolds stress model (RSM) developed based on the secondmoment closure. The numerical results show that a cubic NLEVM that performs considerably well in other benchmark turbulent flows, such as the Craft, Launder and Suga model and the Huang and Ma model, is able to capture the major features of the highly curved turbulent U-duct flow, including the damping of turbulence near the convex wall, the enhancement of turbulence near the concave wall, and the subsequent turbulent flow separation. The predictions of the cubic models are quite close to that of the RSM, in relatively good agreement with the experimental data, which suggests that these models may be applied to simulating the turbulent curved flows in engineering applications.

Study on the Orbit and Attitude Control of Spacecraft Formation Flying

ZHANG Zhi-guo, LI Jun-feng

2008, 29(1): 38-46.

Abstract(2689) PDF(863)

Abstract:
Formation flying is a novel concept of distributing the functionality of large spacecraft among several smaller, less expensive, cooperative satellites. Some applications require that a controllable satellite keep relative position and attitude to observe a specific surface of another satellite among the cluster. Specially, the target space vehicle is malfunctioning. The problem of how to control a chaser satellite to fly around an outofwork target satellite closely in earth orbit and to track a specific surface is focused on. Relative attitude and first approximate relative orbital dynamics equations are presented. Control strategy is derived based on feedback linearization and Lyapunov theory of stability. Further, the uncertainty of inertia being considered, an adaptive control method is developed to obtain the correct inertial ratio. The numerical simulation is given to verify the validity of proposed control scheme.

Research Progress on the Thermal Protection Materials and Structures in Hypersonic Vehicles

YANG Ya-zheng, YANG Jia-ling, FANG Dai-ning

2008, 29(1): 47-56.

Abstract(3085) PDF(1366)

Abstract:
Hypersonic vehicles represent future trends of military equipments and play an important role in future war. Thermal protection materials and structures, which relate to the safety of hypersonic vehicles, are one of the most key techniques in design and manufacture of hypersonic vehicles. Among these materials and structures, such as metallic temperature protection structure, the a-high temperature ceramics and carbon/ carbon composites are usually adopted in design. The recent progresses of research and application of ultra-high temperature materials in preparation, oxidation resistance, mechanical and physical characterization were summarized.

Solution of a Nonlinear Wave Equation of Elastic Rod

GUO Peng, ZHANG Lei, LÜ Ke-pu, DUAN Wen-shan

2008, 29(1): 57-61.

Abstract(2449) PDF(584)

Abstract:
The longitudinal oscillation of a nonlinear elasticrod with lateral inertia were studied. A nonlinear wave equation is derived. The equation is solved by the method of full approximation.

Strain Analysis of Nonlocal Viscoelastic Kelvin Bar in Tension

ZHAO Xue-chuan, LEI Yong-jun, ZHOU Jian-ping

2008, 29(1): 62-68.

Abstract(2834) PDF(683)

Abstract:
Based on viscoelastic Kelvin model and nonlocal relationship of strain and stress, a nonlocal constitutive relationship of viscoelasticity was obtained and the strain response of a bar in tension was studied. By transforming governing equation of the strain analysis into Volterra integration form and by choosing a symmetric exponential form of kernel function and adapting Neumann series, the close form solution of strain field of the bar was obtained. The creep process of the bar is presented. When time approaches infinite, the strain of bar is equal to the one of nonlocal elasticity.

Global Qualitative Analysis of a New Monod Type Chemostat Model With Delayed Growth Response and Pulsed Input in a Polluted Environment

MENG Xin-zhu, ZHAO Qiu-lan, CHEN Lan-sun

2008, 29(1): 69-80.

Abstract(2881) PDF(755)

Abstract:
A new Monod type chemostat model is considered with time delay and pulsedinput concentration of the nutrient in a polluted environment. Using the discrete dynamical system deter mined by the stroboscopic map, a-microorg anismex tinction. periodic solution is obtained. Further more, the sufficient conditions for the global attractivity of the micro organism-extinction periodic solution are established. Using new computational techniques for impulsive and delayed differential equation, it is proved that the system is permanent under appropriate conditions. The results show that time delay is "profitless".

Interaction of Underwater Explosion Bubble With Complex Elastic-Plastic Structure

ZHANG A-man, YAO Xiong-liang

2008, 29(1): 81-92.

Abstract(3025) PDF(851)

Abstract:
Considering structure of elastic-plasticity, the combination of boundary element method and finite element method (FEM) was employed to present the calculation method for solving the complex coupling dynamic problem of bubble, plastic-elastic structure and free surface, and the complete threedimensional calculation program was developed as well. The error between calculated result yielded by the program and experimental result is within 10%. Taking surface ship as an example, the three-dimensional calculation program was converted in order to conveniently settle complex elastic-plastic structure problem in engineering field. Finally, a full system of coupling dynamic analysis program was completed, which is fit for solving interaction of three-dimensional bubble with elasticplastic structure in engineering application, aiming at present preference for further research on dynamics of bubble induced by ship underwater explosion. By employing the program, the response of ship under the bubble loading is analyzed. From the wall pressure-time history and stress-time history curves of typical elements of structure, it can be seen that the pressure reaches maximum when the bubble collapses and this validates that the pressure generated by the collapsing of bubble and the jet causes serious damage to the ship structure. From the dynamic process of the interaction of the threedimensional bubble and ship, the low order mode of the ship is provoked and the ship presents whipshaped motion. And the ship does elevation and subsidence movement with the expansion and shrinkage motion of the bubble.

An Algorithm for Phase Contrast X-ray Tomography Based on the Nonlinear Phase Retrieval

NI Wen-lei, ZHOU Tie

2008, 29(1): 93-103.

Abstract(2455) PDF(680)

Abstract:
A new algorithm for phase contrast X-ray tomography under holographic measurement was proposed. The main idea of the algorithm was to solve the nonlinear phase retrieval problem using the Newton iterative method. The linear equations for the Newton directions were proved to beill-posed and the regularized solutions were obtained by the conjugate gradient method. Some numerical experiments with computer simulated data were presented. The efficiency, feasibility and the numerical stability of the algorithm were illustrated by the numerical experiments. Compared with the results produced by the linearized phase retrieval algorithm, it can be seen that the new algorithm is not limited to be only efficient for the data measured in the nea-rfield of the Fresnel region and thus it has a broader validity range.

2008 Vol. 29, No. 1