应用数学和力学

2014 Vol. 35, No. 10

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Symplectic Integration for Multibody Dynamics Based on Quaternion Parameters

XU Xiao-ming, ZHONG Wan-xie

2014, 35(10): 1071-1080. doi: 10.3879/j.issn.1000-0887.2014.10.001

Abstract(1314) PDF(942)

Abstract:
The quaternion representation was introduced into multibody dynamics for the description of rigid body rotation, based on which the constrained dynamics was derived and the relevant Lagrange system was established. Then, the segmental action for discrete systems was introduced and approximated with the finite element method. According to the theory of analytical structural mechanics, the symplectic numerical integration was derived with the constraints strictly satisfied at the integration points and the integration process was symplectic conservative in the sense of variation principle. The proposed method has the characteristics of less calculation and less unknown numbers, which is confirmed with the numerical results of an exemplary multibody hinged system.

An Unusual Phenomenon in the Complex Mode Orthogonality Theory and the Strategy Against It

ZHANG Miao, YU Lan>, JU Wei

2014, 35(10): 1081-1091. doi: 10.3879/j.issn.1000-0887.2014.10.002

Abstract(1200) PDF(1190)

Abstract:
The label phenomenon was revealed through verification of the correctness of the complex mode orthogonality theory used in engineering with numerical experiment. Firstly, the decoupling function of the state vectors under different state space schemes was theoretically analyzed. The related conclusions were also proposed on the orthogonal properties of the state vectors in the cases of symmetric and asymmetric structures with repeated frequencies. Secondly, the label phenomenon was found out and the method to eliminate its undesirable influence was given. Finally, through a general example of sensitivity analysis, the likely risk out of ignorance of the label phenomenon was demonstrated. The research indicates that, through necessary orthogonality check and adjustment of the state vectors’ orders, the decoupling of the state vectors is realized and the adverse effect of the label phenomenon on the calculation accuracy is eliminated.

An Analog Equation Method-Based Numerical Scheme for Initial Value Problems of Stochastic Fractional Differential Equations

SUN Chun-yan, XU Wei

2014, 35(10): 1092-1099. doi: 10.3879/j.issn.1000-0887.2014.10.003

Abstract(1726) PDF(2225)

Abstract:
An analog-equation-method (AEM)-based numerical scheme was proposed for initial value problems of stochastic fractional differential equations with 2 fractional derivative terms. 2 stochastic analog equations comprising respective undetermined functions were introduced, to convert the problem to a fractional differential equation with only 1 fractional derivative term. The Laplace transform and its inverse were employed to get the integration representations for the solution to the fractional differential equation and establish the relation between the 2 analog equations. In view of the initial conditions, an iterative algorithm to solve the initial value problem of the stochastic fractional differential equation was obtained. In a typical case, the numerical solution to a linear stochastic ordinary differential equation with 2 fractional derivative terms was derived based on the AEM. The numerical results of both the definite and stochastic systems demonstrate the effectiveness, stability and accuracy of the presented AEM scheme, of which the error only lies in the truncation error of the integration approximation and the rounding error of the computation software.

A Galerkin Numerical Method for the Pipe Conveying Supercritical Fluid Under Forced Vibration

HUANG Hui-chun, ZHANG Yan-lei, CHEN Li-qun

2014, 35(10): 1100-1106. doi: 10.3879/j.issn.1000-0887.2014.10.004

Abstract(1305) PDF(877)

Abstract:
For the pipe conveying fluid, as the flow rate increased over a critical value, the equilibrium configuration was found to get unstable and bifurcate into curved equilibrium patterns. The nonlinear dynamic model for the simply-supported pipe was built and converted to variable-coefficient partial differential control equations through coordinate transformation. The 4-term Galerkin truncation procedure was then applied and the control equations of motion were transformed to 2nd-order ordinary differential equations to be solved with numerical techniques. The natural frequencies of the simply-supported pipe conveying fluid were calculated, and the result comparison was made between the 2-term and 4-term Galerkin truncation methods to give that the latter had higher accuracy. For specific system parameters, the 2nd-order natural frequency was approximately two times of the 1st-order one within a certain range of flow velocity, and the 2-to-1 internal resonance occurred. Massive computation of the amplitude-frequency responses of the pipe conveying fluid before and after internal resonance was conducted with the Runge-Kutta numerical technique. The results show that, as the flow rate and tuning parameter vary, the softening, hardening and double jumping phenomena will be respectively identified by the amplitude-frequency responses of the pipe.

Effect of Surface Mechanical Attrition Treatment (SMAT) on the Tensile Performance of Fibre Reinforced Aluminium Laminates

WAN Yun, WANG Zhen-qing, ZHOU Li-min, ZHANG Ji-feng

2014, 35(10): 1107-1114. doi: 10.3879/j.issn.1000-0887.2014.10.005

Abstract(948) PDF(766)

Abstract:
The surface mechanical attrition treatment (SMAT), as a technology that the metal sample surface is hit in random directions by a large amount of tiny hard balls in high frequency vibration within a short period of time, was applied to aluminium laminates. Then, the metal’s grain sizes, especially those near the surface, got smaller; and therefor the metal’s yield strength got enhanced. After the SMAT process, the aluminium laminates’ultimate stress and ultimate strain decreased a little, while the yield stress increased obviously. The glass fibre reinforced aluminium laminates were fabricated through heat pressing process with SMATed aluminium and glass fibre epoxy prepreg. From the tensile tests and theoretical calculation, the results show that the SMATed aluminium effectively improves the yield strength of the aluminiumbased composite.

Control of Time-Delay Vehicle Following Systems With Random Factors

SHI Ji-zhong, SONG Qian-kun, ZHANG Ji-ye, XU Xiao-hui

2014, 35(10): 1115-1123. doi: 10.3879/j.issn.1000-0887.2014.10.006

Abstract(1181) PDF(939)

Abstract:
The time delays due to information transmission and vehicle dynamic response falling behind control instruction, and the random factors in vehicle dynamic system modeling were considered to build a time-delay stochastic vehicle following system. The stability and controller design of the system was studied. The stochastic dynamic model of the vehicle was built on the base of Ito stochastic differential equation. The controller for the system was designed with the sliding mode control method. According to the system stability criterion, the convergence region of the system control parameters was obtained. The numerical simulation results show that, in the proposed system, the acceleration, velocity and displacement of the following vehicles respectively approach the corresponding indices of the leading vehicle in a short time; the vehicle spacing error of the system converges pretty fast, returning to 0 within only 10 seconds.

Effects of Bleeding on the Aerodynamic Performance of AxialFlow Compressors

HOU Li-na, DU Gang, CHEN Jiang

2014, 35(10): 1124-1134. doi: 10.3879/j.issn.1000-0887.2014.10.007

Abstract(1157) PDF(713)

Abstract:
Different ways of bleeding have different effects on axial-flow compressors’ performance and flow fields. The numerical simulation of single-stage axial-flow compressors was performed. Several schemes, of bleeding in circumferential slots or bleeding in uniform circular holes circumferentially distributed, were designed to study the effects of different bleeding ways on the aerodynamic performance of axial-flow compressors. The results show that introduction of bleeding improves the compressors’ performance to different extents. The bleeding scheme with circular holes set in the same direction with the flow has the largest surge margin up to 82%; while the circular holes set in the reverse direction of the flow bring the pressure ratio and efficiency of the compressors a major increase.

Effects of Tilted Free-Stream on the Transonic Flow Past a Circular Cylinder

XU Chang-yue, SUN Zhi, WANG Cong-lei

2014, 35(10): 1135-1142. doi: 10.3879/j.issn.1000-0887.2014.10.008

Abstract(1126) PDF(801)

Abstract:
The transonic flow past a tilted cylinder at an angle of 60°was investigated numerically with the large eddy simulation technique. Based on the previous experimental results and computational researches on transonic flow past the nontilted cylinder, the freestream Mach number was chosen as 0.75 and Reynolds number as 2×105. Compared with the transonic flow past a corresponding nontilted cylinder, effects of the tilted freestream on the force and flow characteristics of the tilted cylinder were analyzed. Because of flow control of the tilted freestream, the mean drag coefficient of the tilted cylinder is less than that of the nontilted cylinder with a drag reduction up to 45%, while less suppression of the fluctuating force is obtained. Fluid compressibility in the tilted cylinder flow is weakened due to elimination of shocks and shocklets, however, no change occurs in the whole flow modes. Owing to the tilted freestream, the shear layer shed from the tilted cylinder is more stable, which leads to a higher basepressure distribution. Two main mechanisms are associated with the more stable shear layer behind the tilted cylinder, i.e., the oblique vortexshedding mode and faster kineticenergy damping in the initial stage of shear layer developement.

Zakharov-Type Equations for Resonances of an Infinite Number of Ocean Surface Waves

HUANG Hu

2014, 35(10): 1143-1150. doi: 10.3879/j.issn.1000-0887.2014.10.009

Abstract(1148) PDF(742)

Abstract:
Based on the fundamental wave conservation laws of energy, momentum and action, together with the law of symmetry deciding interactions and the Hamilton structure, 2 main categories of resonance conditions for an infinite number of wave interactions and the corresponding 2 major Zakharov-type equations for an infinite number of wave resonances were derived by means of the complex Hamiltonian canonical equation for ocean surface waves, the canonical transformation and the Poisson bracket conditions. The presented Zakharov-type equations, in connection with the classical conditions for the 3,4 and 5-wave resonances, therefore build an indispensable, advanced and complete theoretical framework for the most fundamental and universal ocean wave turbulence.

Effects of Gas Hydrate Phase Transition on the Pressure Wave Velocity of Water-Oil Emulsion Flow in Pipeline Transportation Systems

QIU Yi-jie, JING Jia-qiang, KONG Xiang-wei, JING Pei-yu

2014, 35(10): 1151-1162. doi: 10.3879/j.issn.1000-0887.2014.10.010

Abstract(1105) PDF(620)

Abstract:
The pressure wave velocity equation for water-oil emulsion flow with gas hydrate in pipeline transportation systems was established in view of gas hydrate phase transition, compressibility of oil phase, influence of angular frequency, virtual mass force and system temperature and pressure. The results show that the gas hydrate has great influences on the pressure wave velocity of the water-oil system during pipeline transportation. In the gas hydrate decomposition region, the emergence of gas increases the compressibility of the system significantly. As a result, the pressure wave velocity falls rapidly. In the gas hydrate formation region, the compressibility of the system decreases, while the pressure wave velocity rises on the contrary. The pressure, temperature, oil-water ratio, density of oil phase, and pipe diameter all have distinct impact on the pressure wave velocity. The pressure wave velocity shows a falling tendency with the decrease of oil-water ratio, pipe diameter and temperature. A rising tendency of the pressure wave velocity occurs with the increase of pressure and density of oil phase. The pressure and temperature have effects on the hydrate decomposition rate, in turn influence the pressure wave velocity.

MOF-MMALE Numerical Simulation of Multi-Material Large Deformation Flow Problems

ZENG Qing-hong, SUN Wen-jun

2014, 35(10): 1163-1176. doi: 10.3879/j.issn.1000-0887.2014.10.011

Abstract(1117) PDF(634)

Abstract:
In the numerical simulation of multi-material large deformation flow problems, the most important thing is tracking the material interfaces accurately while dealing with the large deformation of fluid simultaneously. The multi-material arbitrary Lagrangian Eulerian (MMALE) method coupled with the moment-of-fluid (MOF) interface reconstruction, was named a MOF-MMALE method and applied to multi-material large deformation flow problems. For the MOF-MMALE method, the mesh lines were allowed to cross the material interfaces and the mixed cells were introduced. In the mixed cells, the MOF interface reconstruction was used to determine the position and direction of the material interface. The numerical results of several typical examples, including the 2-material shock tube problem, the triple point problem, the Rayleigh-Taylor instability problem and the shock wave-Helium bubble interaction problem, show high accuracy and good resolution of the MOF-MMALE method, which is validated to be an effective way to simulate multi-material fluid flow problems with large deformation.