#### Table of Content

25 January 2008, Volume 40 Issue 1
Research paper
Numerical simulation of granular flow in Chinese Fish Basin''
Heng Li Qingdong Cai
2008, 40(1):  1-8.  DOI: 10.6052/0459-1879-2008-1-2006-525
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As demonstrated in experiments, highly nonlinear reactions exist in the Chinese Fish Basin'', which finally lead to the surface discontinuity. It is difficult to deal with such problems in numerical simulation. In this paper, Molecular Dynamics Method is employed to simulate three-dimensional granular flow in Chinese Fish Basin. we consider particles in the container from the viewpoint of discretization, without the requirement of continuous media. When the number of particles in the simulation is large enough, the behaviors of granular flow are statistically equivalent to those of the continuous media. We first develop a parallel program based on message passing interface(MPI), which can be used to simulate large scale granular flow. Interesting phenomena in the Chinese Fish Basin'' are demonstrated with our simulation results. As a result of the excitation from outside, energy from the boundary spreads to the interior of the basin in the form of wave, and dissipates quickly. And particles spout upward near the excited points, which is in consistent to the water spouting in the real Fish Basin.
Numerical simulation of unsteady vortical flows by a fast Lagrangian vortex method
Baoshan Zhu
2008, 40(1):  9-18.  DOI: 10.6052/0459-1879-2008-1-2006-048
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In this paper, a fast Lagrangian vortex method is used to numerically simulate the unsteady vortical flows. Discrete vortices are used to model the vorticity generation, accumulation and transport mechanisms for unsteady separated flow fields. The velocity field is computed using a generalized Biot-Savart formula combined with a fast summation algorithm. The discrete vortices are transported by the local velocity field and the viscosity diffusion is considered with a corrected vortex core spreading model. The effectiveness of the present method was examined through comparing the numerical simulation of unsteady separated flows past a cylinder and a NACA0012 airfoil with available experimental results. Specific results are provided for an impulsively started NACA0012 airfoil at a high angle of attack. Detailed unsteady behavior at discrete time steps for the early stages of the flow development as well as the fully developed flow pattern is presented and discussed.
Study on the dissipative effect of approximate riemann solver on hypersonic heatflux simulation
Zuowu Li
2008, 40(1):  19-25.  DOI: 10.6052/0459-1879-2008-1-2006-359
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TVD-type schemes are frequently adopted in hypersonic flow simulation. In construction of such kind schemes, approximate Riemann solvers are fundamental. It is investigated through analysis and numerical examination in the present paper that how the dissipative property of approximate Riemann solver affects the aerodynamic heating in numerical simulation of hypersonic flow. Numerical examples show that approximate Riemann solver severely contaminates the boundary layer resolution. If exact Riemann solver adopted, the accuracy of numerical aerodynamic heating could be greatly improved and the grid cell size might be coarser by a factor of 10.
The interaction between multiple underwater explosion bubbles near free surface
Aman Zhang Xiongliang Yao
2008, 40(1):  26-34.  DOI: 10.6052/0459-1879-2008-1-2007-132
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A boundary integral method is adopted to simulate the bubble motion in the fluid field on the assumption that the fluid field is inviscid, irrotational and incompressible. A corresponding three-dimensional computation program is exploited and the calculated results agree well with the experimental data. The interaction between multiple bubbles near the free surface including in-phase and out-of-phase bubbles is simulated with the program presented here. From calculation it's found out that the bubble period increases along with the decrease in the distance between bubble centers because of the depression effect among multiple bubbles and the effect is more evident especially for out-of-phase bubbles. The depression effect exists between all bubbles no matter whether there is a free surface or not. There are great differences on the dynamic behavior of in-phase bubble coupling and that of out-of-phase bubble coupling due to the depression effect. These phenomena can provide reference for the future research on the power of underwater explosion bubble induced by multiple charges exploding simultaneously or continuously.
Finite element simulation of leaky lamb wave at fluid-solid interfaces excited thermoelastically by pulsed laser
Yan Zhao Zhonghua Shen Jian Lu Xiaowu Ni
2008, 40(1):  35-39.  DOI: 10.6052/0459-1879-2008-1-2006-065
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Based on the variation principle, the corresponding finite element equations for the thermoelstic and heat conduction equations are obtained. The finite element equations for the fluid-solid interface waves propagated along the water-aluminum, air-aluminum interfaces are solved by using the numerical method of integration, and then the transient waveforms excited thermoelastically by a pulsed laser line source are obtained. The results show that the leaky Lamb wave exists at the liquid-solid interface and also exists at air-solid interface; in reverse to the Lamb wave, the S_0 mode of leaky Lamb wave is antisymmetric, and the A_0 is symmetric; due to the difference of the two kinds fluid-solid interfaces, the waveforms and amplitudes of the two leaky Lamb waves are different.
Effects of thermal environments on the thermal shock resistance of ultra-high temperature ceramics
Weiguo Li Daining Fang
2008, 40(1):  40-45.  DOI: 10.6052/0459-1879-2008-1-2007-081
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In the present study, the temperature-dependent thermal shock resistances of Ultra-High Temperature Ceramics (UHTCs) were measured based on the current evaluation theories of thermal shock resistance parameters, since the material parameters of the UHTCs are very sensitive to the changes of temperature. The influence of some important thermal environment parameters，such as the surface heat transfer coefficient, heat transfer condition, thermal stress decay modulus and initial temperature of the thermal shock，on the thermal shock resistance parameters, critical temperature of rupture and critical temperature difference of rupture of the UHTCs were studied considering the effects of temperature on the physical and mechanical properties of the UHTCs within the range of thermal shock temperature. The results show that thermal shock behaviour of the UHTCs is strongly affected by the thermal environments.
Multiple three-dimensional cracks in fully coupled electromagnetothermoelastic multiphase composites
Bojing Zhu Taiyan Qin
2008, 40(1):  46-58.  DOI: 10.6052/0459-1879-2008-1-2007-273
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This work presents hypersingular integral equation method to analyze the multiple three-dimensional cracks problem in fully coupled electromagnetothermoelastic multiphase composites under extended electro-magneto-thermo-elastic coupled loading through intricate theoretical analysis and numerical simulations. First, the problem is reduced to solving a set of hypersingular integral equations. Analytical solutions for the extended singular stresses, the extended stress intensity factors, the extended strain energy factors and the extended energy release rate near the cracks front are obtained, respectively. Then, the numerical method for the hypersingular integral equations subjected to extended coupled loads is proposed. Finally, numerical solutions of the extended stress intensity factors and the extended strain energy factors for two interacting three-dimensional cracks are given, and the effect of cracks orientation, interaction and shielding is discussed.
Accuracy controllable time-domain difference approach to calculate foundation resisting force
Xiuli Du Jianfeng Zhao Qiang Han
2008, 40(1):  59-66.  DOI: 10.6052/0459-1879-2008-1-2006-162
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Interaction forces between foundation and structure is one of key problems in nonlinear dynamic response analysis of structures accounting for soil-structure dynamic interaction. Currently there are two kinds of method dealing with it: one is the direct integrity analysis approach, the other is time-domain substructure approach. Because of far less computational cost comparison to the former, time-domain substructure approach is very important in engineering field. The fact that foundation impedance complexly vary with frequency makes the calculation of time-domain foundation resisting force time-consuming. To simplify the calculation of time-domain foundation resisting force, many lumped-parameter models have been proposed. Lumped-parameter model reflects the singular component of foundation impedance which is not square integrable and correspond to simultaneous effect. Nevertheless the regular component can't be reflected accurately, which correspond to time-delay effect and be square integrable. Time-domain recursive model proposed by Safak (2006) used for representing time-domain foundation resisting force can simulate the regular component of foundation impedance. But the whole essential of foundation impedance can not be reflected in this model because the corresponding filter function has intrinsically limitation at Nyquist frequency. Thus, time-domain foundation resisting force can not be simulated accurately. Combining lumped-parameter model and time-domain difference recursive filter model, a time-domain difference approach of accuracy controllable foundation resisting force is proposed. Numerical examples results demonstrate that the proposed procedure can perfectly fit the frequency dependent impedance in interested frequency band.
Effect of track support failure on dynamic response of tangent track
Xinbiao Xiao Xuesong Jin Zefeng Wen
2008, 40(1):  67-78.  DOI: 10.6052/0459-1879-2008-1-2006-236
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In order to investigate the effect of track support failure on dynamic response of tangent track, a vehicle-track coupling dynamic model is established, in which the rails are assumed to be Timoshenko beams resting on the discrete sleepers. The failure situation of track components under the tangent track is simulated by the abrupt changes of track stiffness along the track. The effect of the discrete sleeper supports on the coupling dynamics of the vehicle and track is taken into consideration by the excitation model of moving sleeper supported. As to the interaction of wheel and rail system, the creepage formulas of wheel/rail rolling contact are deduced, in which the lateral, vertical and torsional motions of rail are taken into account. The normal forces of wheel/rail are calculated by Hertzian contact theory and the creep forces of wheel/rail in rolling contact are decided by the nonlinear creep theory of Shen et al. The motion equations of the vehicle/track coupling system are solved with the new explicit integration method. Effect of zero, two, four and six track supports in failure situation on tangent track dynamic response is analyzed and evaluated. The numerical results indicate that track support failure greatly affects dynamic response of tangent track. With the increasing of failure number, the wheel/rail normal forces, displacement and acceleration of track components increase quickly, which will deteriorate the track.
Model and application of uniformity expansion in randomized structure of intravascular stent
Jie Yang Nan Huang Quanxing Du
2008, 40(1):  79-85.  DOI: 10.6052/0459-1879-2008-1-2006-646
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The expansion of intravascular stent may be considered as an extension in instable serial structure from the viewpoint of mechanics. The randomization of the width and thickness of a stent will hare great influence on the uniformity expansion in the instable serial structure. In this paper, a mathematical model to describe that problem is established on the basis of randomized unstable serial structure. The concept, method and probability calculation formula of uniformity index are proposed. Regarding the serial structure made up of two expanded units, a detailed study is carried out on the influence of the random variation of beam thickness on expansion uniformity indexes. We obtain the uniformity index probability's relationships with beam thickness random variation, load variation and hardening coefficient variation. The research shows that material harding coefficient has great effects on uniformity index when the total expansion displacement remains constant. The serial expansion theory of random unstable structure provides an important guide to the design of new-type intravascular stent.
Time-varying optimal control via canonical transformation of hamiltonian system
Zhigang Wu Shujun Tan
2008, 40(1):  86-97.  DOI: 10.6052/0459-1879-2008-1-2007-235
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This paper presents a unified canonical transformation and generating function approach, including associated numerical algorithms, for linear time-varying optimal control problems with various terminal constraints. Generating functions are employed to find the optimal control law by solving Hamiltonian two-point-boundary-value problems. The time-varying optimal control laws constructed by the second type generating function do not have infinite feedback gain at terminal time, which is different from other existing solutions. Motivated by practical design of time-varying optimal control systems, a structure-preserving matrix recursive algorithm is proposed to solve coupled time-varying matrix differential equations of the generating function; derivation of the recursive algorithm is based on symplectic formulation of canonical transformation. To preserve symplectic structure of matrices in the recursive computation, state transition matrices of the Hamiltonian system are calculated by Magnus series. In fact, the canonical transformation and generating function method leads to a geometric perspective to the design and computation of optimal control systems. %control systems synthesis and computation.
Mechanism analysis of delayed nonlinear vibration absorber
Yanying Zhao Jian Xu
2008, 40(1):  98-106.  DOI: 10.6052/0459-1879-2008-1-2007-078
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In a two-degree-of-freedom system with delayed nonlinear dynamical vibration absorber, the method of multiple scales is employed to study its performance of vibration suppression. The amplitude-delay response curves of the primary system are obtained. The results show that for the delayed nonlinear dynamical vibration absorber, the gain and the delay may be tuned to control the vibration of the primary system. With the delay varying for a fixed gain, it is easy to see that the vibration can be suppressed at some values of the delay under the conditions of the system is stable. The maximum vibration suppression point'' may be predicted at which the amplitude of the primary system is the minimum for a fixed gain. For different values of the gain, the amplitudes of the primary system are different at their maximum vibration suppression point''. Correspondingly, the optimum values of the gain and the delay may be obtained to suppress the amplitude of the primary system to a minimum. The results of this paper show that the vibration of the primary system can be suppressed about 90{\%} when the optimum values of the gain and the delay are obtained by comparing with the nonlinear dynamical vibration absorber. All the analytical predictions of this paper are in good agreement with the numerical simulation.
Numerical modeling of human ear for sound transmission
Yingxi Liu Sheng Li Xiuzhen Sun
2008, 40(1):  107-113.  DOI: 10.6052/0459-1879-2008-1-2007-051
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A complete finite element model of the human ear can provide better understanding of sound transmission. In this paper, a three-dimensional finite element model of the human ear is established, including the external ear canal, tympanic membrane, ossicular bones, middle ear suspensory ligaments/muscles, and inner ear fluid. This model is constructed based on a complete set of computerized tomography section images of a healthy volunteer (right ear) to describe the complicated structures and boundary conditions. The validity of this model is confirmed by comparing the model-predicted motion of the tympanic membrane and stapes footplate with published experimental data. The acoustic-structural coupled finite element analysis among the ear canal, middle ear ossicles and inner ear fluid is conducted and employed to predict the effects of ear canal, incudostapeblial joint and cochlear fluid on sound transmission mechanics. The results revealed that the final model is reasonable in predicting the ear acoustic mechanical properties.
Brief Report
Direct numerical simulation of a compressible transitional mixing layer with combustion chemical reactions
Wenbo Miao Xiaoli Cheng Qiang Wang
2008, 40(1):  114-120.  DOI: 10.6052/0459-1879-2008-1-2007-296
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A fifth-order upwind/sixth-order symmetric compact hybrid difference scheme coupled with a third-order explicit Runge-Kutta time-marching method is used as a direct numerical simulation algorithm to investigate a three-dimensional temporally-developing compressible plane free shear mixing layer with H$_{2}$/O$_{2}$ non-premixed combustion. The reacting mixing layer with product formation and energy release is perturbed by a pair of conjugate oblique waves, and hence experiences an instable transitional evolution. At the beginning of transition, some well-known large scale coherent structures, such as ${\it\Lambda}$ vortex and horseshoe vortex, are found, and a three-dimensional paring phenomenon of two horseshoe vortices following flow instabilities is also revealed. Furthermore, these large scale structures are approximately symmetric. At the last stage of the development of this flow, large scale structures break down continuously, and small scale structures gradually get dominant. The reacting mixing layer finally behaves very similar to turbulence and shows clear asymmetry. On the analogy of the stability theory for incompressible boundary layer, the large scale structures obtained here are due to a subharmonic secondary instability mechanism, which is well known as Herbert type secondary instability.
Electro-magnetic control of hydrofoil wake
Yaohui Chen Baochun Fan Benmou Zhou Zhihua Chen Hui Zhang Hongzhi Li
2008, 40(1):  121-127.  DOI: 10.6052/0459-1879-2008-1-2006-015
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An actuator, consisting of a specific array of alternating stripwise electrodes and permanent magnets, will generate a wall-parallel Lorentz force as submerged in a weakly conducting fluid, which influences the flow in the boundary layer. The experiments have been conducted in a rotating annular tank filled with a copper sulphate (CuSO$_4$) electrolyte, to investigate the flow around a hydrofoil and its electromagnetic control. To reveal the transient behavior of controlled flow from the initial to the final steady state, the flow fields are visualized by potassium permanganate (KMnO$_4$) used as a marker and record by a camera. To verify the influence of flow control on the lift and the drag of a hydrofoil, force measurements have been carried out by strain gages attached to a fixed beam to which the hydrofoil is suspended. It has been shown from the experimental results that, for the absence of the Lorentz force, there exist two kinds of vortex, i.e. shedding on the leading edge and the trailing edge respectively, which affect each other and finally leave the leeward surface of the hydrofoil periodically to form a wake. The influences of the Lorentz force on the flow around the hydrofoil are just something like the variations of the attack angle. The Lorentz force in streamwise direction can suppress the flow separation and the wake, as happened in the cases with a small or zero attack angles. In contradiction, for the reversed Lorentz force, the vortex street on the leeward surface of hydrofoil is introduced, as happened in the cases with a big attack angle.
Convergence control of probabilistic structural design optimization based on performance measure approach
Ping Yi Dixiong Yang
2008, 40(1):  128-134.  DOI: 10.6052/0459-1879-2008-1-2007-195
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The evaluation of probabilistic constraints in Probabilistic Structural Design Optimization (PSDO) can be carried out using the recently proposed performance measure approach (PMA). The advanced mean-value (AMV) method is well suitable for PMA due to its simplicity and efficiency. However, when the AMV iterative scheme is applied to search for the minimum performance target point for some nonlinear performance functions, the iterative sequences could fall into the periodic oscillation and even chaos. Then both PMA Two-level and PMA with SAP (Sequential Approximate Programming), which are based on this evaluation of probabilistic constraints, could yield convergent failure. In the present paper, the convergence control of AMV iterative procedure is first implemented by using the stability transformation method of chaos feedback control. The unstable fixed points embedded in the periodic and chaotic orbit are stabilized and the expected stable convergent solutions are obtained. Once the evaluation of probabilistic constraints can be carried out successfully, the design optimization is performed by PMA Two-level or PMA with SAP. The numerical results demonstrate that the convergence control using stability transformation method is effective and PMA with SAP is more efficient.
Time-optimal deployment of a tethered subsatellite based on differential inclusion
Hao Wen Dongping Jin Haiyan Hu
2008, 40(1):  135-140.  DOI: 10.6052/0459-1879-2008-1-2007-063
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This paper presents the nonlinear time-optimal control for the three-dimensional deployment process of a tethered subsatellite model, which also takes tether elasticity and the mission-related state-control constraints into consideration. Instead of the commonly used state-space model, a second-order differential inclusion formulation is exploited in this work to achieve a significant reduction of the number of system variables. The optimal control is solved by discretizing the optimal control problem based on a direct algorithm, and numerically solving the resulting large-scale optimization problem via an NLP (nonlinear programming) solver. The case studies in the paper well demonstrate the performance of the proposed strategy.