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2011 Vol. 43, No. 5

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Investigations on spiked body flying with angle of attack and mechanisms of action by bayonet shaped plates
Guilai Han Z.-L. Jiang
Three-dimensional Navier-Stokes equation was numerically solved to investigate the flow structure and characteristics of spiked body flying at M_{\infty }=6.0 with 10^\circ angle of attack. With reasons for the deterioration of aerodynamic force pointed out, bayonet shaped plates were set to improve the flow field and aerodynamic characteristics. By comparing the actions of plates with two different configurations, the mechanisms for the bayonet structure can be stated as formation of circumfluence and shear layer at windward side due to the plates splitting the flow field and depressing flow in toroidal direction, which will drive conical shock to move away from axial line, lower the strength of interaction between flow structures around the blunt body and weaken the perturbation at leeward side.
2011, 43(5): 795-802. doi: 10.6052/0459-1879-2011-5-lxxb2010-816
Osculating inward turning cone (OIC) wave rider-design methods and performace analysis
Xuzhao He Hongli Ni
Osculating outer cone waverider design are mainly focused in the present osculating waverider design methods. Osculating inwardturning cone (OIC) methods are developed in this paper. Internalconical flow A (ICFA) is used as stream tracing flow field in OIC waverider.Inlet capture curve (ICC) and front capture tube (FCT) are defined first andthe OIC waverider is then generated by using Osculating aixymmtric methodand streamline tracing technique. The designed OIC waverider's flow fieldsand aerodynamic characteristics are numerically simulated under designconditions and the numerical simulation results are compared withtheoretical results. Both theoretical and numerical results are consistentwith each other well.
2011, 43(5): 803-808. doi: 10.6052/0459-1879-2011-5-lxxb2010-526
Lattice boltzmann simulation of flow over a transversely oscillating circular cylinder
Shuai Gong Zhaoli Guo
The lattice Boltzmann method (LBM) is used to simulate the incompressible flow past a transversely oscillating circular cylinder. Simulations are conducted at Reynolds number $Re=185$. The results show that as the oscillation frequency of the cylinder is increased relative to the natural vortex shedding frequency of the corresponding stationary cylinder, the initially formed concentration of vorticity moves closer to the cylinder until a limiting position reaches. At this point, the vorticity concentration abruptly switches to the opposite side of the cylinder. When the oscillation frequency is near the natural vortex shedding frequency of a corresponding stationary cylinder, frequency synchronization occurs. When the oscillation frequency is away from the natural vortex shedding frequency, frequency synchronization also disappears. In several subharmonic and superharmonic excitation situations, vortex shedding frequency in the near wake region also equals to the natural one of the corresponding stationary cylinder.
2011, 43(5): 809-818. doi: 10.6052/0459-1879-2011-5-lxxb2010-608
On the numerical study and characteristic analysis of bubbly flow created by ventilated cavity
Min Xiang Zibo Zhang Jiyuan Tu Weihua Zhang
Considering the significant influence that the bubblyflow created at the tail of the ventilated cavity makes on the vehiclehydrodynamics and the cavity control mechanism, a Eulerian--Euleriantwo-fluid model was proposed for simulation on the bubbly wakes created byventilated cavity. The population balance approach integrated withMultiple-Size-Group (MUSIG) model was adopted to predict the bubble sizedistribution. Furthermore, a new model for the turbulence dispersioncoefficient was introduced to take into account the effect of void fraction.Based on the simulation model, the characteristics of the multiphase flowfield including a vortex mixing area with high void fraction weresuccessfully captured. The bubbles were found to be broken up into smallones right after entrained into the mixing region due to the high turbulencedissipation rate. The void fraction and velocity distribution in the wakewere obtained to compare with experimental data. The water velocity in thewake was found to be in accordance with the distribution law in the wakecreated by single phase flow passing bluff body. The model was validated inpredicting the bubbly flow created by ventilated cavity for good agreementwith two experimental cases.
2011, 43(5): 819-825. doi: 10.6052/0459-1879-2011-5-lxxb2010-272
An efficient method on aerodynamic damping coefficient calculation for turbomachinery
Chen-An Zhang Weiwei Zhang Zhengyin Ye Feng Liu
It is always difficult to perform aeroelastic analysis onturbomachinery efficiently and precisely due to the complexity of the flowfield and structures. The authors develop an unsteady aerodynamicReduced-Order-Model (ROM) which can be used on small amplitude vibratingblades of turbomachinery. Based on this ROM and classic energy method, anefficient method on aerodynamic damping coefficient calculation forturbomachinery is introduced. With this method, only one unsteady CFDcomputation is needed to calculate the aerodynamic damping coefficients atall Inter Blade Phase Angles (IBPA) under one specific modal and frequency.The aeroelastic characteristics of STCF4 and NASA Rotor 67 are analyzed byusing this ROM with classic energy method. The numerical results indicatethat the aerodynamic damping coefficients attained by ROM and unsteady RANSmethod agree well with each other in the condition of small amplitude ofvibration. The efficiency is improved by almost 10 times than multi-passagesRANS method. In addition, this ROM can be used in aeroelastic analysis withmistuning effects.
2011, 43(5): 826-833. doi: 10.6052/0459-1879-2011-5-lxxb2010-222
Fully nonlinear numerical simulation for wave-current propagation over a submerged bar
Lifen Chen Dezhi Ning Bin Teng Weihua Song
A fully nonlinear numerical flume model is developedbased on the time-domain higher-order boundary element method. The fullynonlinear free surface boundaries are satisfied on the instantaneous freesurface in this model. The mixed Eulerian-Lagrangian scheme is adopted totrack the transient free surface with the fourth-order Runge-Kutta methodfor refreshing wave profile and velocity potential at the next time step. Animage Green function is utilized to increase the speed of computation. Themeshes are regidded at each time step to avoid numerical instabilitiescaused by mesh motions. The experimental study on evolution of waves over asubmerged bar in uniform current is carried out in a wave flume. And thenumerical solutions are compared well with experimental data. The effects ofcurrents and the submerged bar on the higher-order harmonic waves are furtherstudied.
2011, 43(5): 834-843. doi: 10.6052/0459-1879-2011-5-lxxb2010-792
Cellular automaton model considering tollbooths with lane expansion
Yuxia Liu Rongjun Cheng Xiufang Feng Hongxia Ge
Based on the variable security gap sensitive drivingmodel, a cellular automaton model describing the tollbooth on the road isproposed. Compared with NS tollbooth model, when stochastic probability ofbraking is large (p=0.5), the present model not only makes the capacity ofroad to be fully restored, but also makes it improve to a certain extent.When the value of the length of lane expansion L_{\rm B}is no less than 7, the capacity of road recovers well; while thecapacity of road will decrease.
2011, 43(5): 844-849. doi: 10.6052/0459-1879-2011-5-lxxb2010-735
An estimation approach of wave speed in real traffic flow
Wei Shi Ximin Liu Shoufeng Lu
A formula for determining the propagation speed oftraffic waves in real traffic flows is derived based on the physicalmechanism of car-following, which can be used to calculate the starting wavespeed at the urban signalized intersections as the red light turns to greenone and the incident wave speed on expressways. It is proved that thepresented formula is reasonable and applicable through the comparisonbetween the calculated results and in situ measured data. In addition, thecharacters of traffic wave speed, especially expressway incident wave speed,are discussed and consistent with daily knowledge in realistic traffic.
2011, 43(5): 850-855. doi: 10.6052/0459-1879-2011-5-lxxb2010-709
Study of estimating inner-scale of temperature field
Xiaoqing Wu
The three velocity components and air temperature weremeasured using a triaxial ultrasonic anemometer in Hefei region of China.The mean dissipation rates of turbulent kinetic energy \varepsilon and1/2 temperature variance \varepsilon _\theta have been estimated byKolmogorov's `four-fifths' law and Yaglom's `four-thirds' law, respectively.It is pointed that the traditional method is not suitable for estimatinginner scale of temperature field. A new relation between the inner scale oftemperature field and 1/2 temperature variance \varepsilon _\theta ispresented. The results of estimating inner scale by the new proposed methodperfectly show that strong turbulence has small inner scales and weakturbulence larger inner scales.
2011, 43(5): 856-960. doi: 10.6052/0459-1879-2011-5-lxxb2010-694
Finite element simulations of the high velocity expansion and fragmentation of ductile metallic rings
Lei Chen Fenghua Zhou Tiegang Tang
In this paper, we numerically simulated the freeexpansion and fragmentation processes of an OFHC ring under an initialvelocity. The conventional Johnson-Cook thermo-viscoplastic constitutivemodel was used to describe the dynamic plastic behavior of the material. TheJohnson-Cook failure model incorporating a cohesive fracture criterion wasused to model the separation progress of the material. ABAQUS/Explicit codewith element erosion was used for the numerical simulations. Multiplesimulations were conducted with a same initial velocity on these meshes,creating a group of fragment samples. The average fragment sizes of eachsample group were obtained. It was found that the Grady-Kipp model based onthe momentum diffusion mechanism gives reasonably close predictions of thefragment sizes; The FEM simulation results show apparent unloading waves(the Mott wave) propagations, confirming that the momentum diffusion didcontrol the 1D ductile fragmentation process.
2011, 43(5): 861-870. doi: 10.6052/0459-1879-2011-5-lxxb2010-675
Linear transformation between the bending solutions of functionally graded and homogenous circular plats
Shirong Li Jinghua Zhang Hua Xu
Based on the first-order shear deformation theory (FSDT),linear transformation relationship between bending solutions of functionallygraded material (FGM) and homogenous circular plates was studied. Firstly,through theoretically analyzing and comparing the displacement-typegoverning equations for axially symmetrically bending of FGM and homogenouscircular plates based on the first-order shear deformation theory, linearlydependent relationship between the rotational angles of FGM circular plateand those of homogenous one was found. By giving the material properties ofFGM circular plates changing as continuous functions in the thicknessdirection, the corresponding transition factor between the solutions of thetwo kind plates were derived in analytical forms. Furthermore, a linearrelationship between the deflections of FGM circular plate based on FSDT andthose of homogenous one based on the classical plate theory were derived. Asa result, solutions for static bending based on the first-order sheardeformation plate theory of a non-homogenous circular plate can be reducedto that based on classical plate theory of a homogenous one and thecalculation of the transformation factors. This approach provides a simpleand facile procedure for solutions of the non-homogenous moderately thickFGM circular plates, which can be very easily and conveniently used inengineering. By using the above mentioned approach, analytical bendingsolutions of FGM circular plates with simply supported as well as clampedboundary conditions under uniformly distributed lateral force werepresented, which show a very good agreement with the results given by Reddy.
2011, 43(5): 871-877. doi: 10.6052/0459-1879-2011-5-lxxb2010-810
Topology optimization of pressure-dependent material structures based on D-P criterion
Yangjun Luo
Many widely used materials, such as concrete, rocks,ceramics and polymers, have the feature of increasing shear strength as aresult of hydrostatic pressure increases. Structures made of thesepressure-dependent materials would typically hold the characteristic ofbetter stress limit in tension than in compression. In this case, the vonMises criterion is incompetent while the D-P criterion describedin terms of stress invariants is available as one of the simplest plasticityyield models. To take into account the asymmetrical compression and tensionbehaviors in the conceptual design of continuum structures, a practicabletopology optimization strategy for pressure-dependent materials based onD-P yield criterion is presented in this paper. By using theelement artificial relative densities as design variables, the optimizationproblem is formulated as to minimize the total material volume underD-P yield constraints on each element. In this optimizationmodel, the SIMP interpolation for element stiffness and the power-lawinterpolation for the local stress of porous microstructures are adopted. Inorder to circumvent the stress singularity phenomenon, the \varepsilon-relaxation strategy is applied for relaxing the local yield constraintsinvolved in the low-density elements. In this context, the sensitivity ofthe element constraints with respect to the design variables is efficientlyderived by the adjoint variable method. Then, the optimal design is obtainedby employing the gradient-based optimization algorithm. Finally, threenumerical examples with different strength limits in compression and tensionhave been solved to illustrate the validity of the proposed optimizationmodel as well as the efficiency of the numerical techniques. It is observedthat the optimal material distribution designed by the present method mayhave a significant difference compared with one designed by the conventionalvon Mises stress constraint approach. The obtained optimization solutionsare reasonable since they can make the best use of their strength inwithstanding the compression. The meaning of the proposed method forpressure-dependent material structures is thus demonstrated.
2011, 43(5): 878-885. doi: 10.6052/0459-1879-2011-5-lxxb2011-003
Multi-variable method for flexible multi-body systems with contact/impact
Shilei Han J.-Z. Hong
Multi-variable method is proposed to dealwith flexible multi-body systems with contact/impact. With this method, thefloating reference frame technique is combined with the nonlinear finiteelement technique to raise the solving efficiency of the whole system andthe computation accuracy in the local contact/impact region. The motion ofthe non-contact/impact region is described with the floating reference frametechnique and the modal reduction approach is used to raise thesolving efficiency. The nonlinear finite element technique is employed fordescribing the nonlinear and plastic deformation in the local contact/impactregion. Some numerical examples are presented with the proposed method. Inaddition, experimental investigations with a Laser-Doppler vibrometer arepresented. The numerical results agree well with the experimental ones.
2011, 43(5): 886-893. doi: 10.6052/0459-1879-2011-5-lxxb2010-657
Using the delayed feedback to control the vibration of the auto-parametric dynamical system
Yanying Zhao Jian Xu
The delayed feedback control is applied to suppress the vibration of the primary system in an auto-parametric dynamical system. The multiple scale method is employed to obtain the range of the saturation control when the system is excited by the harmonic vibration. The delayed feedback control is used to control the vibration of the primary system when the system is in saturation control. The effects of the gain and delay on the vibration suppression of the primary system are analyzed. The results show that the vibration of the primary system can be suppressed at some values of the gain and delay. As the delay varies for a fixed gain, it is seen that the vibration of the primary system can be suppressed at some values of the delay. There is a “maximum vibration suppression point” at these values of delay, where the amplitude of the primary system can be suppressed to a minumum value. As the gain increases, the performance of the vibration suppression is improved at the “maximum vibration suppression point”. It implies that if the suitable delay and gain are achieved the vibration of the primary system almost could be suppressed to zero.
2011, 43(5): 894-904. doi: 10.6052/0459-1879-2011-5-lxxb2010-652
Random vibration frequency response analysis of nonlinear systems based on volterra series
Changming Cheng Zhike Peng Guang Meng
Volterra series is a powerful mathematical tool fornonlinear system analysis, which is essentially an extension of theconvolution operation from linear systems to nonlinear systems. In thisstudy, based on the Volterra series, an analytical expression is derived tocalculate the power spectrum density (PSD) for the output of nonlinearsystems subjected to Gaussian white noise excitation. This expressionreveals that the PSD of the nonlinear system can be expressed as polynomialfunction of the input intensity. This expression provides an efficient wayto study the effect of the input intensity of a Gaussian white noiseexcitation on the PSD of nonlinear system output.
2011, 43(5): 905-913. doi: 10.6052/0459-1879-2011-5-lxxb2010-741
The construction of homoclinic and heteroclinic orbit in two-dimentsional nonlinear systems based on the quasi-Pade approximation
Qichang Zhang Jingjing Feng Wei Wang
The conventional quasi-Pad\'{e} approximants aredeveloped to study the homoclinic and heteroclinic solutions in nonlineardynamic system, and in the solution process in which the disturbanceparameters of system don't be restricted in advance. Firstly, the systemwith cubic nonlinear oscillators is considered. The value ranges of itsparameters can be determined when the homoclinic and heteroclinic orbits areoccurred. Respectively suppose the general formulations homoclinic andheteroclinic solutions which reflect the parameters of the systemdirectly.Meanwhile, the homoclinic and heteroclinic solutions ofthe strongly nonlinear autonomous system are derived successfully. Secondly,the periodic solutions of the non-autonomous system are derived under thedirect consideration of the disturbance parameters, which are satisfied theconditions of the homoclinic and heteroclinic solutions. Finally, twoheteroclinic solutions functions are constructed in order to reduce thecomputational complexity. The validity and accuracy of the quasi-Pad\'{e}approximants are proved by comparing with the numerical computation.
2011, 43(5): 914-921. doi: 10.6052/0459-1879-2011-5-lxxb2011-074
Nonlinear free vibration of stiffened plate with four edges clamped
Niujing Ma Ronghui Wang
One approach is presented to study the nonlinear freevibration characteristic of stiffened plates. The stiffened plate is dividedinto plate and stiffeners. The plate is considered to be geometricallynonlinear, and the stiffeners are taken as Euler beams. Assuming thedisplacement of the stiffened plate, Lagrange equation and modalsuperposition method are used to derive the dynamic equilibrium equations ofthe stiffened plate according to energy of the system. The single-moderesults are obtained through Elliptic function and the perturbation method,and the multimode results are obtained through incremental-iterativemethods. At last, a stiffened plate with four immovable clamped edges isstudied through both the present approach and FE software ANSYS. Theconvergence of solution is analyzed, and the relationship between nonlinearnatural frequency and its amplitude is discussed when the number ofstiffeners in the two direction is different. Some nonlinear vibrationcharacteristics of stiffened plate are obtained, which can providereferences for engineering design.
2011, 43(5): 922-930. doi: 10.6052/0459-1879-2011-5-lxxb2010-852
Numerical method of multibody dynamics based on \theta _1 method
Xiuteng Ma Yanbo Zhai Shuqiang Luo
In the numerical integration of ordinary differentialequations (ODEs) in structural dynamics community, \theta _1 method hascharacteristics of controlled numerical dissipation and second-orderaccuracy for systems with or without physical damping. Based on thesecharacteristics, \theta _1 method is extended to the numerical integrationof motion equations in multibody system dynamics. The solved motionequations are index-3 differential-algebraic equations (DAEs) andindex-2 over-determined DAEs (ODAEs). Numerical experiments validate the\theta_1 method, experiments also show the relationship of numericaldissipation with parameter \theta_1.As for theintegration of index-3 DAEs by \theta _1 method, it has violation ofvelocity constraint, while for index-2 ODAEs, there are no violation ofposition and velocity constraint in the view of computer precision. Inaddition, experiments illustrate that, for non-conservative system motionequations in the form of index-3 DAEs and index-2 ODAEs, \theta _1 methodhas second-order accuracy. In the end, \theta _1 methods for motionequations are compared with other direct-time integrations from the CPU timepoint of view.
2011, 43(5): 931-938. doi: 10.6052/0459-1879-2011-5-lxxb2010-730
Development and validation of fe models for long bones of lower limb in vehicle-to-pedestrian crashes
Guanjun Zhang Libo Cao Fengjiao Guan Guangyong Sun Yang King Hay
FE models are used widely in the pedestrian safety, whichhas become a very important topic. Based on THUMS model, FE models of femur,tibia and fibula were improved on materials, element properties, and so on.Based on the analysis of loading characteristics of lower limb long bones onpedestrian in vehicle-to-pedestrian crashes, the FE models of long boneswere fully validated against experimental results as follows: (1)quasi-static 3-point bending tests of femur, tibia, and fibula with A-P andL-M loading directions, (2) dynamic 3-point bending tests of femur, tibia,and fibula with different impact locations of proximal 1/3, middlediaphysis, and distal 1/3. The simulation results demonstrate that theimproved models have high biofidelity to accurately simulate fractures andcollision responses. They can be used for further development of thepedestrian lower limb. Simultaneously, they also provide a useful researchtechnique to investigate injury mechanisms and assess the protectiveperformance of the vehicle-front structures.
2011, 43(5): 939-947. doi: 10.6052/0459-1879-2011-5-lxxb2010-342
SH waves in a piezoelectric/piezomagnetic layered half-space with a weak interface
Xing Zhao Yongmao Zhao Jin-Xi Liu
This paper investigates the dispersioncharacteristics of shear horizontal (SH) waves propagating in apiezoelectric/piezomagnetic layered half-space with a weak interface. Theso-called ``spring'' model is used to describe the interfacial property. Thesurface of the piezoelectric layer is electrically closed or open. Thecloses-form dispersion equation is derived, and the numerical examples areprovided to show the influences of the interfacial property and theelectrical boundary conditions on the dispersive characteristics of SHwaves. The results show that: (1) weak bonding lowers the propagationvelocity, and it makes the dispersion curve of the first mode for theelectrically closed condition have a minimum less than the velocity of theB-G surface wave; (2) when the surface of the piezoelectric layer iselectrically open, the phase velocities of the first mode are always morethan the bulk shear wave speed of the piezoelectric medium.
2011, 43(5): 948-952. doi: 10.6052/0459-1879-2011-5-lxxb2010-718
Fatigue model of steel honeycomb sandwich beams at high temperature
Guangping Zou Jie Lu Yang Cao Baojun Liu
In this work fatigue behaviors of steel honeycombsandwich beams at high temperature are investigated through three-pointbending tests. The results show that fatigue properties are significantlyinfluenced by different core configurations. Specimens with W-direction arefit for fatigue loads. A fatigue modulus reduction approach is adopted whichis based on the interpolation by the empirical functions of experimentalresults, whose coefficients depends on the material properties and loadingconditions. This approach permits to predict the fatigue life of the steelsandwich structures while avoiding a large number of experiments. Theresults show a second-order polynomial function is fit for describingresidual modulus degradation rules of L-direction specimens, whileexponential function for W-direction specimens. Two non-linear cumulativedamage models, derived from the chosen stiffness degradation equation, areexamined in context with the linear Miner damage rule and compared withexperimental results. The developed models give a reasonable explanation forthe damage of steel honeycomb sandwich beam under high temperature.
2011, 43(5): 953-957. doi: 10.6052/0459-1879-2011-5-lxxb2010-751
Study of plastic flow unified constitutive relation for steel DH-36
Weihua Meng Weiguo Guo Jing Su Xiaoqiong Zhang
Through systematically analysing the dynamicstrain aging behaviour and the testing data of structural steel DH-36, theconstitutive model of the third-type dynamic strain aging has beendeveloped. Then based on thermal-activated physical concept constitutivemodel and the combinatorial principle of plastic flow stress, a unifiedconstitutive model is finally obtained with the description for thethird-type dynamic strain aging. This model not only can describe thethird-type dynamic strain aging phenomenon, but also the mechanicalbehaviour of DH-36 steel in a wide range of temperatures(77~1000K) and strain rates(0.001~3000s^{-1}). There is a good agreementbetween theoretical predictions and experimental results.
2011, 43(5): 958-962. doi: 10.6052/0459-1879-2011-5-lxxb2010-676
Restrained torsion theory of open thin-walled beams and its application
Z.-Q. Wang Jincheng Zhao
Based on Vlasov's thin-walled beam theory, a first-ordertorsion theory of restrained torsion of open thin-walled beam is developedin consideration with the effects of shear deformation. It is assumed thatthe total rotation of a cross section is divided into a free warpingrotation and a restrained shear rotation. In the restrained torsion, St.Venant torque is only related to the free warping rotation and theexpression of St. Venant torque is derived by using a semi-inverse method.The torsion shear coefficient is derived by using the energy method. Thegoverning equation of the restrained torsion theory is derived by using thededuced formulae. In order to solve the governing equation efficiently, thecorresponding initial method is presented, and the influence function isobtained. When the St. Venant constant is negligible, an approximateanalytical approach is obtained, and there exists an analogy between it andTimoshenko beam theory. To validate the new approach, an example isillustrated, and the results obtained from the current theory are comparedwith those of the existing theory, which demonstrate the efficiency of thecurrent theory.
2011, 43(5): 963-967. doi: 10.6052/0459-1879-2011-5-lxxb2011-063
An improved kane's method for multibody dynamics
Quan Hu Jia Yinghong Shijie Xu
This paper presents an improved Kane's method forautomatically generating the equations of motion of arbitrary multibodysystems. The notions of partial velocity matrix and partial angular velocitymatrix are introduced. Each body's contribution to the system's generalizedinertial force is expressed in a similar manner, which makes it amenable tocomputer solutions. All the kinematic quantities' recursive relations aredeveloped to improve the modeling efficiency. The motion constraints arehandled by the new form of Kane's equation. The final mathematical model isof the same dimensions with the generalized speeds and involves no Lagrangemultipliers; therefore, it's useful for control system design. Thesimulation of a space platform with two manipulators is compared between theproposed method and recursive algorithm. The results validate thealgorithm's accuracy.
2011, 43(5): 968-972. doi: 10.6052/0459-1879-2011-5-lxxb2010-856