力学学报

EXPERIMENTAL STUDY OF DYNAMIC AERODYNAMIC SWEPT EFFECT ON YAW OSCILLATING AIRFOIL

Li Guoqiang, Chen Li, Huang Xia

The design of large wind turbines has put forward higher requirements for obtaining more comprehensive and accurate dynamic loads of airfoil. It is of great significance to study the influence of yaw oscillation on the dynamic aerodynamic characteristics of airfoil. With the help of "electronic cam" technology and synchronous acquisition of dynamic data, the wind tunnel test of yaw oscillation was first carried out for the dynamic "sweep effect" of the airfoil in this paper. The study shows that the aerodynamic curve of the yaw oscillating airfoil has obvious hysteresis effect, the periodic pressure fluctuation of the airfoil suction surface is the main inducement, and the aerodynamic hysteresis characteristics are enhanced with the increase of the oscillation frequency, the initial angle of attack and the amplitude. The hysteresis loop of the lift and pressure difference drag changing with yaw angle is "W" type, the hysteresis loop of the pitching moment is "M" type, and the hysteresis loop of the lift difference is "$\infty$" type. The aerodynamic force of the airfoil under the negative stroke is higher than that under the positive stroke, and the aerodynamic coefficients of the airfoil under negative stroke increase slightly with the increase of the oscillation frequency, but decrease obviously under positive stroke with the increase of the oscillation frequency. The power spectral density (PSD) distribution of the airfoil lift coefficient has obvious energy concentration characteristics at the integer multiple of the oscillating frequency, and with the increase of the oscillation frequency, the amplitude of the energy concentration is obviously increased, which reflects the enhancement of the unsteady flow around the yaw motion airfoil. There is hysteresis effect of the pressure coefficient changing with the yaw angle on different suction surface position, in which the hysteresis areas of the pressure coefficient are larger on 1.2% chord position and 40% chord position, as the result of the periodic generation, development, movement, breakdown and reconstruction of the shear layer vortex and the dynamic separation vortex on the airfoil surface. When the amplitude of yaw oscillation $\beta_1=10^{\circ}$, the shape of $C_\text L-\beta$ curve is "$^\wedge$" type. When the amplitude of yaw oscillation $\beta_1=30^{\circ}$, the shape of $C_\text L-\beta$ curve is "$^{\wedge\wedge\wedge}$" type, that is, when the yaw angle $\beta>20^{\circ}$ or $\beta<-20^{\circ}$, the shape of the lift coefficient hysteresis loop of the airfoil presents "drooping" phenomenon.

2018, 50(5): 977-989. doi: 10.6052/0459-1879-18-183

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NUMERICAL SIMULATION OF SHOCK WAVE DYNAMICS IN TRANSIENT TURBULENT CAVITATING FLOWS

Wang Changchang, Wang Guoyu, Huang Biao

To investigate the cloud cavity collapse induced shock wave dynamics in unsteady cavitating flows,especially the shock wave formation,propagation,and the interaction between shock wave and cavity,numerical simulation is conducted to study the shock wave dynamics dominated unsteady cloud cavitating flows.The numerical method is achieved by implementing phase change model into the native pressure-based compressible two-phase flow solver,based on the open source software OpenFOAM,considering the compressibility of both liquid and vapor.The numerical results are presented for the typical shock wave dominated unsteady partial cavitating flow,characterized by low Strouhal number around a NACA66 hydrofoil at $\alpha=6$°and $\sigma=1.25$.The results show that the predicted unsteady cavity behaviors agree well with the experiments,especially the large scale cloud cavity collapse induced shock wave phenomena.The large scale cloud cavity collapse process can be depicted into three stages:(1) the formation of U-shape cloud cavity; (2) the collapse of U-shape cloud cavity head; (3) the collapse of U-shape cloud cavity legs.The shock wave is generated and emitted during the third stage and will propagate both upstream and downstream.When the shock wave propagates to the new attached cavity sheet,it will cause the attached cavity sheet collapse,and with the shock wave propagation within the cavity sheet,the attached cavity sheet is shorten until totally collapsed.Following,the shock wave rebound phenomena occurs.The shock wave propagation and rebound are responsible for the increase in cavity evolution cycle and thus the low cavitation Strouhal number.The shock wave dynamics analysis shows that the flow parameters across the shock wave front during the interaction between shock wave and cavity satisfies the 1-D shock wave relationship.

2018, 50(5): 990-1002. doi: 10.6052/0459-1879-18-215

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ACCURATE AERO-HEATING PREDICTIONS BASED ON MUL-TI-DIMENSIONAL GRADIENT RECONSTRUCTION ON HYBRID UNSTRUCTURED GRIDS¹⁾

Wan Yunbo, Ma Rong, Wang Nianhua, Zhang Laiping, Gui Yewei

The prediction of hypersonic aerodynamic environment is highly sensitive to numerical algorithms and computational grids. Due to the geometry complexity of modern lifting-body hypersonic vehicles, the time cost of generating high quality structured grids increases horribly, and it is difficult to meet the need of engineering applications. In order to shorten the task cycle, it is necessary to develop numerical methods for accurate aero-heating prediction on hybrid unstructured grids, due to the capability for complex configurations. Gradient reconstruction method is one of the important factors influencing the accuracy of heat flux prediction on unstructured grids. In this work, a multi-dimensional gradient reconstruction was introduced into the second-order cell-centered unstructured finite-volume solver developed by the authors, and compared with the widely used Green-Gauss methods and least squares methods in aerodynamic force simulations. The benchmark cases of hypersonic flows over a 2D cylinder, were tested to validate the multi-dimensional approach. The numerical results demonstrate that the multi-dimensional approach can improve the accuracy of aero-heating prediction and the convergence performance. Finally, the multidimensional gradient reconstruction method is applied to predict the heat flux over a 3D cylinder and the double ellipsoid configuration on the general hybrid grids. The numerical results agree well with experimental data, which demonstrates the potential capability for complex engineering applications.

2018, 50(5): 1003-1012. doi: 10.6052/0459-1879-18-082

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EFFECTS OF ROUNDED CORNER ON AERODYNAMICS OF SQUARE CYLINDERS AND ITS FLOW MECHANISMS

Du Xiaoqing, Tian Xinxin, Ma Wenyong, Li Erdong

Corner rounding modification is commonly used to improve the aerodynamics of a square cylinder. However, its flow mechanism has not been clarified yet. Aerodynamic performances and flow field characteristics of sharp and rounded-corner square cylinders have been investigated using large eddy simulation (LES) in a uniform flow at the Reynolds number of 2.2$\times $10$^{4}$. The effect of attack angle has been evaluated, and characteristics of the shear layer and the separation bubble have been quantitatively analyzed. The physical mechanism behind the corner modification is discussed as well. Results show that the overall surface pressures, aerodynamic forces and vortex shedding intensity of rounded-corner square cylinders have a downward trend in comparison to sharp-corner cylinders. The "separation bubble'' flow pattern occurs in a lower attack angle for rounded-corner cylinders. As the increase of the attack angle, the length of the separation bubble decreases until it disappears. Besides, the separation point of rounded-corner cylinders moves downstream, which leads to a thinner shear layer and a narrower wake and a weaker vortex shedding. All these factors result in a reduced drag coefficient and an increased Strouhal number of rounded-corner square cylinders.

2018, 50(5): 1013-1023. doi: 10.6052/0459-1879-18-123

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STUDY ON SPREADING CHARACTERISTICS OF NANOFLUIDS DROPLET IMPINGING ON SOLID SURFACE

Liu Hailong, Shen Xuefeng, Wang Rui, Cao Yu, Wang Junfeng

The spreading characteristics of a nanofluids droplet impinging on the solid surface are the key factors in efficient heat and mass transfer technology which based on droplet deposition. However, the dynamic behaviors and characteristics of the nanofluid droplet haven't been fully understood since the presence of the non-Newtonian fluid behavior and the interaction between the microstructure of nanoparticle and micro-flow field in the droplet which complicates the spreading process. In this study, we prepared homogeneous and stable nanofluids by dispersing different nanoparticles (multiwall carbon nanotube (MWCNT), graphene and nano-graphite powder) to epoxy resin with two-step method. The rheological behaviors of these nanofluids have been measured and analyzed. The evolution of droplet morphology during the spreading process has been captured by means of high speed camera visualization technique. Based on the image processing technique, the transient dimensionless height, transient spreading factor and dynamic contact angle (DCA) of the droplet have been studied. The results show that the nanoparticles bring the base fluid non-Newtonian shear thinning property. The shear viscosity of test fluid plays important role during the spreading phase and the nanofluid with a lower shear viscosity over the entire range of the shear rate results inlarger variations of the spreading factor and dimensionless height. Nanofluids droplet impacting on the hydrophobic surface could be faster to reach equilibrium condition. The inertial force of impacting droplet dominants the initial spreading process, the spreading variation and velocity are proportional to the impact velocity. This study can provide theoretical basis and specific guidance for the development of gain cooling technology and the manufacture of micro high thermal and electrical conductivity materials.

2018, 50(5): 1024-1031. doi: 10.6052/0459-1879-18-187

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PERMEABILITY OF MICROCRACKED POROUS SOLIDS THROUGH A MICROMECHANICAL MODEL

Li Le

This paper investigates the permeability of solids containing a crack network with finite connectivity through micromechanical method. The main factors of permeability include crack density, connectivity, crack opening and permeability of porous matrix. Firstly, for solids with unconnected cracks, the interaction direct derivative (IDD) method is employed to obtain the crack-altered permeability considering crack density $\rho $ and crack opening $b$. Then, for networks containing randomly oriented cracks with intersection, the amplification of permeability by crack connectivity is quantified for local crack clusters. This amplification effect is modeled by arranging parallel cracks on transport direction. By introducing the definition of hypothetically parallel crack density $\rho^{\rm h}$, the hypothetically parallel cracks are embedded in a host matrix whose permeability are those of the effective medium. In this way the IDD model is extended to evaluate the permeability of part-connected networks before total percolation occurs, considering the permeability of porous matrix $K_{\rm m}$, crack density $\rho $, opening aperture $b$ and parallel crack density $\rho^{\rm h}$. Finally, the representative volume element is built for cracked solids with cracks having random spatial locations and the permeability is solved by finite element method. Through this numerical tool, the validity and accuracy of IDD solutions for non-connected and part-connected crack networks are confirmed by several case analysis. The results show that: (1) For non-connected networks, crack opening is found to have little impact on the effective permeability due to the continuous matrix and its low permeability; (2) For part-connected networks, when crack density $\rho <1.1$ (uncorrelated networks, the fractal dimension is 2.0), 1.2 (correlated networks, the fractal dimension is 1.75), the IDD extended model show a good agreement with numerical results and loses its accuracy due to the clustering effect at more higher $\rho $ level.

2018, 50(5): 1032-1040. doi: 10.6052/0459-1879-18-065

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SIMULATION AND MICRO-MECHANICS ANALYSIS OF INHERENT ANISOTROPY OF GRANULAR BY DISTINCT ELEMENT METHOD

Qian Jinsong, Chen Kangwei, Zhang Lei

The particles tend to be spatially arranged in directional orientation after the paving of granular materials, and thus leading to the inherent anisotropy of mechanical property. Based on the actual irregular shape of granular materials, three-dimensional complex shape particles were modelled utilizing distinct element method to simulate the interlocking between particles. Five numerical test specimens with different bedding angles and an isotropic specimen were established respectively, and the mechanical properties of various specimens were compared during the triaxial compression simulations. Besides, the fabric tensor was introduced to quantify the anisotropy, the rose diagram was drawn to exhibit the distribution characteristics of contact normal and contact force, and then the development of anisotropy was investigated. It is shown that, as the long axis of particles change toward the horizontal direction, the stress ratio and the shear dilatancy of specimen increase continuously. Compared with isotropic structure, the peak stress ratio and the maximal volume compression strain of anisotropic structure when the bedding angle $\theta=0^\circ$ is 12.6% and 18.8% larger respectively. This is because the rotation and contact sliding ratio of particles is smaller, the internal adjustment time is shorter, and specimen can be sheared more densely. The inherent anisotropy has little effect on the distribution characteristics of contact force, but significantly affects the distribution characteristics of contact normal. When $\theta$ is $90^\circ$, the contact normal anisotropy coefficient drops quickly and then gradually increases during the shear process. Otherwise, the coefficient shows a steady or slight drop trend after an increase, and the coefficient grows faster as the $\theta$ decreases.

2018, 50(5): 1041-1050. doi: 10.6052/0459-1879-18-061

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PARAMETER DETERMINATION METHOD OF GOTOH YIELD CRITERION BASED ON NON-ASSOCIATED FLOW RULE

Wang Haibo, Zhou Wei, Yan Yu, Li Qiang, He Dong

Yield criterion has an important influence on theoretical analysis, process optimization and finite element simulation of sheet metal forming process. By enhancing the anisotropy characterization ability of the yield criterion, the reliability of the forming process and the accuracy of the actual prediction can be ensured. In this paper, a new set of parameter solving method for the Gotoh yield criterion is given based on non-associated flow rule. On the basis of common yield criteria and different flow rules, the 5754O aluminum alloy, DP980 advanced high-strength steel and SAPH440 structural steel sheet were taken as examples, the anisotropic deformation behavior of which were predicted under different loading paths. The yield function and plastic potential function derived from Gotoh yield criterion and the theoretical functions based on associated flow rule were used to calculate the distributions trend of yield stress and r-value along different loading angle. Furthermore, the yield locus under the plane stress state is analyzed, and the prediction accuracy the anisotropic yield behavior based on different yield criteria and the flow rules is verified. By comparing the theoretical and experimental results, it is shown that different yield criteria with same flow rule have significant differences in anisotropic characterization ability for the same sheet. There are also obvious deviations in the characterization process when the yield criterion is adopted based on different flow rules. The yield criterion based on non-associated flow rule can greatly improve its own flexibility and accuracy, and the characterization ability is significantly enhanced. The final results will provide an important reference for the actual application strategy of the yield criteria in the plastic forming field.

2018, 50(5): 1051-1062. doi: 10.6052/0459-1879-18-194

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THE CRITICAL STRENGTH CRITERION OF METAL MATERIALS UNDER QUASI-STATIC LOADING

Yu Simiao, Cai Lixun, Yao Di, Bao Chen, Chen Hui, Peng Yunqiang, Han Guangzhao

For 10 types of specimens with different constraints, ductile fracture tests of 9 metal materials under unidirection loading were performed, and their load-displacement relations were measured. Based on the load-displacement curves of notched round bar, the full-range equivalent constitutive relationships of materials up to failure were obtained by FAT (finite-element-analysis aided testing) method. Further, the simulated force-displacement curves for different specimens were obtained based on the full-range constitutive relations, which agree well with the experimental force-displacement curves. The results demonstrate that the full-range constitutive relations up to failure obtained by FAT method have uniqueness for the materials. The critical fracture parameters such as critical stress, critical strain and critical stress triaxiality are investigated by failure simulations for the 36 specimens with different constraints. The first principal stress is suggested to be the master parameter to control ductile fracture. By analyzing the critical behaviors of the specimens which are smooth, notched and cracked, respectively, a unified strength criterion for ductile materials with stress triaxiality varying from $-1$ to 3 is proposed.

2018, 50(5): 1063-1080. doi: 10.6052/0459-1879-18-172

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NON-LINEAR CONTACT MODEL FOR SUPER-QUADRIC ELEMENT CONSIDERING THE EQUIVALENT RADIUS OF CURVATURE

Wang Siqiang, Ji Shunying

The super-quadric elements based on the continuous function representation can effectively describe the non-spherical particles in nature and industrial applications, and accurately calculate the contact force between the elements through a non-linear iterative method. For the super-quadric elements with complex geometric shapes, the linear contact force model cannot precisely calculate the contact force under various contact patterns. Considering different shapes and surface curvatures between non-spherical elements, a corresponding non-linear viscoelastic contact force model is developed. In this model, the equivalent radius of curvature is introduced to calculate the elastic contact stiffness and viscous force in normal direction. Meanwhile, the elastic force and the viscous force in tangential direction are simplified based on the contact force model of spherical element. To validate the super-quadric algorithms and the contact force model, the normal collision between spherical particles, the oblique contact between ellipsoidal elements, the static packing of cylinders and the dynamic hopper discharge of ellipsoids are simulated with the super-quadric elements. The proposed method is well verified by finite element numerical results and physical experimental data. The non-linear contact force model of super-quadric element with considering the equivalent radius of curvature can accurately calculate the inelastic collision, so as to reasonably reflect the motion law of the non-spherical particle system. Based on the aforementioned method, the effects of aspect ratio and blockiness on the flow characteristics in the discharging process are further analyzed. The results show spherical particles have the fastest flow rate while cube-like particles have the slowest flow rate. Meanwhile, the flow rate of ellipsoids and cylinder-like particles decreases with increasing or decreasing the aspect ratio. In addition, cube-like particles are more likely to form face-face contacts and have a lower flow rate. The super-quadric element with non-linear contact force model can provide an effective numerical approach to simulate the flow characteristics of non-spherical granular materials.

2018, 50(5): 1081-1092. doi: 10.6052/0459-1879-18-103

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A QUADRILATERAL QUADRATURE PLATE ELEMENT BASED ON REDDY'S HIGHER-ORDER SHEAR DEFORMATION THEORY AND ITS APPLICATION

Shen Zhiqiang, Xia Jun, Song Dianyi, Cheng Pan

Plate structures made of advanced composite materials or functionally graded materials have been widely used in engineering practice recently, which is characterized by the variation of material properties along the plate thickness. Several plate elements have been presented utilizing the finite element formulation based on Reddy's higher-order shear deformation theory which yields more accurate transverse shear strain distributions of these structures. However, the $C^{1}$ continuous plate elements is very limited. Based on Reddy's higher-order shear deformation theory, a $C^{1}$ continuous quadrilateral plate element is established using the weak form quadrature element method in this work. The element presented here is then used for linear flexural and free vibrational analyses of the rectangular and skew plates made of homogenous or composite materials with constant thickness as well as the homogenous rectangular plates with variable thickness. The numerical results of quadrature element formulation are compared with those of other numerical method from the open literatures in order to validate the correctness and efficiency of the presented quadrature plate element. It is shown that only one quadrature element is fully competent for linear analysis of a quadrilateral plate regardless of its thickness variation and component materials. As for rectangular plates with constant or variable thickness, one quadrature element with only 9$\times $9 numerical integration points is needed. And for skew plates, the number of numerical integration points required for acceptable accuracy gradually increases to 15$\times $15 with the skew angle enlargement. As a completive numerical formulation, the quadrilateral quadrature plate element can be further applied in nonlinear and transient analyses of composite material plate structures.

2018, 50(5): 1093-1103. doi: 10.6052/0459-1879-18-225

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INVESTIGATION ON TRANSITION BETWEEN TIP-SAMPLE INTERACTION REGIMES IN BIMODAL AMPLITUDE MODULATION ATOMIC FORCE MICROSCOPY

Zhou Xilong, Li Faxi

Bimodal amplitude modulation atomic force microscopy (AM-AFM) has two interaction regimes in measurements or imaging, i.e., the attractive regime and the repulsive regime. The investigation on the transition between the interaction regimes is critical for the setting of parameters for imaging in a specific interaction regime, the control of the ranges of the interaction regimes as well as the correct understanding and interpretation of the imaging results in bimodal AM-AFM. Combining finite difference method and the in-phase and quadrature method, the influences of the magnitudes setting of modal free resonance amplitudes, the variation of mechanical properties of the sample, and the setting of excitation frequencies on the transition between the interaction regimes in bimodal AM-AFM are studied by a numerical simulation. Results show that the higher the sum of the modal free resonance amplitudes, the larger the critical setpoint when the attractive regime transitions to the repulsive regime, i.e., the setpoint range of the attractive regime becomes smaller. The higher the elastic modulus and the smaller the viscosity coefficient of the sample, the earlier the attractive regime transitions to the repulsive regime during the approach of the probe to the sample surface. When the probe is excited at the frequencies away from the modal free resonance frequencies, the range of the attractive regime is smaller than that excited at the free resonance frequencies. The saltation of the state of motion of the probe does not necessarily correspond to the transition between the interaction regimes. Furthermore, the phase values are invalid to be employed to determine the attractive or repulsive regime by judging whether the phase value is higher or lower than 90°.

2018, 50(5): 1104-1114. doi: 10.6052/0459-1879-18-137

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A SMOOTHED MESHFREE GALERKIN METHOD FOR 2D ELASTICITY PROBLEM

Ma Wentao

Despite clear general progress with element-free Galerkin method (EFGM), its low computational efficiency becomes a technical issue in the simulation of realistic problems. To improve the efficiency of EFGM, a smoothed meshfree Galerkin method is presented for the 2D elasticity problem. In the method presented, displacement fields are constructed using the moving least square (MLS) approximation and strains are smoothed over two-level nesting smoothed triangular cells based on the generalized gradient smoothing technique. Then, the generalized smoothed Galerkin (GS-Galerkin) weak form is used to create the discretized system equations. Each two-level nesting smoothed triangular cells include the triangular background cell itself and four equal-area triangular sub-cells, respectively. According to the Richardson extrapolation method, an optimal combination of the two-level smoothed strains can be obtained. Since the present method uses the linear interpolation on the boundary of problem domain, the boundary conditions including the essential and natural boundary conditions can directly impose as that in FEM. Several examples, including the cantilever beam, infinite plate with a circle hole, infinite plate with a central crack and the twin-arched tunnel, are investigated to demonstrate the accuracy and efficiency of the present method. The numerical results show that with more smoothing sub-cells by using in the smoothed meshfree Galerkin method, higher numerical accuracy can be obtained. In addition, the present method is higher efficient than EFGM. As a consequence, the smoothed meshfree Galerkin method with two-level nesting smoothed triangular cells significantly outperforms the EFGM and is very successful and attractive numerical method for solving the elasticity problems.

2018, 50(5): 1115-1124. doi: 10.6052/0459-1879-18-135

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HYSTERESIS MECHANICAL MODEL AND EXPERIMENTAL STUDY OF SPRING METAL-NET RUBBER COMBINATION DAMPER

Zou Guangping, Zhang Bing, Chang Zhongliang, Liu Song

Metal-net rubber is a porous material composed entirely of metal wire woven. Compared with the traditional spiral coiled metal rubber material, the molding technology of metal-net rubber material is improved, which eliminates a large number of manual process interferences in preparation process. The metal-net rubber material has higher mechanization degree, better coincidence and more stable mechanical properties. With the excellent characteristics of bearing capacity, large damping, high temperature resistance, low temperature resistance, aging resistance, oil and corrosion resistance, metal-net rubber material is better than traditional rubber in many ways, which is widely used in aerospace, shipbuilding, military weapons and other military industries. Spring metal-net rubber combination damper has designable stiffness and high bearing capacity. Because of its complex nonlinear hysteresis characteristics, the constitutive model of related materials is difficult to describe its mechanical properties accurately. Based on the static hysteresis mechanical performance experiment of spring metal-net rubber combination damper, combined with the hysteresis characteristics of dry friction damping, a theoretical modeling model of hysteresis mechanical properties is proposed. According to the characteristics of restoring force-displacement curve of damper hysteresis experiment, the hysteresis curve is decomposed into elastic recovery force and dry friction damping force by parameter separation method. The equivalent stiffness and dry friction damping coefficient are solved respectively by modeling to establish the theoretical model of the combination damper. By comparing with the experimental results, the error analysis is carried out to verify the accuracy of the theoretical model.

2018, 50(5): 1125-1134. doi: 10.6052/0459-1879-18-165

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ON THE DEGREES OF FREEDOM OF A MECHANICAL SYSTEM

Hu Haiyan

The definition of degrees of freedom of a mechanical system originated from the number of independent coordinates to describe the system configuration. The definition turned to be the number of independent variations of generalized coordinates after the studies on non-hololomic constraints in the development of analytic mechanics. The paper points out that the above definition of degrees of freedom has some flaws for the mechanical system with non-holonomic constraints and may impose excessive limits on the system dynamics. The paper, hence, studies the accessible state manifold of a mechanical system with non-holonomic constraints in the state space and shows that the dimensions of the accessible state manifold is equal to the number of minimal unknown variables to describe the system dynamics, governed by a set of ordinary differential equations of the first order, such as the Gibbs-Appell equations together with the relation of generalized velocities and psudo-velocities. Then, the paper defines the degrees of freedom of a mechanical system as a half of the dimensions of the accessible state manifold. Afterwards, the paper demonstrates how to understand the concept of a half degree of freedom of a mechanical system with a single non-holonomic constraint via two case studies, that is, the vibration system having a viscoelastic mounting and the sleigh system moving on an inclined plane, presenting the relation between a half degree of freedom and the two neighboring integer degrees of freedom. Furthermore, the paper gives two examples of mechanical systems, each of which has two non-holonomic constraints and results in the reduction of a single degree of freedom, and addresses the dimensions of tangent and cotangent bundles of the two systems.

2018, 50(5): 1135-1144. doi: 10.6052/0459-1879-18-219

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NON-SMOOTH BURSTING OSCILLATION MECHANISMS IN A FILIPPOV-TYPE SYSTEM WITH MULTIPLE PERIODIC EXCITATIONS

Qu Zifang, Zhang Zhengdi, Peng Miao, Bi Qinsheng

The main purpose of this paper is to explore non-smooth bursting oscillations as well as the bifurcation mechanisms in a Filippov-type system with different scales and two periodic excitations. By using the coupling of Duffing and Van der Pol oscillators as the dynamical system model and introducing two periodically changed electrical sources, the two periodic excitations can be converted into a function of a single periodic exciting term which can be considered as a slow-varying parameter when there is an order gap between the exciting frequency and the natural one. The equilibrium branches as well as the bifurcation mechanisms which are caused by fold or Hopf bifurcations with the variation of the slow-varying parameter are obtained in the case of two different frequencies of parametric excitation when the amplitudes of two periodic excitations are constants. Based on the transformed phase portraits and the evolutions of stable limit cycles produced by Hopf bifurcations, the critical conditions of multisliding bifurcations and various oscillation modes determined by a slow-varying parameter are derived. The oscillation mechanisms and the analysis of the non-smooth dynamic behaviors are also described in detail. By contrasting the equilibrium branches with two different frequencies of the parametric excitation, we find the equilibrium branches become more tortuous although the equilibrium branches are similar in the structure. The number of the corresponding extreme points are also changed, and the results are verified by numerical simulations.

2018, 50(5): 1145-1155. doi: 10.6052/0459-1879-18-136

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THE COMPLETED FORM OF ELASTIC MODEL FOR ANCF THIN PLATE ELEMENT AND ITS APPLICATION ON DYNAMIC MODELING OF THE LEAF SPRING

Lan Peng, Cui Yaqi, Yu Zuqing

The absolute nodal coordinate formulation(ANCF) was widely used in the research of multi-body dynamics. But the thin plate element which designed for modeling thin shell structure couldn't be adopted for initial curved structure directly because of its deficiency of position vector gradient. Thin plate element was chosen for modelling the leaf spring to avoid the troublesome locking problem when using fully parameterized ANCF element. One explored the way to express the elastic force of existing thin plate element via common continuum mechanics system by adopting the unitized normal vector on the centroid plane as the added position vector gradient for thickness direction. So as to modify its elastic force formulation. The completed form of the element was given which could eliminated the introduced initial stress when describing initially curved leaf using the standard procedure which could only be performed on fully parameterized ANCF element. The modification for elastic force would not affect the element property. By setting undeformed structure which differs from initial one, the controlled initial stress could be introduced into the model for describing the assemble process. Numerical results were given to verify the validity of this modification. An initial curved double-leaf spring model was built. In order to specify the exact contact region, a cross element search strategy using a local material coordinate system built on the entire leaf was developed. Introduced a more precise calculation procedure for contact and friction force using penalty method and smooth Coulomb law. The rigid-flexible coupled leaf spring model combined with ANCF reference nodes was built, integrated with shackle, chassis and their mechanism movement.

2018, 50(5): 1156-1167. doi: 10.6052/0459-1879-18-133

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ONE KIND OF TRANSVERSE ISOTROPIC STRENGTH CRITERION AND THE TRANSFORMATION STRESS SPACE

Wan Zheng, Song Chenchen, Zhao Xiaoguang

Considering the original anisotropic properties of the geomaterials in the process of natural formation, it is simplified as a kind of cross-anisotropy material. Based on a strength criterion, according to the spatial location relationship of depositional plane(DP) and the effective spatial mobilized plane(ESMP) in physical space, the angle of above two planes is regarded as the primary influential factor to measure the strength degree of geomaterial anisotropy. According the concept of ESMP, when the angle between DP and ESMP is larger, the frictional behavior capacity can be fully employed. The stress ratio strength is larger and vice in contrary. Based on the above thought, the stress ratio strength formula for cross-anisotropy material is established. The formula can be employed to revise a strength criterion and a strength criterion considering cross-anisotropy is obtained. The transformation idea of a criterion for transversely isotropic materials formula to isotropic Von-Mises criterion formula is adopted. Based on cross-anisotropy a strength criterion, the transformed stress equation is derived and it can be employed to transform the cross-anisotropy stress space to isotropic stress space. By using the proposed transformed stress(TS) method, it is convenient to convert the traditional two-dimensional constitutive models established on the basis of Von-Mises criterion to the three-dimensional models considering cross-anisotropy. By comparison of the prediction and test results of strength and stress-strain relationship for geomaterials under triaxial loading condition, the validity and applicability of proposed criterion and TS method is demonstrated.

2018, 50(5): 1168-1184. doi: 10.6052/0459-1879-18-134

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COMPLEX MODE SUPERPOSITION METHOD BASED ON FREQUENCY DEPENDENT VISCOUS DAMPING MODEL

Sun Panxu, Yang Hong, Wu Jiafeng, Wang Zhijun

According to the viscous damping model, energy dissipation is related to external excitation frequencies in each cycle. There is divergence in time domain calculation results of complex damping model. In order to overcome the two kinds of disadvantages of damping models, frequency dependent damping model is obtained by time-frequency transformation principle on the basis of complex damping model. Energy dissipation is not related to external excitation frequencies in each cycle. In addition, time-history calculation of frequency dependent damping model is convergent. Real mode superposition method is not directly adopted, because the damping matrix of mixed structure of multiple damping characteristic materials is non-proportional. By the transformations of frequency dependent damping model and complex damping model, complex mode superposition method is proposed based on frequency dependent damping model. And it can be directly applied to mixed structure. The analysis results of the cases show that compared with complex mode superposition method based on viscous damping model, the calculation results of the complex mode superposition method based on frequency dependent damping model are unique. In addition, the method does not increase matrix dimensions and has high computational efficiency. The analysis results of small damping cases show that calculation results of the two methods are approximately equal. They are consistent with frequency domain calculation results of complex damping model. When the damping ratios are larger, the difference of calculation results by the two methods will increase. While the calculation results of complex mode superposition method based on frequency dependent damping model will remain consistent with frequency domain calculation results of complex damping model.

2018, 50(5): 1185-1197. doi: 10.6052/0459-1879-18-170

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GENERALIZED FINITE DIFFERENCE METHOD FOR BIOHEAT TRANSFER ANALYSIS ON SKIN TISSUE WITH TUMORS

Li Ailun, Fu Zhuojia, Li Powei, Chen Wen

Bioheat transfer analysis is widely used in clinical medical treatment and diagnosis, such as cryosurgery, tumor hyperthermia, disease diagnosis and so on. The presence of a tumor inside healthy skin tissues makes the temperature increment in the vicinity of the tumor. This characteristic is often used to detect tumor growth in skin tissue. Therefore it is necessary to do some numerical investigation on bioheat transfer analysis. Considering the skin tissue containing tumor, a novel meshless collocation method-generalized finite difference method (GFDM) is applied to Pennes bioheat equation, which can be used to describe the heat transfer process of the skin tissue containing tumors. Based on Taylor expansion and moving least squares method, the derivative of physical quantity at each discrete node can be expressed by the linear combination of physical quantities and weight coefficients at several adjacent nodes in the GFDM. Then the linear system of equations is constructed with the unknown physical quantities at discrete nodes. The proposed method not only has the advantages without mesh and numerical integration, but also overcomes the problem of highly ill-conditioned resultant matrix in most meshless collocation methods. It provides a possibility for the application of this kind of methods in large-scale engineering numerical calculation. The GFDM numerical model for simulating the bioheat transfer process in skin tissue with tumors is first introduced. Then the numerical accuracy and convergence of the GFDM are verified through some benchmark examples with/without regular-shaped tumors. Finally the effects of the arbitrary-shaped tumor including the location, geometry and size on the thermal behavior inside the skin tissue are investigated.

2018, 50(5): 1198-1205. doi: 10.6052/0459-1879-18-155

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MECHANISM OF EXPLOSION-INDUCED DISTURBANCE IN NATURAL MAGNETIC FIELD

Li Jianqiao, Ma Tianbao, Ning Jianguo

Electromagnetic effect generated by explosions has a significant influence on the explosion test. Some metallized explosives even disable the electronic equipment. The mechanism and numerical simulations are investigated to the magnetic disturbance of natural magnetic field observed during the conventional explosion for getting the theoretical model and the properties of the explosion-induced electromagnetic effect. The mechanism of the generated magnetic disturbance is proposed based on a thermodynamic equilibrium ionization model and the magnetic hydrodynamic (MHD) model considering magnetic diffusion. The magnetic disturbance is considered to be induced by the motion of the conductive detonation products in the geomagnetic field. The conductivity, which makes direct influence on the disturbance duration, is described by the ionization model. Combined with the MHD governing equations and the method utilized in explosion issues, two kinds of numerical simulations are performed to investigate the magnetic disturbance during explosions of rectangular explosive in different initial magnetic fields. It is found that the magnetic disturbances are extremely different in value while almost the same in distribution. The distributions of fluid and magnetic parameters are compared at the same time and a conclusion can be obtained that the same distribution of conductivity leads to a similar distribution of magnetic field. The conductivity of detonation products has a huge difference in space distribution and this makes the magnetic field diffused except in the region with high conductivity. Therefore, obvious magnetic disturbance can be only observed in the region of high conductivity. The difference of magnetic field in value is related to both the initial magnetic field and velocity of fluid and can be only extremely observed in the early stage of explosion. A magnetic disturbance induced by the electromagnetic wave generated in the explosion is simulated and compared with the result in reference. The comparison shows a good agreement in the time duration scale of the magnetic disturbance, which proves the reliability of the numerical method used in this paper. The influence of the configuration of explosives in the geomagnetic field on the magnetic disturbance is first considered and the difference in the magnetic disturbance is predicted. The above achievement has not been reported in the previous published investigations. The prediction proposed in this paper needs a further experimental verification and this will be the next stage of our investigation.

2018, 50(5): 1206-1218. doi: 10.6052/0459-1879-18-081

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TRAFFIC FLOW DYNAMIC MODEL CONSIDERING THE INFLUENCES ON DRIVERS BASED ON FIELD FORCE

Chen Yong, He Hong, Zhang Wei, Zhou Ning

In order to study the quantitative influence of driver's behavior on road traffic, the cellular automaton dynamic model with influences on drivers (IDCA) is proposed based on the NaSch model in this paper for the characteristics of the driver's behavior. The improved model combines field force and graph theory to simulate road traffic flow. According to the driver's behavior characteristics, these factors are considered in the model, such as the direct physical and indirect psychological effects on driver, relative speed and vehicle characteristic. The influences of driver types and vehicle flow evolution mechanism on traffic flow are studied based on the model through computer numerical simulation. The simulation results show that the IDCA model can simulate abundant traffic behaviors better than the NaSch model, which reappears synchronous flow and other complex traffic phenomena. Traffic flows have better stability and higher dissolving congestion efficiency in the IDCA model through the analysis of the fluctuation of vehicles' speed and the vehicles' headway-distance. In addition, by using the computer numerical simulation of the IDCA model, the density-velocity and density-flow diagrams of the mixed traffic flow composed of different driver types are obtained. The conclusions are obtained: the larger the proportion of aggressive drivers, the larger the vehicle speed and traffic flow under the same road medium density and high density, and traffic flow decreases with the increase of the proportion of conservative drivers. The phenomenon of high speed car-following is simulated at last. The result of the rate of high speed car-following in the small headway areas more than 7% is obtained, which is consistent with the measured results.

2018, 50(5): 1219-1234. doi: 10.6052/0459-1879-18-109

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RESEARCH ON THE CONVERSION METHOD OF AEROHEATING ENVIRONMENT OF HYPERSONIC VEHICLE

Zhao Jinshan, Zhang Zhigang, Shi Yilei, Chen Ting, Xiao Yu, Su Siyao, Liao Junhao, Peng Zhiyu

Wind tunnel experiment is a key means to research and predict aeroheating for hypersonic vehicles. The flow field parameters and model scales in wind tunnel are different from flight condition, owing to the limitation of its simulation capability. The aeroheating data obtained from wind tunnel experiments can not be directly used for the aeroheating prediction and thermal protection system design in flight condition. So the method of predicting the aeroheating environment on flight condition, by using the wind tunnel experimental data, has been a technically difficult problem. In the past, the correlation and extrapolation method of wind tunnel aeroheating experiment data for specific aircrafts has a strong directionality, because this method is a kind of data fitting based on aeroheating data and does not take into account the specific parameters of aeroheating. It has certain limitations and is difficult to extrapolate to other shapes of aircraft. To solve the problem of the wind tunnel experimental data extrapolation, the main parameters of the influence of aeroheating were analyzed on the basis of the dimensionless Navier-Stokes equations and boundary layer equations, and the correlation and extrapolation method was developed for laminar and turbulence conditions by deducing the approximate solution of the aeroheating. Because the parameters of the local boundary layer edge can be taken into consideration, the correlation method has certain versatility. Then the experimental data of scale model on Reentry-F was obtained from wind tunnel experiments, the correlation analysis and validation for Reentry-F configuration was accomplished, the wind tunnel experimental data was extrapolated to flight condition by the extrapolation method and it agreed well with flight data. It showed that the method can be used for extrapolation of aeroheating experimental data, and multiple points of flight condition can be extrapolated from a few experimental results.

2018, 50(5): 1235-1243. doi: 10.6052/0459-1879-18-070

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THE SUPPORTED PROJECTS ON MECHANICS OF NSFC IN 2018

Zhan Shige, Bai Kunchao, Cao Dongxing, Wang Gang

The paper brief introduced the supported NSFC projects for General Programs, Young Scientists Fund, Fund for Less Developed Regions on mechanics in 2018. The projects list is also given.

2018, 50(5): 1246-1265. doi: 10.6052/0459-1879-18-292

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2018, 50(5): 1266-1275. doi: 10.6052/0459-1879-18-294

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