Orientation distribution of fibers and rheological property in fiber suspensions flowing in a turbulent boundary layer

A model relating the translational and rotational transport of orientation distribution function （ODF） of fibers to the gradient of mean ODF and the dispersion coefficients is proposed to derive the mean equation for the ODE Then the ODF of fibers is predicted by numerically solving the mean equation for the ODF together with the equations of turbulent boundary layer flow. Finally the shear stress and first normal stress difference of fiber suspensions are obtained. The results, some of which agree with the available relevant experimental data, show that the most fibers tend to orient to the flow direction. The fiber aspect ratio and Reynolds number have significant and negligible effects on the orientation dis- tribution of fibers, respectively. The additional normal stress due to the presence of fibers is anisotropic. The shear stress of fiber suspension is larger than that of Newtonian solvent, and the first normal stress difference is much less than the shear stress. Both the additional shear stress and the first normal stress difference increase with increasing the fiber concentration and decreasing fiber aspect ratio.     

An analytical and numerical study of chaotic dynamics in a simple bouncing ball model

Dynamics of a ball moving in gravitational field and colliding with a moving table is studied in this paper. The motion of the limiter is assumed as periodic with piecewise constant velocity-it is assumed that the table moves up with a constant velocity and then moves down with another constant velocity.The Poincaré map,describing evolution from an impact to the next impact,is derived and scenarios of transition to chaotic dynamics are investigated analytically and numerically.     

ANALYSIS OF THE CHAOTIC MOTION FOR A ROTOR SYSTEM WITH A TRANSVERSE CRACK

The chaotic motion of an elastic shaft-disk rotor system including the geometricnonlinearity of the shaft with a transverse crack is investigated.The critical condition for thesystem to enter chaotic state is given by the Melnikov method.Meanwhile,whether the chaosoccurs is determined by the Poincaré map,phase portrait and time-displacement history diagram.     

Large eddy simulation of vertical turbulent jets under JONSWAP waves

The effect of random waves on vertical plane turbulent jets is studied numerically and the mechanism behind the interaction of the jet and waves is analyzed. The large eddy simulation method is used and the σ-coordinate system is adopted. Turbulence is modeled by a dynamic coherent eddy model. The σ-coordinate transformation is introduced to map the irregular physical domain with a wavy free surface and an uneven bottom onto a regular computational domain. The fractional step method is used to solve the fil...     

ON THE DYNAMICAL STRUCTURE OF THE WIND FIELD OF JUPITER''''S GREAT RED SPOT

Based on the geographic approximation the two-dimensional dynamical structure of the wind fields of Jupiterls Great Red Spot and White Oval BC is obtained. The results of calculation are in good agreement with the observations. Thus, an explanation of the observed dispersion of the velocities along the horizontal streamline is given. The major physical mechanism of this dispersion is as follwos: The distance between two adjacent elliptical streamlines varies along the elliptical streamline; leading to the variance of the normal pressure gradient. Thus, the horizontal velocity V_T has to vary correspondingly so that the Coriolis force can approximately balance the normal pressure gradient Another less important factor, i.e., the change of the Coriolis force parameter with the latitude, is also taken into account. The distributions of the vorticities of GRS and White Oval BC are also calculated.     

NORMAL CONTACT STIFFNESS OF THE ELLIPTIC AREA BETWEEN TWO ASPERITIES

A new expression for contact deformation is given, and the normal contact stiffness between single asperities is derived according to Hooke’s law. A contact model between two ellipsoidal asperities is simulated by the FE method, the result compared with the theoretical solution. It is found that the curves of the normal contact stiffness versus the included angle in the principal curvature direction show similar trends and evolve as a cosine feature. The effects of the parameters on normal contact stiffness are found to show that normal contact stiffness increases and reaches the upper limit gradually with an increase in these parameters.     

Bandgap calculation for mixed in-plane waves in 2D phononic crystals based on Dirichlet-to-Neumann map

In this paper, a method based on the Dirichlet-to-Neumann map is developed for bandgap calculation of mixed in-plane waves propagating in 2D phononic crystals with square and triangular lattices. The method expresses the scattered fields in a unit cell as the cylindrical wave expansions and imposes the Bloch condition on the boundary of the unit cell. The Dirichlet-to-Neumann (DtN) map is applied to obtain a linear eigenvalue equation, from which the Bloch wave vectors along the irreducible Brillouin zone are calculated for a given frequency. Compared with other methods, the present method is memory-saving and time-saving. It can yield accurate results with fast convergence for various material combinations including those with large acous- tic mismatch without extra computational cost. The method is also efficient for mixed fluid-solid systems because it considers the different wave modes in the fluid and solid as well as the proper fluid-solid interface condition.     

Dynamical analysis and performance evaluation of a biped robot under multi-source random disturbances

During bipedal walking,it is critical to detect and adjust the robot postures by feedback control to maintain its normal state amidst multi-source random disturbances arising from some unavoidable uncertain factors.The radical basis function（RBF）neural network model of a five-link biped robot is established,and two certain disturbances and a randomly uncertain disturbance are then mixed with the optimal torques in the network model to study the performance of the biped robot by several evaluation indices and a specific Poincar′e map.In contrast with the simulations,the response varies as desired under optimal inputting while the output is fluctuating in the situation of disturbance driving.Simulation results from noise inputting also show that the dynamics of the robot is less sensitive to the disturbance of knee joint input of the swing leg than those of the other three joints,the response errors of the biped will be increasing with higher disturbance levels,and especially there are larger output fluctuations in the knee and hip joints of the swing leg.     

CONSTITUTIVE EQUATION WITH ORDERED PARAMETERS FOR VISCOELASTIC MATERIAL CONTAINING DEFECTS

Based on the experimental results of local temperature field formed in the evolution pc-riod of defects,the defect field is defined by this internal temperature field.The evolutionary processesof statistically correlative meso-scopic defects are analysed with Ihe growth rate and nucleation rate ofthe meso-defect,and it is deemed that the dynamic failure process of the viscoelastic material with de-fects can be quantitatively described by the normal method of the procedure of heat wave transmission.The defect field is regarded as a complex system of the union of the real sets and null sets,its maincharacteristics depending on the stratum hypothesis about the activities of the subsystems of the higheststratum described by ordered parameters.The fluctuation of ordered parameters is demonstrated bymeans of the projection operator method.The constitutive equation with ordered parameters for themeso-defect evolutionary state of viscoelastic material with defects is deduced from the nonlinear rheo-logical dynamic approach,and its solution is obtained.     

STOCHASTIC DISCRETE MODEL OF TWO-STAGE ISOLATION SYSTEM WITH RIGID LIMITERS

The possible intermittent impacts of a two-stage isolation system with rigid limiters have been investigated. The isolation system is under periodic external excitation disturbed by small stationary Gaussian white noise after shock. The maximal impact Poincare map is proposed based on the multi-body dynamics with unilateral constrains. Then in the period after shock, the zero order approximate stochastic discrete model and the first order approximate stochastic model are developed. The real isolation system of an MTU diesel engine is used to evaluate the established model. After calculating of the numerical example, the effects of noise excitation on the isolation system are discussed. The results show that the property of the system is complicated due to intermittent impact. The difference between zero order model and the first order model may be great. The effect of small noise is obvious. The results may be expected useful to the naval designers.     

强共振情况下冲击成型机的亚谐与Hopf分岔

通过理论分析与数值仿真研究了双质体冲击振动成型机的周期运动在强共振条件下的亚谐分岔与Hopf分岔，证实了此系统的1／1周期运动在强共振(λ0^4=1)条件下可以分岔为稳定的4／4周期运动及概周期运动．讨论了冲击映射的奇异性，分析了冲击振动系统的“擦边”运动对强共振条件下周期运动及全局分岔的影响。     

Codimension two bifurcation and chaos of a vibro-impact forming machine associated with 1：2 resonance case

A vibro-impact forming machine with double masses is considered. The components of the vibrating system collide with each other. Such models play an important role in the studies of dynamics of mechanical systems with impacting components. The Poincaré section associated with the state of the impact-forming system, just immediately after the impact, is chosen, and the period n single-impact motion and its disturbed map are derived analytically. A center manifold theorem technique is applied to reduce the Poincaré map to a two-dimensional map, and the normal form map associated with codimension two bifurcation of 1:2 resonance is obtained. Unfolding of the normal form map is analyzed. Dynamical behavior of the impact-forming system, near the point of codimension two bifurcation, is investigated by using qualitative analyses and numerical simulation. Near the point of codimension two bifurcation there exists not only Neimark-Sacker bifurcation associated with period one single-impact motion, but also Neimark-Sacker bifurcation of period two double-impact motion. Transition of different forms of fixed points of single-impact periodic orbits, near the bifurcation point, is demonstrated, and different routes from periodic impact motions to chaos are also discussed. The project supported by the National Natural Science Foundation of China (10572055, 50475109) and the Natural Science Foundation of Gansu Province Government of China (3ZS051-A25-030(key item)) The English text was polished by Keren Wang.     

Dynamics of pseudo-rigid ball impact on rigid foundation

This paper concerns the dynamics induced by the ideally elastic normal impact of a linearly elastic pseudo-rigid sphere on a rigid, stationary foundation. An impact map is derived and studied by numerical and analytical means. Periodic, quasi-periodic, and chaotic response is observed consistently with the symplectic nature of the map.     

一类碰撞振动系统在内伊马克沙克-音叉分岔点附近的局部两参数动力学

考虑一类具有对称性的三自由度碰撞振动系统.系统的庞加莱映射在一定条件下存在对称不动点,对应于系统的对称周期运动.根据对称性导出庞加莱映射P是另外一个隐式虚拟映射Q的二次迭代.推导了庞加莱映射对称不动点的解析表达式.根据映射不动点的稳定性及分岔理论,映射P的对称不动点发生内伊马克沙克-音叉(Neimark--Saker-pitchfork)分岔对应于映射Q发生内伊马克沙克-倍化(Neimark--Sakerflip)分岔.利用隐式虚拟映射Q,通过对范式作两参数开折分析,研究了映射P的对称不动点在内伊马克沙克-音叉分岔点附近的局部动力学行为.碰撞振动系统在这个余维二分岔点附近的局部动力学行为可能表现为投影后的庞加莱截面上的单一对称不动点、一对共轭不动点、单一对称拟周期吸引子以及一对共轭拟周期吸引子.数值模拟得到了内伊马克沙克-音叉分岔点附近的各种可能情况.内伊马克沙克-分岔和音叉分岔互相作用可能产生新的结果:对称不动点虽然首先分岔为两个共轭不动点,但是这两个共轭不动点是不稳定的,最终收敛到同一个对称拟周期吸引子.     

Pseudo-rigid ball impact on an oscillating rigid foundation

The problem of dissipative normal impact of a linearly elastic pseudo-rigid ball on a sinusoidally oscillating rigid foundation is considered. This problem yields a four-dimensional smooth impact map that produces sticking, regular and chaotic responses. Parameter values that furnish such responses are identified with the aid of a perturbation analysis.     

一种新的实时相关极值匹配算法设计与仿真

对传统相关极值匹配算法局限性进行了分析,并利用二维高斯样条函数张量积方法对局部重力异常离散格网基准图进行逼近以获取该局部基准图的连续解析表达式,在此基础上对相关极值匹配算法进行重新建模并采用拟牛顿BFGS非线性寻优方法对该模型进行解算。考虑到相关极值算法存在实时性差的缺点,采用固定初始序列长度的方式对初始序列采样结构进行改善,推导出了刚性变换中心从序列质心到原点的转换公式,最终完成能够实现单点迭代的基于局部重力异常基准图实时相关极值匹配算法设计,该匹配算法突破了传统离散匹配算法受限于基准图分辨率的局限。最后在2′×2′卫星测高反演重力异常数据基础上进行了两组仿真实验进行对比分析,实验结果表明,在重力测量噪声和初始定位误差较大的情况下,通过该匹配算法获得的匹配定位仍能以较高的精度实时跟踪真实航迹。     

2024铝合金在干摩擦往复运动条件下的磨损图研究

研究了 2 0 2 4铝合金 / 4 5 #钢摩擦副在干摩擦往复运动条件下的摩擦学特性 ,系统考察了载荷 98～ 4 90 N和速度0 .0 83～ 1.16 7m/ s范围内摩擦副材料的磨损行为 ;通过对磨损表面、断面以及铝在摩擦偶件的转移膜及磨屑的显微分析 ,建立了 2 0 2 4铝合金的磨损机制转变图 .结果表明 :2 0 2 4铝合金在低速和轻载条件下的磨损机制主要是磨粒磨损和剥层磨损 ;而在高速重载条件下的磨损机制主要是严重熔融磨损 ,并伴随向偶件材料表面的大量转移     

Codimension two bifurcation of a vibro-bounce system

A three-degree-of-freedom vibro-bounce system is considered. The disturbed map of period one single-impact motion is derived analytically. A center manifold theorem technique is applied to reduce the Poincaré map to a three-dimensional one, and the normal form map associated with Hopf-flip bifurcation is obtained. Dynamical behavior of the system, near the point of codimension two bifurcation, is investigated by using qualitative analysis and numerical simulation. It is found that near the point of Hopf-flip bifurcation there exists not only Hopf bifurcation of period one single-impact motion, but also Hopf bifurcation of period two double-impact motion. The results from simulation show that there exists an interesting torus doubling bifurcation near the codimension two bifurcation. The torus doubling bifurcation makes the quasi-periodic attractor associated with period one single-impact motion transform to the other quasi-periodic attractor represented by two attracting closed circles. The torus bifurcation is qualitatively different from the typical torus doubling bifurcation occurring in the vibro-impact systems. Different routes from period one single-impact motion to chaos are observed by numerical simulation.The project supported by the National Natural Science Foundation of China (10172042, 50475109) and the Natural Science Foundation of Gansu Province Government of China (ZS-031-A25-007-Z (key item))     

碰撞振动系统分岔与混沌的研究进展

针对工程实际中普遍存在的碰撞振动系统这种典型的非光滑动力系统, 其研究具有重要的理论意义和工程实用价值. 碰撞振动系统动力学的分析与研究方法主要有理论分析、数值模拟以及应用与实验研究. 为了研究碰撞振动系统的周期运动稳定性、分岔及混沌, 采用的手段有建立Poincar\'{e}映射、中心流形和范式方法, 映射的分岔与混沌理论是碰撞振动系统研究的理论基础. 首先简述了碰撞振动系统的分析与研究方法, 光滑非线性系统动力学的分析方法部分可以推广到碰撞振动系统, 碰撞振动的不连续性导致一些方法的适用性和有效性问题. 进一步综述了碰撞振动系统周期运动稳定性、分岔、混沌及奇异性的理论研究和工程应用现状. 最后着重结合相关离散型映射系统的动力学发展, 对碰撞振动系统的分岔与混沌研究及存在的主要问题进行了讨论, 并展望了其发展趋势.      

Vibro-impact dynamics near a strong resonance point

Two typical vibratory systems with impact are considered, one of which is a two-degree-of-freedom vibratory system impacting an unconstrained rigid body, the other impacting a rigid amplitude stop. Such models play an important role in the studies of dynamics of mechanical systems with repeated impacts. Two-parameter bifurcations of fixed points in the vibro-impact systems, associated with 1:4 strong resonance, are analyzed by using the center manifold and normal form method for maps. The single-impact periodic motion and Poincaré map of the vibro-impact systems are derived analytically. Stability and local bifurcations of a single-impact periodic motion are analyzed by using the Poincaré map. A center manifold theorem technique is applied to reduce the Poincaré map to a two-dimensional one, and the normal form map for 1:4 resonance is obtained. Local behavior of two vibro-impact systems, near the bifurcation points for 1:4 resonance, are studied. Near the bifurcation point for 1:4 strong resonance there exist a Neimark–Sacker bifurcation of period one single-impact motion and a tangent (fold) bifurcation of period 4 four-impact motion, etc. The results from simulation show some interesting features of dynamics of the vibro-impact systems: namely, the “heteroclinic” circle formed by coinciding stable and unstable separatrices of saddles, T _in, T _on and T _out type tangent (fold) bifurcations, quasi-periodic impact orbits associated with period four four-impact and period eight eight-impact motions, etc. Different routes of period 4 four-impact motion to chaos are obtained by numerical simulation, in which the vibro-impact systems exhibit very complicated quasi-periodic impact motions. The project supported by National Natural Science Foundation of China (50475109, 10572055), Natural Science Foundation of Gansu Province Government of China (3ZS061-A25-043(key item)). The English text was polished by Keren Wang.