The Journal covers all disciplines in the field of theoretical and applied mechanics, including solid mechanics, fluid mechanics, dynamics and control, and biomechanics. It explores analytical, computational and experimental progresses in all areas of mechanics. The Journal also encourages research in interdisciplinary subjects, and serves as a bridge between mechanics...

Morphology as well as kinematics is a critical determinant of performance in flapping flight. To understand the effects of the structural traits on aerodynamics of bioflyers, three rectangular wings with aspect ratios (AR) of 1, 2, and 4 performing hovering-like sinusoidal kinematics at wingtip based Reynolds number of 5 300 are experimentally investigated. Flow structures on sectional cuts along the wing span are compared. Stronger K-H instability is found on the leading edge vortex of wings with higher aspect ratios. Vortex bursting only appears on the outer spanwise locations of high-aspect-ratio wings. The vortex bursting on high-aspect-ratio wings is perhaps one of the reasons why bio-flyers normally have low-aspect-ratio wings. Quantitative analysis exhibits larger dimensionless circulation of the leading edge vortex (LEV) over higher aspect ratio wings except when vortex bursting happens. The average dimensionless circulation of AR1 and AR2 along the span almost equals the dimensionless circulation at the 50% span. The flow structure and the circulation analysis show that the sinusoidal kinematics suppresses breakdown of the LEV compared with simplified flapping kinematics used in similar studies. The Reynolds number effect results on AR4 show that in the current Re range, the overall flow structure is not sensitive to Reynolds number.

The advantage of solar sails in deep space exploration is that no fuel consumption is required. The heliocentric distance is one factor influencing the solar radiation pressure force exerted on solar sails. In addition, the solar radiation pressure force is also related to the solar sail orientation with respect to the sunlight direction. For an ideal flat solar sail, the cone angle between the sail normal and the sunlight direction determines the magnitude and direction of solar radiation pressure force. In general, the cone angle can change from 0° to 90°. However, in practical applications, a large cone angle may reduce the efficiency of solar radiation pressure force and there is a strict requirement on the attitude control. Usually, the cone angle range is restricted less more than an acute angle (for example, not more than 40°) in engineering practice. In this paper, the time-optimal transfer trajectory is designed over a restricted range of the cone angle, and an indirect method is used to solve the two point boundary value problem associated to the optimal control problem. Relevant numerical examples are provided to compare with the case of an unrestricted case, and the effects of different maximum restricted cone angles are discussed. The results indicate that (1) for the condition of a restricted cone-angle range the transfer time is longer than that for the unrestricted case and (2) the optimal transfer time increases as the maximum restricted cone angle decreases.

The low-thrust trajectory optimization with complicated constraints must be considered in practical engineering. In most literature, this problem is simplified into a two-body model in which the spacecraft is subject to the gravitational force at the center of mass and the spacecraft's own electric propulsion only, and the gravity assist (GA) is modeled as an instantaneous velocity increment. This paper presents a method to solve the fuel-optimal problem of low-thrust trajectory with complicated constraints in a full ephemeris model, which is closer to practical engineering conditions. First, it introduces various perturbations, including a third body's gravity, the nonspherical perturbation and the solar radiation pressure in a dynamic equation. Second, it builds two types of equivalent inner constraints to describe the GA. At the same time, the present paper applies a series of techniques, such as a homotopic approach, to enhance the possibility of convergence of the global optimal solution.

The recent development of the elliptic model (He, et al. Phy. Rev. E, 2006), which predicts that the space-time correlation function Cu(r,τ) in a turbulent flow has a scaling form Cu(rE, 0) with rE being a combined space-time separation involving spatial separation r and time delay τ, has stimulated considerable experimental efforts aimed at testing the model in various turbulent flows. In this paper, we review some recent experimental investigations of the space-time correlation function in turbulent Rayleigh-Bénard convection. The experiments conducted at different representative locations in the convection cell confirmed the predictions of the elliptic model for the velocity field and passive scalar field, such as local temperature and shadowgraph images. The understanding of the functional form of Cu(r,τ) has a wide variety of applications in the analysis of experimental and numerical data and in the study of the statistical properties of small-scale turbulence. A few examples are discussed in the review.

Shape modeling is fundamental to the analysis of dynamic environment and motion around asteroid. Chang'E-2 successfully made a flyby of Asteroid 4179 Toutatis and obtained plenty of high-resolution images during the mission. In this paper, the modeling method and preliminary model of Asteroid Toutatis are discussed. First, the optical images obtained by Chang'E-2 are analyzed. Terrain and silhouette features in images are described. Then, the modeling method based on previous radar model and preliminary information from optical images is proposed. A preliminary polyhedron model of Asteroid Toutatis is established. Finally, the spherical harmonic coefficients of Asteroid Toutatis based on the polyhedron model are obtained. Some parameters of model are analyzed and compared. Although the model proposed in this paper is only a preliminary model, this work offers a valuable reference for future high-resolution models.

The motion of a surface vehicle on/above an irregular object is investigated for a potential interest in the insitu explorations to asteroids of the solar system. A global valid numeric method, including detailed gravity and geomorphology, is developed to mimic the behaviors of the test particles governed by the orbital equations and surface coupling effects. A general discussion on the surface mechanical environment of a specified asteroid, 1620 Geographos, is presented to make a global evaluation of the surface vehicle's working conditions. We show the connections between the natural trajectories near the ground and differential features of the asteroid surface, which describes both the good and bad of typical terrains from the viewpoint of vehicles' dynamic performances. Monte Carlo simulations are performed to take a further look at the trajectories of particles initializing near the surface. The simulations reveal consistent conclusions with the analysis, i.e., the openfield flat ground and slightly concave basins/valleys are the best choices for the vehicles' dynamical security. The dependence of decending trajectories on the releasing height is studied as an application; the results show that the pole direction (where the centrifugal force is zero) is the most stable direction in which the shift of a natural trajectory will be well limited after landing. We present this work as an example for pre-analysis that provides guidance to engineering design of the exploration site and routing the surface vehicles.

This paper summarizes a few cases of spacecraft orbital motion around asteroid for which averaging method can be applied, i.e., when central body rotates slowly, fast, and when a spacecraft is near to the resonant orbits between the spacecraft mean motion and the central body's rotation. Averaging conditions for these cases are given. As a major extension, a few classes of near resonant orbits are analyzed by the averaging method. Then some resulted conclusions of these averaging analyses are applied to understand the stability regions in a numerical experiment. Some stability conclusions are obtained. As a typical example, it is shown in detail that near circular 1:2 resonant orbit is always unstable.

Asteroid exploration is currently one of the most concerned topics among international space agencies. Orbital dynamics and navigation are obviously crucial for asteroid exploration. This paper aims to give a brief review on the dynamics, control and navigation of asteroid reconnaissance orbits, including the heliocentric transfer orbit and near asteroid orbit. The developments in optimization techniques of the transfer segment are discussed in detail. We surveyed global researches in this field and made comments on several important progresses. The final section proposed a prospective of future studies with emphasis on the key techniques of these issues in the asteroid exploration missions.

A method for classifying orbits near asteroids under a polyhedral gravitational field is presented, and may serve as a valuable reference for spacecraft orbit design for asteroid exploration. The orbital dynamics near asteroids are very complex. According to the variation in orbit characteristics after being affected by gravitational perturbation during the periapsis passage, orbits near an asteroid can be classified into 9 categories: (1) surroundingto-surrounding, (2) surrounding-to-surface, (3) surroundingto-infinity, (4) infinity-to-infinity, (5) infinity-to-surface, (6) infinity-to-surrounding, (7) surface-to-surface, (8) surfaceto-surrounding, and (9) surface-to-infinity. Assume that the orbital elements are constant near the periapsis, the gravitation potential is expanded into a harmonic series. Then, the influence of the gravitational perturbation on the orbit is studied analytically. The styles of orbits are dependent on the argument of periapsis, the periapsis radius, and the periapsis velocity. Given the argument of periapsis, the orbital energy before and after perturbation can be derived according to the periapsis radius and the periapsis velocity. Simulations have been performed for orbits in the gravitational field of 216 Kleopatra. The numerical results are well consistent with analytic predictions.

Three surface integral approaches of the acoustic analogies are studied to predict the noise from three conceptual configurations of three-dimensional high-lift low-noise wings. The approaches refer to the Kirchhoff method, the Ffowcs Williams and Hawkings (FW-H) method of the permeable integral surface and the Curle method that is known as a special case of the FW-H method. The first two approaches are used to compute the noise generated by the core flow region where the energetic structures exist. The last approach is adopted to predict the noise specially from the pressure perturbation on the wall. A new way to construct the integral surface that encloses the core region is proposed for the first two methods. Considering the local properties of the flow around the complex object–the actual wing with high-lift devices–the integral surface based on the vorticity is constructed to follow the flow structures. The surface location is discussed for the Kirchhoff method and the FW-H method because a common surface is used for them. The noise from the core flow region is studied on the basis of the dependent integral quantities, which are indicated by the Kirchhoff formulation and by the FW-H formulation. The role of each wall component on noise contribution is analyzed using the Curle formulation. Effects of the volume integral terms of Lighthill's stress tensors on the noise prediction are then evaluated by comparing the results of the Curle method with the other two methods.

Morphology as well as kinematics is a critical determinant of performance in flapping flight. To understand the effects of the structural traits on aerodynamics of bioflyers, three rectangular wings with aspect ratios (AR) of 1, 2, and 4 performing hovering-like sinusoidal kinematics at wingtip based Reynolds number of 5 300 are experimentally investigated. Flow structures on sectional cuts along the wing span are compared. Stronger K-H instability is found on the leading edge vortex of wings with higher aspect ratios. Vortex bursting only appears on the outer spanwise locations of high-aspect-ratio wings. The vortex bursting on high-aspect-ratio wings is perhaps one of the reasons why bio-flyers normally have low-aspect-ratio wings. Quantitative analysis exhibits larger dimensionless circulation of the leading edge vortex (LEV) over higher aspect ratio wings except when vortex bursting happens. The average dimensionless circulation of AR1 and AR2 along the span almost equals the dimensionless circulation at the 50% span. The flow structure and the circulation analysis show that the sinusoidal kinematics suppresses breakdown of the LEV compared with simplified flapping kinematics used in similar studies. The Reynolds number effect results on AR4 show that in the current Re range, the overall flow structure is not sensitive to Reynolds number.

The phase change between the forewing and hindwing is a distinct feature that sets dragonfly apart from other insects. In this paper, we investigated the aerodynamic effects of varying forewing-hindwing phase difference with a 60° inclined stroke plane during hovering flight. Force measurements on a pair of mechanical wing models showed that in-phase flight enhanced the forewing lift by 17% and the hindwing lift was reduced at most phase differences. The total lift of both wings was also reduced at most phase differences and only increased at a phase range around in-phase. The results may explain the commonly observed behavior of the dragonfly where 0° is employed in acceleration. We further investigated the wing-wing interaction mechanism using the digital particle image velocimetry (PIV) system, and found that the forewing generated a downwash flow which is responsible for the lift reduction on the hindwing. On the other hand, an upwash flow resulted from the leading edge vortex of the hindwing helps to enhance lift on the forewing. The results suggest that the dragonflies alter the phase differences to control timing of the occurrence of flow interactions to achieve certain aerodynamic effects.

The dynamic performance and wake structure of flapping plates with different shapes were studied using multi-block lattice Boltzman and immersed boundary method. Two typical regimes relevant to thrust behavior are identified. One is nonlinear relation between the thrust and the area moment of plate for lower area moment region and the other is linear relation for larger area moment region. The tendency of the power variation with the area moment is reasonably similar to the thrust behavior and the efficiency decreases gradually as the area moment increases. As the mechanism of the dynamic properties is associated with the evolution of vortical structures around the plate, the formation and evolution of vortical structures are investigated and the effects of the plate shape, plate area, Strouhal number and Reynolds number on the vortical structures are analyzed. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to flapping locomotion.

The choices of insect wing kinematic programs is not well understood, particularly the mechanism by which an insect selects a distortion to achieve flight control. A methodology to evaluate prospective kinematic control inputs is presented based on the reachable states when control actuation was constrained to a unit of power. The method implements a computationally-derived reduced order model of the insect's flight dynamics combined with calculation of power requirement. Four kinematic inputs are evaluated based on this criterion for a Drosophila size insect in forward flight. Stroke bias is shown to be the dominant control input using this power normalized evaluation measure.

Flexible wings of insects and bio-inspired micro air vehicles generally deform remarkably during flapping flight owing to aerodynamic and inertial forces, which is of highly nonlinear fluid-structure interaction (FSI) problems. To elucidate the novel mechanisms associated with flexible wing aerodynamics in the low Reynolds number regime, we have built up a FSI model of a hawkmoth wing undergoing revolving and made an investigation on the effects of flexible wing deformation on aerodynamic performance of the revolving wing model. To take into account the characteristics of flapping wing kinematics we designed a kinematic model for the revolving wing in two-fold: acceleration and steady rotation, which are based on hovering wing kinematics of hawkmoth, Manduca sexta. Our results show that both aerodynamic and inertial forces demonstrate a pronounced increase during acceleration phase, which results in a significant wing deformation. While the aerodynamic force turns to reduce after the wing acceleration terminates due to the burst and detachment of leading-edge vortices (LEVs), the dynamic wing deformation seem to delay the burst of LEVs and hence to augment the aerodynamic force during and even after the acceleration. During the phase of steady rotation, the flexible wing model generates more ver-tical force at higher angles of attack (40°-60°) but less horizontal force than those of a rigid wing model. This is because the wing twist in spanwise owing to aerodynamic forces results in a reduction in the effective angle of attack at wing tip, which leads to enhancing the aerodynamics performance by increasing the vertical force while reducing the horizontal force. Moreover, our results point out the importance of the fluid-structure interaction in evaluating flexible wing aerodynamics: the wing deformation does play a significant role in enhancing the aerodynamic performances but works differently during acceleration and steady rotation, which is mainly induced by inertial force in acceleration but by aerodynamic forces in steady rotation.

Passive flexibility was found to enhance propulsive efficiency in swimming animals. In this study, we numerically investigate the roles of structural resonance and hydrodynamic wake resonance in optimizing efficiency of a flexible plunging foil. The results indicates that (1) optimal efficiency is not necessarily achieved when the driving frequency matches the structural eigenfrequency; (2) optimal efficiency always occurs when the driving frequency matches the wake resonant frequency of the time averaged velocity profile. Thus, the underlying principle of efficient propulsion in flexible plunging foil is the hydrodynamic wake resonance, rather than the structural resonance. In addition, we also found that whether the efficiency can be optimized at the structural resonant point depends on the strength of the leading edge vortex relative to that of the trailing edge vortex. The result of this work provides new insights into the role of passive flexibility in flapping-based propulsion.

The dynamic flight stability of a model dronefly in hovering and upward flight is studied. The method of computational fluid dynamics is used to compute the stability derivatives and the techniques of eigenvalue and eigenvector used to solve the equations of motion. The major finding is as following. Hovering flight of the model dronefly is unstable because of the existence of an unstable longitudinal and an unstable lateral natural mode of motion. Upward flight of the insect is also unstable, and the instability increases as the upward flight speed increases. Inertial force generated by the upward flight velocity coupled with the disturbance in pitching angular velocity is responsible for the enhancement of the instability.

The welding heat source models and the plastic tension zone sizes of a typical weld joint involved in the double floor structure of high speed train under different welding parameters were calculated by a thermal-elastic-plastic FEM analysis based on SYSWELD code. Then, the welding distortion of floor structure was predicted using a linear elastic FEM and shrinkage method based onWeld Planner software. The effects of welding sequence, clamping configuration and reverse deformation on welding distortion of floor structure were examined numerically. The results indicate that the established elastic FEM model for floor structure is reliable for predicting the distribution of welding distortion in view of the good agreement between the calculated results and the measured distortion for real double floor structure. Compared with the welding sequence, the clamping configuration and the reverse deformation have a significant influence on the welding distortion of floor structure. In the case of 30mm reverse deformation, the maximum deformation can be reduced about 70% in comparison to an actual welding process.

The running safety of high-speed trains has become a major concern of the current railway research with the rapid development of high-speed railways around the world. The basic safety requirement is to prevent the derailment. The root causes of the dynamic derailment of highspeed trains operating in severe environments are not easy to identify using the field tests or laboratory experiments. Numerical simulation using an advanced train-track interaction model is a highly efficient and low-cost approach to investigate the dynamic derailment behavior and mechanism of high-speed trains. This paper presents a three-dimensional dynamic model of a high-speed train coupled with a ballast track for dynamic derailment analysis. The model considers a train composed of multiple vehicles and the nonlinear inter-vehicle connections. The ballast track model consists of rails, fastenings, sleepers, ballasts, and roadbed, which are modeled by Euler beams, nonlinear spring-damper elements, equivalent ballast bodies, and continuous viscoelastic elements, in which the modal superposition method was used to reduce the order of the partial differential equations of Euler beams. The commonly used derailment safety assessment criteria around the world are embedded in the simulation model. The train-track model was then used to investigate the dynamic derailment responses of a high-speed train passing over a buckled track, in which the derailment mechanism and train running posture during the dynamic derailment process were analyzed in detail. The effects of train and track modelling on dynamic derailment analysis were also discussed. The numerical results indicate that the train and track modelling options have a significant effect on the dynamic derailment analysis. The inter-vehicle impacts and the track flexibility and nonlinearity should be considered in the dynamic derailment simulations.

When the operation speed of the high-speed train increases and the weight of the carbody becomes lighter, not only does the sensitivity of the wheel/rail contact get higher, but also the vibration frequency range of the vehicle system gets enlarged and more frequencies are transmitted from the wheelset to the carbody. It is important to investigate the vibration characteristics and the dynamic frequency transmission from the wheel/rail interface to the carbody of the high-speed electric multi-uint (EMU). An elastic highspeed vehicle dynamics model is established in which the carbody, bogieframes, and wheelsets are all dealt with as flexible body. A rigid high-speed vehicle dynamics model is set up to compare with the simulation results of the elastic model. In the rigid vehicle model, the carbody, bogieframes and wheelsets are treated as rigid component while the suspension and structure parameters are the same as used in the elastic model. The dynamic characteristic of the elastic high speed vehicle is investigated in time and frequency domains and the difference of the acceleration, frequency distribution and transmission of the two types of models are presented. The results show that the spectrum power density of the vehicle decreases from the wheelset to the carbody and the acceleration transmission ratio is approximately from 1% to 10% for each suspension system. The frequency of the wheelset rotation is evident in the vibration of the flexible model and is transmitted from the wheelset to the bogieframe and to the carbody. The results of the flexible model are more reasonable than that of the rigid model. A field test data of the high speed train are presented to verify the simulation results. It shows that the simulation results are coincident with the field test data.

Generating electric energy from mechanical vibration using a piezoelectric circular membrane array is presented in this paper. The electrical characteristics of the functional array consisted of three plates with varies tip masses are examined under dynamic conditions. With an optimal load resistor of 11 kΩ, an output power of 21.4mW was generated from the array in parallel connection at 150 Hz under a pre-stress of 0.8N and a vibration acceleration of 9.8m/s2. Moreover, the broadband energy harvesting using this array still can be realized with different tip masses. Three obvious output power peaks can be obtained in a frequency spectra of 110 Hz to 260 Hz. The results show that using a piezoelectric circular diaphragm array can increase significantly the output of energy compared with the use of a single plate. And by optimizing combination of tip masses with piezoelectric elements in array, the frequency range can be tuned to meet the broadband vibration. This array may possibly be exploited to design the energy harvesting for practical applications such as future high speed rail.

The influences of steady aerodynamic loads on hunting stability of high-speed railway vehicles were investigated in this study. A mechanism is suggested to explain the change of hunting behavior due to actions of aerodynamic loads: the aerodynamic loads can change the position of vehicle system (consequently the contact relations), the wheel/rail normal contact forces, the gravitational restoring forces/moments and the creep forces/moments. A mathematical model for hunting stability incorporating such influences was developed. A computer program capable of incorporating the effects of aerodynamic loads based on the model was written, and the critical speeds were calculated using this program. The dependences of linear and nonlinear critical speeds on suspension parameters considering aerodynamic loads were analyzed by using the orthogonal test method, the results were also compared with the situations without aerodynamic loads. It is shown that the most dominant factors affecting linear and nonlinear critical speeds are different whether the aerodynamic loads considered or not. The damping of yaw damper is the most dominant influencing factor for linear critical speeds, while the damping of lateral damper is most dominant for nonlinear ones. When the influences of aerodynamic loads are considered, the linear critical speeds decrease with the rise of cross wind velocity, whereas it is not the case for the nonlinear critical speeds. The variation trends of critical speeds with suspension parameters can be significantly changed by aerodynamic loads. Combined actions of aerodynamic loads and suspension parameters also affect the critical speeds. The effects of such joint action are more obvious for nonlinear critical speeds.

One of the major problems in structural fatigue life analysis is establishing structural load spectra under actual operating conditions. This study conducts theoretical research and experimental validation of quasi-static load spectra on bogie frame structures of high-speed trains. The quasistatic load series that corresponds to quasi-static deformation modes are identified according to the structural form and bearing conditions of high-speed train bogie frames. Moreover, a force-measuring frame is designed and manufactured based on the quasi-static load series. The load decoupling model of the quasi-static load series is then established via calibration tests. Quasi-static load-time histories, together with online tests and decoupling analysis, are obtained for the intermediate range of the Beijing—Shanghai dedicated passenger line. The damage consistency calibration of the quasi-static discrete load spectra is performed according to a damage consistency criterion and a genetic algorithm. The calibrated damage that corresponds with the quasi-static discrete load spectra satisfies the safety requirements of bogie frames.

The incipient motion of sand particle from sand bed plays a very important role in the prediction of windblown sand. In this paper, we proposed a new method for predicting the incipient motion of sand particle based on wind speed fluctuation as follows, when the wind speed is larger than the critical wind speed, if the total impulse on sand particle is larger than the critical impulse, incipient motion of sand particle would take place, otherwise if not. Furthermore, from the analysis of entrainment in the rolling and lifting modes, we come to the following conclusion. When the average wind speed is smaller than the critical wind speed, if the average wind speed is used to judge the incipient motion of sand particle, one will underestimate the number of sand particles jumping from the bed, if the instantaneous wind speed is used to judge incipient motion of sand particle, one will overestimate the number of sand particles jumping from the bed; When the average wind speed is larger than the critical wind speed, either the average or the instantaneous wind speeds is used to judge the incipient motion of sand particles, one will overestimate the number of sand particles jumping from the bed.

An accurate evaluation of strongly singular domain integral appearing in the stress representation formula is a crucial problem in the stress analysis of functionally graded materials using boundary element method. To solve this problem, a singularity separation technique is presented in the paper to split the singular integral into regular and singular parts by subtracting and adding a singular term. The singular domain integral is transformed into a boundary integral using the radial integration method. Analytical expressions of the radial integrals are obtained for two commonly used shear moduli varying with spatial coordinates. The regular domain integral, after expressing the displacements in terms of the radial basis functions, is also transformed to the boundary using the radial integration method. Finally, a boundary element method without internal cells is established for computing the stresses at internal nodes of the functionally graded materials with varying shear modulus.

Because of the interaction between film and substrate, the film buckling stress can vary significantly, depending on the delamination geometry, the film and substrate mechanical properties. The Mexican hat effect indicates such interaction. An analytical method is presented, and related dimensional analysis shows that a single dimensionless parameter can effectively evaluate the effect.

The mass loss and nose blunting of a projectile during high-speed deep penetration into concrete target may cause structural destruction and ballistic trajectory instability of the penetrator, obviously reducing the penetration efficiency of penetrator. Provided that the work of friction between projectile and target is totally transformed into the heat to melt penetrator material at its nose surface, an engineering model is established for the mass loss and nose-blunting of the ogive-nosed projectile. A dimensionless formula for the relative mass loss of projectile is obtained by introducing the dimensionless impact function I and geometry function N of the projectile. The critical value V0c of the initial striking velocity is formulated, and the mass loss of projectile tends to increase weakly nonlinearly with I/N when V0 > V0c, whilst the mass loss is proportional to the initial kinetic energy of projectile when V0 V0c. The theoretical prediction of V0c is further confirmed to be very close to the experimental value of 1.0 km/s based on 11 sets of different penetration tests. Also the validity of the proposed expressions of mass loss and nose-blunting coefficients of a projectile are verified by the tests. Therefore, a theoretical basis is for the empirical conclusions drawn in previous publications. Regarding the completely empirical determinations of the mass loss and nose-blunting coefficients given in previous papers, the present analysis reveals its physical characteristic and also guarantees its prediction accuracy. The engineering model established in the present paper forms the basis for further discussions on the structural stability and the terminal ballistic stability of ogive-nosed projectiles high-speed penetrating into concrete targets, which will respectively be elaborated in Part II and Part III of the present study.

The initial oblique and attacking angles as well as the asymmetrical nose abrasion may lead to bending or even fracture of a projectile, and the penetration efficiency decreases distinctly. The structural stability of a high-speed projectile non-normally penetrating into concrete and the parametric influences involved are analyzed with the mass abrasion taken into account. By considering the symmetrical or asymmetrical nose abrasion as well as the initial oblique and attacking angles, both the axial and the transverse drag forces acting on the projectile are derived. Based on the ideal elastic-plastic yield criterion, an approach is proposed for predicting the limit striking velocity (LSV) that is the highest velocity at which no yielding failure has occurred and the projectile can still maintain its integral structural stability. Furthermore, some particular penetration scenarios are separately discussed in detail. Based on the engineering model for the mass loss and nose-blunting of ogive-nose projectiles established in Part I of this study, the above approach is validated by several high-speed penetration tests. The analysis on parametric influences indicates that the LSV is reduced with an increase in the asymmetrical nose abrasion, the length-diameter-ratio, and the concrete strength, as well as the oblique and attacking angles. Also, the LSV raises with an increase in the initial caliber-radius-head (CRH) and the dimensionless cartridge thickness of a projectile.

A local pseudo arc-length method (LPALM) for solving hyperbolic conservation laws is presented in this paper. The key idea of this method comes from the original arc-length method, through which the critical points are bypassed by transforming the computational space. The method is based on local changes of physical variables to choose the discontinuous stencil and introduce the pseudo arc-length parameter, and then transform the governing equations from physical space to arc-length space. In order to solve these equations in arc-length coordinate, it is necessary to combine the velocity of mesh points in the moving mesh method, and then convert the physical variable in arclength space back to physical space. Numerical examples have proved the effectiveness and generality of the new approach for linear equation, nonlinear equation and system of equations with discontinuous initial values. Non-oscillation solution can be obtained by adjusting the parameter and the mesh refinement number for problems containing both shock and rarefaction waves.

Asteroid exploration trajectories which start from a lunar orbit are investigated in this work. It is assumed that the probe departs from lunar orbit and returns to the vicinity of Earth, then escapes from the Earth by performing a perigee maneuver. A low-energy transfer in Sun-Earth- Moon system is adopted. First, the feasible region of lowenergy transfer from lunar orbit to perigee within 5 000 km height above the Earth surface in Sun-Earth-Moon system is calculated and analyzed. Three transfer types are found, i.e., large maneuver and fast transfers, small maneuver and fast transfers, and disordered and slow transfers. Most of feasibility trajectories belong to the first two types. Then, the lowenergy trajectory leg from lunar orbit to perigee and a heliocentric trajectory leg from perigee to asteroid are patched by a perigee maneuver. The optimal full-transfer trajectory is obtained by exploiting the differential evolution algorithm. Finally, taking 4179 Toutatis asteroid as the target, some low-energy transfer trajectories are obtained and analyzed.

A skip entry guidance algorithm blending numerical predictor-corrector and nominal trajectory tracking is presented for lunar return vehicles. The guidance is decoupled into longitudinal and lateral channels. A piecewise bank-vs-energy magnitude profile and a sign profile are adopted in the skip phase. A magnitude parameter is used to adjust the predicted downrange, and a pseudo-crossrange at the beginning of the final phase is selected as the lateral control variable. Prediction biases of both channels are nullified by a false position iteration algorithm. An on-line estimation and modeling method is introduced to compensate for aerodynamic and atmospheric uncertainties. A nominal trajectory for the final phase is generated based on actual reenter conditions, and the obtained nominal trajectory is tracked by a linear feedback law. A lateral corridor is used to manage the lateral state. The proposed guidance algorithm is assessed using three-degree-of-freedom Monte Carlo analyses, and the results show a satisfactory and robust performance under highly stressful dispersions.

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.