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...

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.

The strain-rate dependent response of porcine skin oriented in the fiber direction is explored under tensile loading. Quasi-static response was obtained at strain rates in the range of 10-3 s-1 to 25 s-1. Characterization of the response at even greater strain rates is accomplished by measuring the spatio-temporal evolution of the particle velocity and strain in a thin strip subjected to high speed impact loading that generates uniaxial stress conditions. These experiments indicate the formation of shock waves; the shock Hugoniot that relates particle velocity to the shock velocity and the dynamic stress to dynamic strain is obtained directly through experimental measurements, without any assumptions regarding the constitutive properties of the material.

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 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 present paper presents an experimental effort on the regeneration process of two low-speed laminar streaks in a zero-pressure-gradient laminar boundary layer. Two vertical thin wires separated by a spanwise distance of 30mm are used to introduce disturbances of two rolls of transitional Kármán vortex street to the downstream boundary layer. Both hydrogen bubble visualization and particle image velocimetry (PIV) measurement show that two lowspeed streaks are induced through leading-edge receptivity process. As these streaks develop in the downstream, two additional low-speed streaks begin to appear outboard of the flank of the original two, together with complex dynamics of streak splitting and merging. A flow pattern of four streaks aligned along the spanwise direction occurs finally in the far downstream. It is found that besides the mechanisms of streak breakdown, the streak interaction is also an important factor characterizing the instability of low speed streaks and their regeneration process.

Experimental studies of a model pump-turbine S-curve characteristics and its improvement by misaligned guide vanes (MGV) were extended to prototype pump turbine through 3-D transient flow simulations. The unsteady Reynolds-averaged Navier-Stokes equations with the SST turbulence model were used to model the transient flow within the entire flow passage of a reversible pump-turbine with and without misaligned guide vanes during turbine model start-up. The unstable S-curve and its improvement by using misaligned guide vane were verified by model test and simulation. The transient flow calculations were used to clarify the variations of pressure pulse and internal flow behavior in the entire flow passage. The use of misaligned guide vanes can eliminate the S-curve characteristics of a pump-turbine, and can significantly increase the pressure pulse amplitude in the entire flow passage and the runner radial forces during start-up. The MGV only decreased the pulse amplitude on the guide vane suction side when the rotating speed was less than 50% rated speed. The hydraulic reason is that the MGV dramatically changed the flow patterns inside the entire flow passage, and destroyed the symmetry of the flow distribution inside the guide vane and runner.

Based on the remote sensing images of algae, the present work analyzes the horizontal distribution characteristics of algal blooms in Chaohu Lake, China, which also reveals the frequency of algal blooms under different wind directions. Further, an unstructured-grid, three-dimensional finite-volume coastal ocean model (FVCOM) is applied to investigate the wind-induced currents and the transport process to explain the reason why algal blooms occur at the detected places. We first deduce the primary distribution of biomass from overlaid satellite images, and explain the formation mechanism by analyzing the pollution sources, and simulating the flow field and transportation process under prevailing wind over Chaohu Lake. And then, we consider the adjustment action of the wind on the corresponding day and develop a two-time scale approach to describe the whole formation process of algae horizontal distribution in Chaohu Lake. That is, on the longer time scale, i.e., during bloom season, prevailing wind determines the primary distribution of biomass by inducing the characteristic flow field; on the shorter time scale, i.e., on the day when bloom occurs, the wind force adjusts the primary distribution of biomass to form the final distribution of algal bloom.

The nonlinear radiated waves generated by a structure in forced motion, are simulated numerically based on the potential theory. A fully nonlinear numerical model is developed by using a higher-order boundary element method (HOBEM). In this model, the instantaneous body position and the transient free surface are updated at each time step. A Lagrangian technique is employed as the time marching scheme on the free surface. The mesh regridding and interpolation methods are adopted to deal with the possible numerical instability. Several auxiliary functions are proposed to calculate the wave loads indirectly, instead of directly predicting the temporal derivative of the velocity potential. Numerical experiments are carried out to simulate the heave motions of a submerged sphere in infinite water depth, the heave and pitch motions of a truncated flared cylinder in finite depth. The results are verified against the published numerical results to ensure the effectiveness of the proposed model. Moreover, a series of higher harmonic waves and force components are obtained by the Fourier transformation to investigate the nonlinear effect of oscillation frequency. The difference among fully nonlinear, body-nonlinear and linear results is analyzed. It is found that the nonlinearity due to free surface and body surface has significant influences on the numerical results of the radiated waves and forces.

An experiment is carried out on the surface oscillation of buoyant-thermocapillary convection in an open cylindrical annulus. When the radial temperature difference ΔT reaches a critical value ΔTc, a regular oscillation appears and soon disappears on the open surface, which varies when the liquid layer's thickness h and temperature difference ΔT are varied. With growth of ΔT, dominant frequency of the visible oscillation will grow too but is found within certain frequencies. Driving forces, buoyance and thermocapillarity, are responsible for this phenomanon and the “balance” point is considered to exist when h is between 4.5-5.0 mm. Surface oscillation region is also found restricted within a narrow gap when Bo is smaller than 3.7.

In a semi-discretized Euler-Bernoulli beam equation, the non-nearest neighboring interaction and large span of temporal scales for wave propagations pose challenges to the effectiveness and stability for artificial boundary treatments. With the discrete equation regarded as an atomic lattice with a three-atom potential, two accurate artificial boundary conditions are first derived here. Reflection coefficient and numerical tests illustrate the capability of the proposed methods. In particular, the time history treatment gives an exact boundary condition, yet with sensitivity to numerical implementations. The ALEX (almost EXact) boundary condition is numerically more effective.

Interface imperfection can significantly affect the mechanical properties and failure mechanisms as well as the strength and toughness of nanocomposites. The elastic behavior of a screw dislocation in nanoscale coating with imperfect interface is studied in the three-phase composite cylinder model. The interface between inner nanoinhomogeneity and intermediate coating is assumed as perfectly bonded. The bonding between intermediate coating and outer matrix is considered to be imperfect with the assumption that interface imperfection is uniform, and a linear spring model is adopted to describe the weakness of imperfect interface. The explicit expression for image force acting on dislocation is obtained by means of a complex variable method. The analytic results indicate that inner interface effect and outer interface imperfection, simultaneously taken into account, would influence greatly image force, equilibrium position and stability of dislocation, and various critical parameters that would change dislocation stability. The weaker interface is a very strong trap for glide dislocation and, thus, a more effective barrier for slip transmission.

Using a stiffness matrix method, we investigate the propagation behaviors of elastic waves in one-dimensional (1D) piezoelectric/piezomagnetic (PE/PM) phononic crystals (PCs) with line defects by calculating energy reflection/transmittion coefficients of quasi-pressure and quasi-shear waves. Line defects are created by the replacement of PE or PM constituent layer. The defect modes existing in the first gap are considered and the influences on defect modes of the material properties and volume fraction of the defect layers, the type of incident waves, the location of defect layer and the number of structural layers are discussed in detail. Numerical results indicate that defect modes are the most obvious when the defect layers are inserted in the middle of the perfect PCs; the types of incidence wave and material properties of the defect layers have important effects on the numbers, the location of frequencies and the peaks of defect modes, and the defect modes are strongly dependent on volume fraction of the defect layers. We hope this paper will be found useful for the design of PE/PM acoustic filters or acoustic transducer with PCs structures.

The vibro-acoustic responses and sound absorption characteristics of two kinds of periodically stiffened micro-perforated plates are analyzed theoretically. The connected periodical structures of the stiffened plates can be ribs or block-like structures. Based on fundamental acoustic formulas of the micro-perforated plate of Maa and Takahashi, semi-analytical models of the vibrating stiffened plates are developed in this paper. Approaches like the space harmonic method, Fourier transforms and finite element method (FEM) are adopted to investigate both kinds of the stiffened plates. In the present work, the vibro-acoustic responses of micro-perforated stiffened plates in the wavenumber space are expressed as functions of plate displacement amplitudes. After approximate numerical solutions of the amplitudes, the vibration equations and sound absorption coefficients of the two kinds of stiffened plates in the physical space are then derived by employing the Fourier inverse transform. In numerical examples, the effects of some physical parameters, such as the perforation ratio, incident angles and periodical distances etc., on the sound absorption performance are examined. The proposed approaches are also validated by comparing the present results with solutions of Takahashi and previous studies of stiffened plates. Numerical results indicate that the flexural vibration of the plate has a significant effect on the sound absorption coefficient in the water but has little influence in the air.

Flexible joints are usually used to transfer velocities in robot systems and may lead to delays in motion transformation due to joint flexibility. In this paper, a linkrotor structure connected by a flexible joint or shaft is firstly modeled to be a slow-fast delayed system when moment of inertia of the lightweight link is far less than that of the heavy rotor. To analyze the stability and oscillations of the slowfast system, the geometric singular perturbation method is extended, with both slow and fast manifolds expressed analytically. The stability of the slow manifold is investigated and critical boundaries are obtained to divide the stable and the unstable regions. To study effects of the transformation delay on the stability and oscillations of the link, two quantitatively different driving forces derived from the negative feedback of the link are considered. The results show that one of these two typical driving forces may drive the link to exhibit a stable state and the other kind of driving force may induce a relaxation oscillation for a very small delay. However, the link loses stability and undergoes regular periodic and bursting oscillation when the transformation delay is large. Basically, a very small delay does not affect the stability of the slow manifold but a large delay affects substantially.

The classical Lotka-Volterra (LV) model is a well-known mathematical model for prey-predator ecosystems. In the present paper, the pulse-type version of stochastic LV model, in which the effect of a random natural environment has been modeled as Poisson white noise, is investigated by using the stochastic averaging method. The averaged generalized Itô stochastic differential equation and Fokker-Planck-Kolmogorov (FPK) equation are derived for prey-predator ecosystem driven by Poisson white noise. Approximate stationary solution for the averaged generalized FPK equation is obtained by using the perturbation method. The effect of prey self-competition parameter ε2s on ecosystem behavior is evaluated. The analytical result is confirmed by corresponding Monte Carlo (MC) simulation.

Considering the axial and radial loads, a mathematical model of angular contact ball bearing is deduced with Hertz contact theory. With the coupling effects of lateral, torsional and axial vibrations taken into account, a lumped-parameter nonlinear dynamic model of helical gearrotor- bearing system (HGRBS) is established to obtain the transmission system dynamic response to the changes of different parameters. The vibration differential equations of the drive system are derived through the Lagrange equation, which considers the kinetic and potential energies, the dissipative function and the internal/external excitation. Based on the Runge-Kutta numerical method, the dynamics of the HGRBS is investigated, which describes vibration properties of HGRBS more comprehensively. The results show that the vibration amplitudes have obvious fluctuation, and the frequency multiplication and random frequency components become increasingly obvious with changing rotational speed and eccentricity at gear and bearing positions. Axial vibration of the HGRBS also has some fluctuations. The bearing has self-variable stiffness frequency, which should be avoided in engineering design. In addition, the bearing clearance needs little attention due to its slightly discernible effect on vibration response. It is suggested that a careful examination should be made in modelling the nonlinear dynamic behavior of a helical gear-rotor-bearing system.

The biomimetic locust robot hopping vehicle has promising applications in planet exploration and reconnaissance. This paper explores the bionic dynamics model of locust jumping by using high-speed video and force analysis. This paper applies hybrid rigid-flexible mechanisms to bionic locust hopping and studies its dynamics with emphasis laid on the relationship between force and jumping performance. The hybrid rigid-flexible model is introduced in the analysis of locust mechanism to address the principles of dynamics that govern locust joints and mechanisms during energy storage and take-off. The dynamic response of the biomimetic mechanism is studied by considering the flexibility according to the locust jumping dynamics mechanism. A multi-rigid-body dynamics model of locust jumping is established and analyzed based on Lagrange method; elastic knee and tarsus mechanisms that were proposed in previous works are analyzed alongside the original bionic joint configurations and their machinery principles. This work offers primary theories for take-off dynamics and establishes a theoretical basis for future studies and engineering applications.