Initial Angle Research Articles

Investigation of T-stress and tensile strength effect on crack tip conditions and crack initiation angle in off-axis laminate composite

In this work, five different yield criteria have been used, maximum tangential stress (MTS), maximum energy release rate (MERR), Hill-48, Hill-90, and Barlat-93, in order to determine crack initiation angle. A study is performed to investigate the effect of T-stress on crack initiation angle. For this purpose, the elastic–plastic core region is plotted, and the R-criterion suggests that the crack initiates along local minimum (negative value) or global minimum (positive value) direction depending on the stress state at the crack tip. It is found that a negative value of T-stress makes the crack move toward the loading direction (T-axis), or in other words, the crack initiation angle decreases. It also turns out that MERR and Barlat criteria show a better result for crack initiation angle. The yield surface and elastic–plastic core region have also been plotted for different tensile strengths. For the case when transverse tensile strength equals to z-direction tensile strength, Hill-48, Hill-90, and Barlat show the same yield surface, and approximately, the same crack initiation angle. Also, when transverse tensile strength is smaller than longitudinal tensile strength, crack tends to move toward x-direction (local coordinate placed on crack tip). Finally, a FE simulation is performed to numerically determine SIFs.

Nonlinear combined resonance of axially moving conical shells under interaction between transverse and parametric modes

The purpose of present paper is to establish a conical shell model for exploring combined resonance response of axially moving graphene platelets reinforced metal foams (GPLRMF) conical shells subjected to coupled external and parametric excitations in thermal environments. The Reddy's higher order shear deformation theory (HSDT) is applied to derive the stress-strain relationship, and the governing equations of the shell structure are obtained using Hamilton's principle. The displacements and boundary conditions are characterized by a set of displacement shape functions with orthogonal properties. Then, the combined resonant for the conical shell are solved, where the method of varying amplitude (MVA) is adopted for discretizing and formulating the nonlinear governing motion equations. The correctness of the steady-state approximate solutions is verified by conducting comparative analysis, where the existing valuable literature is served as reference. In addition, the effects of initial phase angle, damping interference, material property, axially moving velocity, temperature change, coning angle as well as external excitation amplitude on the vibrational mechanism are analyzed, and the jumping phenomenon, bifurcation behavior, and chaotic characteristics are discussed in detail.

A waveform command shaping control of a double pendulum with nonzero initial conditions

AbstractIn most material handling industries, input‐ and command‐shaping techniques are extensively used to transfer objects safely. In these techniques, most of the work assumes a single‐degree‐of‐freedom system with zero initial conditions, and some of these cases are not practical. In crane systems, a crane jib cannot be positioned exactly on top of the payload at the start of transfer motion, which forces the system to start with initial angles. Furthermore, when the hook is large and/or far from the payload, the system cannot be considered a single‐degree‐of‐freedom system. Not accounting for such conditions can create unwanted oscillations at the end of the motion. In this work, a closed‐form command shaping control of a double pendulum is suggested to eliminate the residual oscillations while considering nonzero initial angles. The equation of motion is derived and then solved to find the shaper constants analytically. This shaper has a selectable maneuvering time and ensures maximum cruising velocity. Several examples are implemented numerically and experimentally to evaluate the shaper's performance. Despite the nonzero initial conditions, the results showed that the shaper can effectively eliminate all induced vibrations at the end of the maneuver.

Fracture initiation pressure prediction of hydraulic fracturing for layered reservoirs considering borehole deformation

Accurately predicting fracture initiation pressure is crucial for successfully applying hydraulic fracturing technology in layered reservoirs. However, existing models overlook the effects of rock anisotropy and borehole deformation. In this study, we simplified the layered reservoir to a transversely isotropic medium and developed a model to estimate borehole deformation precisely. Based on this estimated deformation, we created a model to predict fracture initiation pressure in hydraulic fracturing. By comparing previous models and experimental data, we validated the effectiveness of these proposed models. We examined the impacts of various factors on borehole deformation, fracture initiation pressure, and initiation angle. The results revealed that circular boreholes in layered reservoirs deform into elliptical boreholes under in situ stress, with the major axis not aligning with the principal stress direction, which highlights the significant impact of rock anisotropy on borehole deformation. Furthermore, the fracture initiation pressure of hydraulic fracturing either increases or decreases following borehole deformation, depending on specific geological parameters. The calculated initiation angle after borehole deformation is within 10°, closer to previous experimental results, underscoring the notable effect of borehole deformation on hydraulic fracturing. Our research indicates that the impact of borehole deformation on hydraulic fracturing is significant and should not be overlooked. This finding will offer fresh avenues for further study in the field of hydraulic fracturing.

Triaxial experimental study of mechanical behavior of non-persistent jointed granite subjected to slight cyclic dynamic disturbances

A slight disturbance can induce fault-slip burst failure in deep rock masses. In this paper, a series of triaxial tests were conducted to investigate the strength, deformation characteristics, and failure behavior of non-persistent jointed granite specimens subjected to slight cyclic loading. A representative stress–strain curve for non-persistent jointed rock was generated and used to study the crack evolution process (initiation → propagation → coalescence). The effects of varying the joint angle and frequency and amplitude of the disturbance were then analyzed. A theoretical (fracture mechanics) model for a non-persistent joint subject to triaxial cyclic loading was also established and used to investigate the combined effects of static confining stress and slight disturbances. Finally, the mechanical mechanism by which a slight dynamic disturbance induces fault-slip burst was discussed. Our results show that the failure mode of a non-persistent jointed rock mass depends more on the joint angle than the amplitude and frequency of the slight disturbance. The disturbance induces the initiation and extension of cracks. It can also induce fracture-slip bursting once the disturbance exceeds a certain threshold. The value of this threshold depends on the initial stress state, joint angle, length, dynamic and static friction coefficients, and fracture toughness of the rock. The study thus enriches our mechanistic understanding of the crucial ingredients involved in the triggering of fault-slip rock bursts in deep rock masses by slight disturbances.

Spatio-temporal distribution of aerodynamic forces and their associated vortex drift patterns around a closed-box girder during torsional vortex-induced vibration

Torsional vortex-induced vibrations (VIVs) pose potential risks to prototype bridges with increasing spans and lower damping levels. However, the underlying mechanism remains unclear. Wind tunnel tests revealed that torsional VIVs occurred at an initial attack angle of + 3°. To unravel the VIV mechanism throughout the lock-in range, encompassing the ascent stage, amplitude extremum, and descent stage, the spatio-temporal distribution of aerodynamic forces around the bridge girder was analyzed. The results demonstrated the presence of traveling pressure waves with approximately 2.5 wavelengths and three uniformly distributed separated vortices over the upper side throughout the lock-in range. The primary source of these travelling pressure waves stemmed from the vortex drift patterns, with the aerodynamic wave travelling velocity equating the vortex drift velocity. The formation of separated vortices, known as the “double-vortex model”, occurred at the windward barrier on the upper side and windward maintenance rail on the lower side. These vortices directly imposed travelling pressure waves on the girder, thereby inducing torsional VIVs. Among them, the former vortices contributed more to the VIVs than the latter. Therefore, the formation of separated vortices and their related aerodynamic waves in the windward edge with the 2nd SVM/AWM modes predominantly governed the occurrence of torsional VIVs. Furthermore, both the ratio of the wave travelling time to the vibration period and the mean value of the wave travelling velocity ratio exhibited an inverse relationship with the VIV responses. However, the actions exerted by the vortex drift patterns were proportional to the VIV responses on both the upper and lower sides. Therefore, there existed evolutionary characteristics of aerodynamic waves and their related vortex drift patterns throughout the lock-in range, which was responsible for the “lock-in” phenomena.

Effects of water-based SiO2 nanofluids on the wettability of coal dust and particle deposition characteristics

Coal wettability plays a crucial role in the prevention of coal mine dust and associated disasters such as coal and gas outbursts. Water-based SiO2 nanofluids have emerged as promising wetting agents because of their sustainable wetting effects on coal. However, the current research on the wetting characteristics of nanofluids has predominantly focused on small coal fragments, with limited studies on coal dust. This study aims to investigate the influence of water-based SiO2 nanofluids with varying particle concentrations on the wettability of coal dust via physical experiments. The findings revealed that the modification by nanofluids significantly reduced the contact angles of the coal dust particles with the particle size ranges of 60–80, 80–100, and 100–150 mesh, compared to the initial contact angles. Moreover, higher particle concentrations resulted in smaller contact angles. Notably, the wetting effects of the nanofluid modification on coal dust were particularly prominent for larger particles. Furthermore, compared with water immersion, nanofluid modification demonstrated a significantly more positive impact on the wettability of coal dust. Notably, the SiO2 nanoparticles exhibited a wide distribution and substantial adsorption capacity on the coal surface, enabling the formation of a hydrophilic structure coverage. This study contributes to a comprehensive understanding of the wetting behavior of coal dust when exposed to water-based SiO2 nanofluids. These findings underscore the potential of nanofluids to enhance coal dust prevention and control, and provide valuable insights for future research in this field.

Comparative analysis of angular contact bearing stiffness calculated by Hertz contact and thermo-elastohydrodynamic lubrication

Stiffness is the key dynamic parameter of the angular contact ball bearing. This work established a dynamic bearing model based on Hertz theory and thermo-elastohydrodynamic lubrication (TEHL) and compared the contact angle, inner race position, and stiffness. In most cases, the stiffness calculated via Hertz was higher than when using TEHL. The axial stiffness values determined via the two theories were close, while the radial stiffness calculated via the Hertz theory was smaller than that determined by TEHL under light load and high speed. Considering the elastic deformation of the races and the initial contact angle, the results obtained by TEHL displayed a lower error rate in the experiment than Hertz.

Determination of notch stress intensity factors under mode I loading using the 3D-DIC and finite element over-deterministic methods

In this paper, the fracture behaviour of Single Edge Notched Tension Specimens (SENT) is investigated experimentally and numerically using the three-dimensional digital image correlation (3D-DIC) experimental method and the Finite Element Analysis (FEA) technique, respectively. The mode I notch stress intensity factors (NSIFs) for the SENT specimens are derived from the measured and simulated displacement fields using the Finite Element Over-Deterministic (FEOD) method. The step-by-step process of a 3D-DIC experimental system for the SENT specimens is described. The SENT specimens were tested with pinned and clamped boundary conditions (BCs) and different notch initial opening angles. There are three main contributions of the paper: (1) the derivation of the NSIFs under Mode I Loading for thin plates subjected not only to the common pinned BCs, but also to the rare, clamped BCs; (2) the application of the FEOD method to derive the NSIFs from the displacement fields measured using the 3D DIC technique and predicted using FEA; (3) the validation of the NSIFs derived numerically via experimentally-determined NSIFs for notched thin plates subjected to both pinned and clamped BCs. Thus, four sets of NSIF data are provided in the paper and enable confident application of the NSIF values for the conservative (pinned BCs) and light-weight (clamped BCs) design of notched thin plates.

Angle monitor of micromirror array for freeform illumination in lithography systems

Source and mask optimization is a critical technique for further resolution enhancement in immersion lithography systems, wherein the optimal illumination source shape is widely generated by the micromirror array. Accordingly, the accurate achievement of the allocated angles of micromirrors is a key prerequisite for the implementation of arbitrary illumination patterns. In this paper, we propose an angle monitor to ensure the high-precision tilting of thousands of biaxial micromirrors. As one of the critical modules for closed-loop control of the two-dimensional micromirror array, the online monitor feeds the monitored high-precision tilt angle back to the processing system. The angle monitor mainly consists of the spot scanning module and the angle detection module. Among them, an f-θ lens and a Fourier transform lens with satisfied performances are designed and evaluated by CODE V. Furthermore, a galvanometer and the designed f-θ lens are adopted for the generation of the spot array irradiated on the electrostatic actuated mirrors. Meanwhile, the designed Fourier transform lenses are employed to detect the corresponding tilt angles. In addition, the performance of the proposed system is identified by simulations and experiments individually. It is demonstrated that the monitorable biaxial tilt range of the system is (−2.5°, +2.5°) with a repeatability of better than 0.005°. The large-format micromirror array can be monitored completely without optical cross-talk. Through the device, a 16 × 16 micromirror array is monitored, where the initial angle with no bias voltage applied is captured and the voltage–angle relation for individual micromirrors is obtained. In general, the proposed system can be utilized in the illumination system, providing an efficient and reliable method for complex source shape generation.

Study on liquid dielectrophoresis based on double flexible electrodes simulating interdigitated pattern electrodes

Dielectrophoresis affects the surface wettability by applying a non-uniform electric field to dipoles inside dielectric liquid, achieving adjustable droplet contact angle and overcoming the saturation limitation of contact angle caused by the electrowettability effect. However, it is difficult to realize useful three-dimensional tunable optical devices because most of the driving electrodes need to be patterned. In this work, a model of double flexible electrodes simulating planar interdigitated pattern electrodes is proposed based on the dielectrophoresis. Double flexible electrodes, which are wrapped with an insulating dielectric layer and are not conductive to each other are arranged at close intervals and wound along the plane substrate to form a two-dimensional planar line wall. A hydrophobic layer is used to fill the gap and increase the initial contact angle. Ultimately, the “droplet-interdigitated planar line wall” dielectrophoresis driven-droplet model is formed after the dielectric droplets have been deposited on the line wall surface. Firstly, considering the influence of penetration depth and electrode gap area, Young’s equation is theoretically modified to adapt to this model. Then, the finite element algorithm simulation is used to used to comparatively analyze the potential distribution of this model and the planar interdigitated pattern electrode model. The field strength distributions of the electrodes with different wire diameters and insulating layer thickness values are analyzed. It can be found that with the increase of the diameter of the electrode wire and the thickness of the insulating layer, the morphology of the model changes from the tip electrode into the planar electrode, the surface field strength attenuates exponentially and the peak value decreases. This shows that the structure of this electrode in this model is superior to that of the planar electrode. After that, the contact angle of the model is measured experimentally in a range of 58°－90° under 0–250 <i>V</i><sub>rms</sub> voltage, which is in line with the theoretical expectation. At the same time, neither obvious contact angle lag nor saturation is observed in the experiment. Finally, the new electrophoretic driving droplet model constructed in this paper transforms the dielectric electrophoretic driving mode from a two-dimensional planar electrode to a one-dimensional flexible linear electrode. Because of its flexibility and plasticity, it is convenient to form a three-dimensional cavity and can be applied to more complex device structures.

Effect of Equation of State and Cutoff Density in Smoothed Particle Hydrodynamics Simulations of the Moon-forming Giant Impact

The amount of vapor in the impact-generated protolunar disk carries implications for the dynamics, devolatilization, and moderately volatile element isotope fractionation during lunar formation. The equation of state (EoS) used in simulations of the giant impact is required to calculate the vapor mass fraction (VMF) of the modeled protolunar disk. Recently, a new version of M-ANEOS (Stewart M-ANEOS) was released with an improved treatment of heat capacity and expanded experimental Hugoniot. Here, we compare this new M-ANEOS version with a previous version (N-SPH M-ANEOS) and assess the resulting differences in smoothed particle hydrodynamics (SPH) simulations. We find that Stewart M-ANEOS results in cooler disks with smaller values of VMF and in differences in disk mass that are dependent on the initial impact angle. We also assess the implications of the minimum “cutoff” density (ρ c ), similar to a maximum smoothing length, that is set as a fast-computing alternative to an iteratively calculated smoothing length. We find that the low particle resolution of the disk typically results in >40% of disk particles falling to ρ c , influencing the dynamical evolution and VMF of the disk. Our results show that the choice of EoS, ρ c , and particle resolution can cause the VMF and disk mass to vary by tens of percent. Moreover, small values of ρ c produce disks that are prone to numerical instability and artificial shocks. We recommend that future giant impact SPH studies review smoothing methods and ensure the thermodynamic stability of the disk over simulated time.

A Novel Passive Shoulder Exoskeleton Using Link Chains and Magnetic Spring Joints.

Work-related musculoskeletal disorders represent a major occupational disability issue, and 53.4% of these disorders occur in the back or shoulders. Various types of passive shoulder exoskeletons have been introduced to support the weight of the upper arm and work tools during overhead work, thereby preventing injuries and improving the work environment. The general passive shoulder exoskeleton is constructed with rigid links and joints to implement shoulder rotation, but there exists a challenge to align with the flexible joint movements of the human shoulder. Also, a force-generating part using mechanical springs require additional mechanical components to generate torque similar to the shoulder joint, resulting in increased overall volume and inertia to the upper arm. In this study, we propose a new type of passive shoulder exoskeleton that uses magnetic spring joint and link chain. The redundant degrees of freedom in the link chains enables to follow the shoulder joint movement in the horizontal direction, and the magnetic spring joint generates torque without additional parts in a compact form. Conventional exoskeletons experience a loss in the assisting torque when the center of shoulder rotation changed during arm elevation. Our exoskeleton minimizes the torque loss by customizing the installation height and initial angle of the magnetic spring joint. The performances of the proposed exoskeleton were verified by an electromyographic evaluation of shoulder-related muscles in overhead work and box lifting task.

Study of the Stability of the Mathematical Model of the Bound Pendulums Motion

The article presents a study of the dynamics of an oscillatory dissipative system of two elastically coupled pendulums in a magnetic field. Nonlinear normal modes of oscillation of a pendulum system have been studied, taking into account the resistance to the medium and the damping moment created by the elastic element. A system with two degrees of freedom is considered, in which the masses of the pendulums differ significantly, which leads to the possibility of localization of oscillations. In the following study, the mass ratio is chosen as a small parameter. For approximate calculations of magnetic forces, the Padé approximation is used, which best satisfies the experimental data. This approximation provides a very accurate description of the magnetic excitation. The presence of external influences in the form of magnetic forces and various types of loads that exist in many engineering systems significantly complicates the analysis of vibration modes of nonlinear systems. Studies have been carried out of nonlinear normal modes of oscillations in this system, one of the modes being a coupled mode, and the second being a localized mode. The oscillation modes are constructed using the multiscale method. Both regular and complex behavior when changing system parameters have been studied. The influence of these parameters was studied for small and large initial angles of inclination of the pendulum. Analytical solution based on the fourth order Runge-Kutta method compared with numerical simulation results. The initial conditions for calculating the vibration modes were determined by the analytical solution. Numerical modeling, consisting of constructing phase diagrams, trajectories in configuration space, and amplitude-frequency characteristics, allows one to evaluate the dynamics of a system, which can be either regular or complex. The stability of oscillation modes was studied using numerical analysis tests, which are implementations of the Lyapunov stability criterion. In this case, the stability of the oscillation modes is determined by assessing the orthogonal deviations of the corresponding trajectories of the oscillation modes in the configuration space.

A three-dimensional failure criterion model considering the effects of fiber misalignment on longitudinal tensile failure

This paper proposes a three-dimensional failure criterion model for unidirectional fiber-reinforced composites. In contrast to previous models that only accounted for the effect of fiber misalignment in the presence of longitudinal compressive stress, the proposed failure criterion model comprehensively considers the effect of localized misaligned regions on the failure under any stress state. Another key contribution of this study is the introduction of the effective misalignment angle. Considering effective misalignment angles, the proposed failure criterion model can reasonably reveal the effect of localized misaligned regions on the failure behavior under different stress states. The agreement between the predicted results and the experimental data proves that the proposed model has good applicability. Furthermore, the influence of initial misalignment angles on failure is analyzed under varying stress conditions. The results indicate that even under longitudinal tensile stress, the initial misalignment angle still plays an important role in the failure behavior of materials.

Research on Crystal Structure Evolution and Failure Mechanism during TSV-Metal Line Electromigration Process

The combined use of Through Silicon Via (TSV) and metal lines, referred to as TSV-metal lines, is an essential structure in three-dimensional integrated circuits. In-depth research into the electromigration failure mechanism of TSV and the microstructure evolution can serve as theoretical guidance for optimizing three-dimensional stacking. This article conducted electromigration experiments on TSV-metal line structural samples at current densities of 1.0 × 105 A/cm2, 5 × 105 A/cm2, and 1 × 106 A/cm2. Additionally, Electron Back Scattered Diffraction (EBSD) technology was employed to systematically investigate the microstructural evolution of the TSV-metal line structure profiles before and after the application of electrical testing. The results indicate that the current induces a change in the crystal orientation at the TSV-metal interface (TSV/metal interface) and the bottom metal line. This phenomenon notably depends on the initial angle between the grain orientation and the current flow direction. When the angle between the current direction and the grain orientations [001] and [010] is relatively large, the crystals are more likely to deviate in the direction where the angle between the grain orientation and the current is smaller. This is because, at this point, the current direction is precisely perpendicular to the <100> crystal plane family, where the atomic density is lowest, and the energy required for electron transport is minimal. Therefore, the current readily rotates in the direction of this crystal orientation. Before the electromigration tests, areas with a high level of misorientation were primarily concentrated at the TSV/metal interface and the corners of the TSV-metal line. However, these areas were found to be more prone to developing voids after the tests. It is conjectured that the high misorientation level leads to elevated stress gradients, which are the primary cause of cracking failures in the TSV-metal line. As the current density increases from 5 × 105 A/cm2 to 1 × 106 A/cm2, the electromigration failure phenomena in the TSV become even more severe.

Evolution of The Generalized Coordinates of Pendulum-Spring System

The pendulum-spring system studied using Hamilton equations consists of three generalized coordinates. The coordinates are the swing angle of the rod, the swing angle of the spring, and the length extension. In this case, the total Hamiltonian is complicated because of the complicated mechanical system. Six equations of motion are obtained from the Hamilton equations. The visualization of the generalized coordinates with respect to time is illustrated. In the visualization, the spring constant and the initial swing angle of the rod were varied. These variations obtained the harmonic and non-harmonic motion. The motion of such a complex system was usually sensitive to the initial values. Solving the mechanical problems with Hamiltonian formalism could familiarize students with a branch of physics with numerous indispensable applications to other branches.

The problem of double thoracic idiopathic scoliosis: a non-systematic literature review

Objective. To analyze the current situation in the community of spine surgeons regarding the determination of the zone of posterior spinal fusion for double thoracic idiopathic scoliosis.Material and Methods. The content of 16 publications containing the results of surgical correction of double thoracic scoliotic deformities was analyzed. The number of studied clinical cohorts was 25, of which in 13 groups only the right-sided main thoracic (MT) curve (MT group) was blocked, and in 12 – both MT and left-sided proximal upper thoracic (PT) curve (MT + PT group). Four parameters were analyzed in both groups: preoperative Cobb angle, preoperative curve mobility, deformity correction, and postoperative deformity progression.Results. Significant differences were found in the MT and MT + PT groups only in two cases: for the initial Cobb angle of the PT curve and the magnitude of its correction (Cobb angle before surgery minus Cobb angle immediately after the intervention). When choosing the extent of the instrumental fusion zone, the authors of the publications included in the review were guided, first of all, by the initial magnitude of the Cobb angle of the proximal thoracic curve. In the MT + PT group, it averaged 37–40° and was 11–13° more than in the MT group. At the same time, PT curve mobility in both groups is not statistically different. The achieved correction was statistically significantly greater in the МT + РT group, despite a more severe proximal curvature as compared to the MT group. Postoperative dynamics of kyphosis (both T2–T5 and T5–T12) is insignificant. The length of the instrumental spinal fusion zone has virtually no effect on the parameters of the sagittal contour of the thoracic spine. A fairly high frequency of the adding-on phenomenon development (20.6 %) indicates the presence of a connection between this complication and the dynamics of PT curve, but the available data are not enough to formulate a final conclusion. Literature data regarding patients’ self-assessment of quality of life after surgical treatment of Lenke types 1 and 2 scoliosis are scarce, although the majority of those operated on assess the result of treatment as positive.Conclusion. The problem of determining the extent of the instrumental fusion zone for double thoracic scoliosis remains unresolved. Most surgeons focus not so much on the mobility of the proximal curve, but on its magnitude. There is no consensus in predicting the development of the adding-on phenomenon; there is little information about changes in the quality of life of patients after surgery. New research is needed.

The Effect of Torsional and Bending Stiffness on the Aerodynamic Performance of Flapping Wing

For large bird-like flapping wing aircraft, the fluid–structure coupling problem is very important. Through the passive torsional deformation of the wing, sufficient thrust is generated and propulsion efficiency is ensured. Moreover, spanwise bending deformation will affect lift and thrust. The flow field on the surface of the wing and the geometric nonlinearity caused by the large deformation of the wing should be considered during the design process. Existing research methods do not solve this problem accurately and efficiently. This paper provides a method to analyze the fluid–structure coupling problem of the flapping wing which adopts the three-dimensional unsteady panel method to solve the aerodynamic force, and adopts the linear beam element model combined with the corotational formulation method to consider the geometric nonlinear deformation of the wing beam. This article compares the performance of the flapping wing with different torsional and bending stiffness, and analyzes the airfoil surface pressure coefficients at different portions of the wing during the period. The results show that torsional stiffness has a large influence on the lift coefficient, thrust coefficient and propulsion efficiency. Meanwhile, the torsional stiffness of the wing beam and the initial geometric twist angle of the wing need to be well coordinated to achieve high efficiency. Moreover, appropriate bending stiffness of the wing is conducive to improving propulsion efficiency.

Scaling behavior of granular columns collapse on erodible-inclined surfaces

This paper explores the effects of slope angle, initial column aspect ratio, and interparticle friction coefficient on the mobility and erodibility of granular columns collapsing on an erodible-inclined layer before spreading and depositing on a nonerodable-horizontal surface using Discrete Element Method. The numerical results showed that the column collapse with higher aspect ratio or smaller friction coefficient induces larger normalized kinetic energy, leading to larger granular masses out the inclined region and longer runout distance. The slope angle, on the other hand, shows trivial impacts on the kinetic energy and apparent friction coefficient. Remarkably, these physical quantities are nontrivially behaved by a new dimensionless number that incorporates the initial column aspect ratio, inclination angle, and interparticle friction coefficient. These findings may significantly complement the better understanding of the behavior of natural disaster events such as landslides, rock and snow avalanches, or pyroclastic flows on complex surfaces.