Measuring the flexibility matrix of an eagle’s flight feather and a method to estimate the stiffness distribution

Flight feathers stand out with extraordinary mechanical properties for flight because they are lightweight but stiff enough.Their elasticity has great effects on the aerodynamics, resulting in aeroelasticity.Our primary task is to figure out the stiffness distribution of the feather to study the aeroelastic effects.The feather shaft is simplified as a beam, and the flexibility matrix of an eagle flight feather is tested.A numerical method is proposed to estimate the stiffness distributions along the shaft length based on an optimal Broyden–Fletcher–Goldfarb–Shanno(BFGS) method with global convergence.An analysis of the compressive behavior of the shaft based on the beam model shows a good fit with experimental results.The stiffness distribution of the shaft is finally presented using a 5 th order polynomial.

Mechanical property and deformation mechanism of gold nanowire with non-uniform distribution of twinned boundaries:A molecular dynamics simulation study

The mechanical property and deformation mechanism of twinned gold nanowire with non-uniform distribution of twinned boundaries(TBs)are studied by the molecular dynamics(MD)method.It is found that the twin boundary spacing(TBS)has a great effect on the strength and plasticity of the nanowires with uniform distribution of TBs.And the strength enhances with the decrease of TBS,while its plasticity declines.For the nanowires with non-uniform distribution of TBs,the differences in distribution among different TBSs have little effect on the Young's modulus or strength,and the compromise in strength appears.But the differences have a remarkable effect on the plasticity of twinned gold nanowire.The twinned gold nanowire with higher local symmetry ratio has better plasticity.The initial dislocations always form in the largest TBS and the fracture always appears at or near the twin boundaries adjacent to the smallest TBS.Some simulation results are consistent with the experimental results.

A non-uniform allowance allocation method based on interim state stiffness of machining features for NC programming of structural parts

For thin-walled parts,uniform allowance to each machining surface is allocated by the traditional machining method.Considering the sequence of the adjacent machining features,it may cause poor stiffness for some side walls due to a minor wall thickness,which may cause the deformation of the final formed parts to be large,or deduce machining efficiency for some machining features due to too thick remains.In order to address this issue,a non-uniform allowance allocation method based on interim state stiffness of machining features for the finishing of thin-walled structural parts is proposed in this paper.In this method,the interim state model of machining features is constructed according to the machining sequence of the parts,and the stiffness of the side wall is taken as the evaluation index to allocate reasonable allowance value to the corresponding machining surface to ensure the stiffness requirement of the parts in the machining process.According to the finite element simulation results,the non-uniform allowance allocation method proposed in this paper can effectively improve the stiffness of the parts and reduce the deformation of the parts,when compared with the traditional uniform allowance machining method.

RELOCATION ALGORITHM FOR NON-UNIFORM DISTRIBUTION IN MOBILE SENSOR NETWORK

Energy is the determinant factor for the survival of Mobile Sensor Networks(MSN).Based on the analysis of the energy distribution in this paper,a two-phase relocation algorithm is proposed based on the balance between the energy provision and energy consumption distribution.Our main objectives are to maximize the coverage percentage and to minimize the total distance of node movements.This algorithm is designed to meet the requirement of non-uniform distribution network applications,to extend the lifetime of MSN and to simplify the design of the routing protocol.In ad-dition,test results show the feasibility of our proposed relocation algorithm.

Study of the Non-Uniform Distribution of Earthquake Risk Within Potential Sources

Potential sources are aggregates of probable future epicenters.In this area,for source models currently,in common use for seismic risk analysis in China,the mean area of each potential source is about 3000-4000 km2.It is assumed that seismic risk has a uniform distribution within the range of each potential source,but studies have shown that the uniform distribution model to a large extent may give an underestimation of the seismic risk.In this paper,the relative distribution of historical epicenters in space within potential sources is discussed,a method is proposed to quantitatively describe the non-uniform distribution of strong earthquakes within potential sources,and some preliminary results are given.By using the results of this paper,seismic risk analysis and seismic zonation can be made more scientific and more reasonable.

Mesh stiffness calculation of cycloid-pin gear pair with tooth profile modification and eccentricity error

Cycloid speed reducers are widely used in many industrial areas due to the advantages of compact size, high reduction ratio and high stiffness. However, currently, there are not many analytical models for the mesh stiffness calculation, which is a crucial parameter for the high-fidelity gear dynamic model. This is partially due to the difficulty of backlash determination and the complexity of multi-tooth contact deformation during the meshing process. In this paper, a new method to calculate the mesh stiffness is proposed including the effects of tooth profile modification and eccentricity error. The time-varying mesh parameters and load distribution of cycloid-pin gear pair are determined based on the unloaded tooth contact analysis （TCA） and the nonlinear Hertzian contact theory, allowing accurate calculations of the contact stiffness of single tooth pair and the torsional stiffness of multi-tooth pairs. A detailed parametric study is presented to demonstrate the influences of tooth profile modification, applied torque and eccentricity error on the torsional mesh stiffness, loaded transmission error, Hertzian contact stiffness and load sharing factor. This model can be applied to further study the lost motion and dynamic characteristics of cycloid speed reducer and assist the optimization of its precision, vibration and noise levels.

Stress analytical solution for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform distributed pressure

The stress state around circular openings,such as boreholes,shafts,and tunnels,is usually needed to be evaluated.Solutions for stresses,strains and ultimate bearing capacities of pressurized hollow cylinder are common cases.Stress analytical method for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform pressure on the outer surface and uniform radial pressure on the inner surface is given.The power series method of complex function is used.The stress analytical solution is obtained with the assumption that two layers of a cylinder are fully contacted.The distributions of normal and tangential contact stress along the interface,tangential stress on the inner boundary and stresses in the radial direction at θ=0°,45° and 90°,are obtained.An example indicates that,when the elastic modulus of the inner layer of a double-layered thick-walled cylinder is smaller than that of the outer layer,the tangential stress is smaller than that in the corresponding point for a traditional cylinder composed of homogeneous materials.In that way,stress concentration at the inner surface can be alleviated and the stress distribution is more uniform.This is a capable way to enhance the elastic ultimate bearing capacity of thick-walled cylinder.

Force Analysis of the Overconstrained Mechanisms Based on Equivalent Stiffness Considering Limb Axial Deformation

Overconstrained mechanism has the advantages of large bearing capacity and high motion reliability,but its force analysis is complex and difficult because the mechanism system contains overconstraints.Considering the limb axial deformation,taking typical 2SS+P and 7-SS passive overconstrained mechanisms,2SPS+P and 7-SPS active overconstrained mechanisms,and 2SPS+P and 7-SPS passive-input overconstrained mechanisms as examples,a new force analysis method based on the idea of equivalent stiffness is proposed.The equivalent stiffness matrix of passive overconstrained mechanism is derived by combining the force balance and deformation compatibility equations with consideration of axial elastic limb deformations.The relationship between the constraint wrench magnitudes and the external force,limb stiffness is established.The equivalent stiffness matrix of active overconstrained mechanism is derived by combining the force balance and displacement compatibility equations.Here,the relationship between the magnitudes of the actuated wrenches and the external force,limb stiffness is investigated.Combining with the equivalent stiffness of the passive overconstrained mechanism,an analytical relationship between the actuated forces of passive-input overconstrained mechanism and the output displacement,limb stiffness is explored.Finally,adaptability of the equivalent stiffness to overconstrained mechanisms is discussed,and the effect of the limb stiffness on overconstrained mechanisms force distribution is revealed.The research results provide a theoretical reference for the design,research and practical application of overconstrained mechanism.

Downlink SINR and Rate Distribution of Ultra-Dense Het Nets with Burst Traffic

SINR distribution and rate overage distribution are crucial for optimization of deployment of Ultra-dense Het Nets.Most existing literatures assume that BSs have full queues and full-buffer traffic.In fact,due to ultra-dense deployment of small cells,traffic in small cell varies dramatically in time and space domains.Hence,it is more practical to investigate scenario with burst traffic.In this paper,we consider a two-tier non-uniform ultra-dense Het Net with burst traffic,where macro BSs are located according to Poisson Point Process(PPP),and pico BSs are located according to Poisson Hole Process(PHP).The closed-form expressions of SINR distribution and rate distribution are derived,and then validated through simulation.Our study shows that different from the result of full buffer case,the SINR distribution and rate distribution of users depend on the average transmission probabilities of BSs in burst traffic case.

A METHOD OF CALCULATING PRESSURE DISTRIBUTION OF PERIODIC PULSATION FLUID TRANSPORTED IN PIPING NETWORK

The pressure pulsation induced by the pumped periodic pulsation fluid is the main factor of causing fluid resonance and stimulating pipelines vibrations and noise. In order to reduce the faults caused by the vibrations of pipelines, two aspects have been researched: one is to develop high quality filters, weaken and restrain the crest of pulsation pressure; the other is to design structural parameters of the piping network and eliminate the fluid resonance. Both need calculating the pressure pulsations of different structural parameters and frequencies, and knowing the amplitude frequency. In this paper the stiffness matrix technique is used for treating the coupling of subsystems of pipelines and calculating the pressure distribution of the piping network and it is tested by simulation and experiments.

The Evolution of the Charge Density Distribution Function for Spherically Symmetric System with Zero Initial Conditions

The evolution of the charge density distribution function is simulated for both the case of a uniformly charged sphere with zero initial conditions and for the case of a non-uniform charged sphere. For the case of a uniformly charged sphere the comparison of a numerical result and an exact analytical demonstrated the agreement between the results. The process of “scattering” of a charged system under the influence of its own electric field has been illustrated on the basis of both the particle-in-cell method and the solution of the Cauchy problem for vector functions of the electric field and vector velocity field of a charged medium.

Mechanism analysis and improved model for stick-slip friction behavior considering stress distribution variation of interface

Studying the evolution of interface contact state, revealing the “black box” behavior in interface friction and establishing a more accurate friction model are of great significance to improve the prediction accuracy of mechanical system performance. Based on the principle of total reflection, a visual analysis technology of interface contact behavior is proposed. Considering the dynamic variation of stress distribution in interface contact, we analyze the nonlinear characteristics of contact parameters in different stages of stick-slip process using the above-mentioned experimental technology. Then,we find that the tangential stiffness of the interface is not a fixed value during the stick-slip process and the stress distribution variation is one of the important factors affecting the tangential stiffness of interface. Based on the previous experimental results, we present an improved stick-slip friction model, considering the change of tangential stiffness and friction coefficient caused by the stress distribution variation. This improved model can characterize the variation characteristics of contact parameters in different stages of stick-slip process, whose simulation results are in good agreement with the experimental data. This research may be valuable for improving the prediction accuracy of mechanical system performance.

Experimental study of the effects of non-uniformly distributed fine soil on mechanical properties of Shenyang–Dandong Railway coarse-grained soil

The stress produced by repeated train loads decreases with increasing railway subgrade bed depth, and slightly weathered coarse particles of subgrade bed fillings can be broken at different levels under continuous load. Thus, the mass of fine soil, with a diameter of not more than 0.075 mm, is different at different depths. Fine soil is also sensitive to frost heave and thaw settlement. In order to study the effects of non-uniformly distributed fine soil on the mechanical properties of coarse-grained soil of the Shenyang-Dandong Railway, triaxial tests were conducted with three types of specimens, un- dergoing six freeze-thaw cycle numbers （0, 1, 3, 7, 9, 12） and three confining pressures （100, 200, 300 kPa）. The freezing temperature is -5 ~C and the thawing temperature is ＋15 ~C. The stress-strain behavior, static strength, resilient modulus, cohesive force and the angle of internal friction were measured for different tested specimens. As a result, the law of static strength and resilient modulus of different specimens following the increase of freeze-thaw cycles under three confining pressures is obtained. The changing law of cohesive force and friction angle of three specimens following the increase of freeze-thaw cycles is also calculated, and the different results of different specimens are also compared.

Micro sliding friction model considering periodic variation stress distribution of contact surface and experimental verification

Micro sliding phenomenon widely exists in the operation process of mechanical systems,and the micro sliding friction mechanism is always a research hotspot.In this work,based on the total reflection method,a measuring device for interface contact behavior under two-dimensional(2D)vibration is built.The stress distribution is characterized by the light intensity distribution of the contact image,and the interface contact behavior in the 2D vibration process is studied.It is found that the vibration angle of the normal direction of the contact surface and its fluctuation affect the interface friction coefficient,the tangential stiffness,and the fluctuation amplitude of the stress distribution.Then they will affect the change of friction state and energy dissipation in the process of micro sliding.Further,an improved micro sliding friction model is proposed based on the experimental analysis,with the nonlinear change of contact parameters caused by the normal contact stress distribution fluctuation taken into account.This model considers the interface tangential stiffness fluctuation,friction coefficient hysteresis,and stress distribution fluctuation,whose simulation results are consistent well with the experimental results.It is found that considering the nonlinear effect of a certain contact parameter alone may bring a greater error to the prediction of friction behavior.Only by integrating multiple contact parameters can the accuracy of friction prediction is improved.

Improving the Performance of Fixed-Bed Catalytic Reactors by Innovative Catalyst Distribution

A comprehensive mathematical model is developed to simulate the interactions of the complex processes that take place in typical catalytic chemical reactors. This mathematical model includes correlations representing various modes of mass transport and chemical reactions. To illustrate the application and value of this approach for reactor optimizations, the model is applied to the case of series reactions with a desirable intermediate compound and the risk of degradation of this compound if the process conditions are not optimized. The modeling results show that in such cases, which are very common in practice, replacing the conventional uniform catalyst distribution with a novel non-uniform distribution will significantly improve the performance of the reactor and the production of the desirable compound. Various catalyst distribution options are compared, and a novel non-uniform loading of catalyst is identified that gives a much better performance compared to the conventional approach. The model is versatile and useful for both the design as well as the optimization of the catalytic fixed-bed reactors in a wide variety of reactor and reaction conditions.

Quantitative research of annual runoff distribution characteristics in the Dagujia River basin,Yantai,China

Mann-Kendall method and minimum variance method are used in this study to analyze the mean value variable-point of the runoff data observed by Fushan Hydrological Station in the Dagujia River basin from 1966 to 2004. Based on the results, the runoff time is divided into four periods with the similar hydrological variation character. The annual runoff distribution characters in the Dagujia River basin are discussed by using the non-uniform coefficients, concentration degree and concentration period, variation range, etc. The results indicate that: (1) River runoff is very unevenly distributed throughout the year in Dagujia River. About 90% of runoff is in the period from June to October, while the runoff from November to April of the next year is lower. (2) The annual runoff distribution characters during 1966-1971 are very similar to that of 1982-1996, and the runoff of 1972-1981 is almost similar to that of 1997-2004. (3) The annual runoff distribution characters have changed obviously during 1997-2004 compared with the other periods, which makes it more difficult to exploit and use the water resource in the future.

Effect of non-uniform stress characteristics on stress measurement in specimen

There is a remarkable difference in stress distribution between a specimen and a plate removed from the specimen.The plate presents a uniform stress distribution whereas the specimen presents a non-uniform stress distribution.Firstly,the real stress distributions in plates with thickness of 30,40 and 50 mm and then in the specimens were obtained through simulation and X-ray surface stress measurement.Secondly,in order to study the impact of specimens shapes and processing ways on the results accuracy,two irregular shapes (parallelogram and trapezoid) and two processing ways (saw and electron discharge machining (EDM)) were compared and analyzed by simulation and experiment using layer removal method,then the specimen effects on measurement results were evaluated.The results show that:1) the non-uniform stress distribution characteristics of the specimen near the surface of the cut is significant,the range of non-uniform stress distribution is approximately one-thickness distance away from the cut,and it decreases gradually along the depth;2) In order to ensure the stability in the results,it is suitable to take the specimen plane size 2-3 times of its thickness;3) Conventional processing methods have little effect on experimental results and the average deviation is less than 5%.

Discrete element modeling of the effect of particle size distribution on the small strain stiffness of granular soils

Discrete element modeling was used to investigate the effect of particle size distribution on the small strain shear stiffness of granular soils and explore the fundamental mechanism controlling this small strain shear stiffness at the particle level. The results indicate that the mean particle size has a negligible effect on the small strain shear modulus. The observed increase of the shear modulus with increasing particle size is caused by a scale effect. It is suggested that the ratio of sample size to the mean particle size should be larger than 11.5 to avoid this possible scale effect. At the same confining pressure and void ratio, the small strain shear modulus decreases as the coefficient of uniformity of the soil increases. The Poisson＇s ratio decreases with decreasing void ratio and increasing confining pressure instead of being constant as is commonly assumed. Microscopic analyses indicate that the small strain shear stiffness and Poisson＇s ratio depend uniquely on the soil＇s coordination number.

S/N Ratio of 4-Channel A/D Geological Radar Non-uniform Sampling Signals

Using the quantitative error probability density method we studied the S/N ratio of alternately sampled signals digitized by a 4-channel A/D. A complete expression for the S/N ratio of a 4-channel A/D non-uniform sampling signal was deduced. First we obtained an expression for the S/N ratio of a 1-channel A/D uniform sampling signal when the sampling frequency was equal to or greater than 2 times the frequency of the sampled signal. Based on the S/N ratio of a 2-channel A/D,alternating,non-uniform sampling signal,we analyzed the distribution of quantitative error using the quantitative error probability density method and the distribution convolution formula. From this the S/N ratio expression of a 4-channel A/D sampling signal was deduced. The simulation result shows that the deduced expression is correct.

Influence of Non-uniform Elevated Temperature on the Structural Stability and Strength of Gypsum-Sheathed Cold-Formed Steel Beam Channel Members

The objective of this paper is to computationally explore the structural stability and strength of gypsum-protected CFS(cold-formed steel)beam channel sections under non-uniform elevated temperatures when exposed to standard fire on one side of the panel and subjected to pure bending.When a CFS member is subjected to fire(or thermal gradients)its material properties change-but this change happens around the cross-section and along the length creating a member which is potentially non-uniform and unsymmetrical in its response even if the apparent geometry is uniform and symmetric.Computational finite element models were analyzed in ABAQUS to establish steady-state thermal gradients of interest.Existing test data were utilized to develop the temperature dependence of the stress-strain response.The time-dependent temperature distribution on the cross-sections obtained from heat transfer analysis was later used in the stability and collapse analyses.The stability of the models was explored to characterize how local,distortional,and global buckling of the member evolves under both uniform and non-uniform temperature distributions.Finally,collapse simulations were performed to characterize the strength under pure bending and explore directly the evolution of strength under the influence of non-uniform temperature.