Accounting for Quadratic and Cubic Invariants in Continuum Mechanics–An Overview

The differential equations of continuum mechanics are the basis of an uncountable variety of phenomena and technological processes in fluid-dynamics and related fields.These equations contain derivatives of the first order with respect to time.The derivation of the equations of continuum mechanics uses the limit transitions of the tendency of the volume increment and the time increment to zero.Derivatives are used to derive the wave equation.The differential wave equation is second order in time.Therefore,increments of volume and increments of time in continuum mechanics should be considered as small but finite quantities for problems of wave formation.This is important for calculating the generation of sound waves and water hammer waves.Therefore,the Euler continuity equation with finite time increments is of interest.The finiteness of the time increment makes it possible to take into account the quadratic and cubic invariants of the strain rate tensor.This is a new branch in hydrodynamics.Quadratic and cubic invariants will be used in differential wave equations of the second and third order in time.

Microstructure and mechanical properties of continuous drive friction welded Ti_(2)AlNb alloy under different rotational rates

Ti_(2)AlNb-based alloy was joined in a continuous drive friction welding machine under different rotational rates(500,1000 and 1500 r/min).The microstructure and mechanical properties of the joints were investigated.It is shown that the weld zone(WZ) is fully composed of recrystallized B2 phase,and the grain size decreases with increasing rotational rate.The thermo-mechanically affected zone(TMAZ) suffers severe deformation during welding,due to which most of original precipitation phase is dissolved and streamlines are present.In the heat affected zone(HAZ),only the fine O phase is dissolved.The as-welded joint produced using 1000 r/min has the best mechanical properties,whose strength and elongation are both close to those of the base metal,while the as-welded joint obtained using 500 r/min exhibits the worst mechanical properties.Post-weld annealing treatment annihilates the deformation microstructure and fine O phase precipitates in the joints,consequently improving the mechanical properties significantly.Decomposed α_(2) phase is a weakness for the mechanical performance of the joint since microcracks are apt to form in it in the tensile test.

INVARIANT MEASURES AND UNIFORM POSITIVE ENTROPY PROPERTY FOR INVERSE LIMITS

In this paper, the interconnection of som e ergodic properties betw een a continuous selfm ap and its inverse lim itis studied. Ithas been proved that(1) theirinvariantBorelproba- bility m easures are identicalup to hom eom orphism and (2) they preserve uniform positive en- tropy property sim ultaneously. As applications, it is also proved that the upper sem i-continu- ous properties of their entropy m aps are restricted each other, and the entropy m ap of the asym ptotically h-expansivecontinuous m ap isuppersem i-continuous, atthe sam e tim e acontin- uous m ap having u.p.e. is topologicalweak-m ixing.

Mechanical properties and damage characteristics of solidified body-coal combination in continuous driving and gangue backfilling

Recovery of the coal buried under buildings,railways and water bodies and the residual coal in irregularly arranged fully mechanized mining faces is a common engineering problem facing underground coal mining.In this study,a mining technology of continuous driving and gangue backfilling(CDGB)was proposed.The technology,which can not only alleviate ground subsidence and gangue discharge,but also release the above-mentioned coals,contributes to green and efficient sustainable development of mining.The stability of the system of the solidified body-reserved coal pillar combination(S-C combination)is crucial to the CDGB technology.Therefore,it is of great significance to explore the mechanical and damage characteristics of S-C combination in the synergistic bearing process.First,four sets of differentshaped S-C combination specimens were fabricated and a S-C combination bearing structure in CDGB was constructed to explore the differences in mechanical characteristics and damage modes of different-shaped S-C combination specimens during CDGB.Subsequently,their surface strain field evolutions and acoustic emission(AE)response characteristics in the load-bearing process were obtained with the aid of the digital image correlation technique and the AE signal monitoring system.Furthermore,a damage evolution model based on AE parameters and mechanical parameters was established to clarify the damage evolution law.The following results were obtained:(1)The free area of S-C combination can serve as a quantitative index to evaluate the stability of the overburden control system;(2)The concept of critical value k of the free area was first proposed.When the free area exceeds the critical value k(free area ratio greater than 1.13),the deformation resistance and the free area changes becomes negatively correlated;(3)As the free area expands,the failure of the S-C combination specimen evolves from tensile failure to shear failure.The distribution characteristics of the axial strain field also verified such a change in the failure mode;(4)When the free area expands,the peak AE count gradually changes from“double peaks”to“a single peak”.In this process,the expansion of free area shortens the time for accumulating and releasing energy during loading.Micro cracks generated in the specimen change from a phased steep growth to a continuous increase,and the process in which micro cracks develop,converge,intersect and connect to form macro cracks accelerates.The damage evolution law concluded based on AE parameters and mechanical parameters can well characterize the damage evolution process of S-C combination,providing certain reference for the study on the synergistic bearing of S-C combination during CDGB.

The Persistence of Invariant Tori in Nearly Small Twist Mappings with Intersection Property

In this paper we investigate the nearly small twist mappings with intersection property. With a certain non-degenerate condition, we proved that the most of invariant tori of the original small twist mappings will survive afer small perturtations. The persisted invariant tori are close to the unperturbed ones when the perturbation are small. The orbits reduced by those mappings are quasi-periodic in the invariant tori with the frequences closing to the original ones.

Perturbation Analysis of Continuous-Time Linear Time-Invariant Systems

In this paper, we consider the perturbation analysis of linear time-invariant systems, which arise from the linear optimal control in continuous-time. We provide a method to compute condition numbers of continuous-time linear time-invariant systems. It solves the perturbed linear time-invariant systems via Riccati differential equations and continuous-time algebraic Riccati equations in finite and infinite time horizons. We derive the explicit expressions of measuring the perturbation bounds of condition numbers with respect to the solution of the linear time-invariant systems. Furthermore, condition numbers and their upper bounds of Riccati differential equations and continuous-time algebraic Riccati equations are also discussed. Numerical simulations show the sharpness of the perturbation bounds computed via the proposed methods.

Mechanical properties and failure behavior of 3D printed thermoplastic composites using continuous basalt fiber under high-volume fraction

Continuous basalt fiber(CBF)is an outstanding inorganic fiber produced from nature,which has a wide range of applications in the field of armor protection of national defense military.However,the mechanical response and failure mechanism of 3D printed CBF reinforced components are still not well understood.Here,the 3D printing thermoplastic composites with high volume fraction CBF have been successfully prepared by fused deposition modelling(FDM)method.The effects of fiber printing direction and polymer matrix type on the tensile and flexural properties of the 3D printed composites have been explored,and the detailed failure morphology has been characterized using scanning electron microscopy and optical microscopy.It was found that under high fiber volume fraction,3D printed CBF reinforced polyamides(PA)composites have the best ability to maintain material integrity of the composites,followed by acrylonitrile butadiene styrene(ABS)and high impact polystyrene(HIPS).Besides,the results from rule of mixtures can accurately predict the longitudinal Young’s modulus of the 3D printed specimens,but there exists a large discrepancy for the prediction of the tensile strength.The microstructure analysis shows that the failure modes of 3D printed composites mainly include fiber debonding,fiber pull-out,stress whitening and matrix cracking.

Improved continuous precipitation kinetics and tensile properties of extruded AZ80 alloy through {10-12} twin formation

This study investigates the effect of{10-12}deformation twins on the continuous precipitation behavior of an extruded Mg-8.0Al-0.5Zn-0.2Mn(AZ80)alloy during aging.The extruded AZ80 alloy is compressed along the transverse direction to introduce{10-12}twins,followed by an aging treatment at 300℃.The extruded material exhibits a twin-free microstructure with low internal strain energy,whereas the pre-twinned material possesses abundant{10-12}twins and has high internal strain energy.The aging results reveal that the peak-aging time of the pre-twinned material(1 h)is one-eighth of that of the extruded material(8 h).Although Mg_(17)Al_(12)continuous precipitates(CPs)are observed in both the peak-aged materials,these CPs are much smaller and more densely distributed in the pre-twinned material despite the significantly shorter aging time.The CPs size in the peak-aged materials increases in the following order:twinned region in the pre-twinned material(0.47μm)<residual matrix region in the pre-twinned material(1.71μm)<matrix region in the extruded material(2.55μm).Moreover,the CPs number density in the twinned region of the pre-twinned material is approximately 11 times higher than that in the matrix region of the extruded material.The peak-aged pre-twinned material exhibits significantly higher tensile strength and ductility than the peak-aged extruded material.These results demonstrate that the formation of{10-12}twins in the extruded AZ80 alloy substantially accelerates the static precipitation of CPs during aging at 300℃and improves the tensile properties of the peak-aged material.

Mechanical deformation properties of Continuous Welded Rail on kilometer-span suspension bridge for high-speed railway

The complex bridge-track interaction between kilometer-span bridges and continuous Welded Rail(CWR)brings great challenges to CWR designing.Taking a suspension bridge with laying CWR as a case,the mechanical properties of CWR on the bridge are analyzed to reveal the sensitive areas of the track,and the design method of CWR and track structures on the beam ends are proposed.The results show that the unidirectional Rail Expansion Joints(REJ)need to be installed on the beam end of the kilometer-span bridge to reduce rail longitudinal force.Due to the bridge characteristics,there is no CWR fixed area on the kilometer-span bridge,and rail longitudinal force on the main span caused by bending loads needs to be concerned.The deformation of track on the beam end is complex,which is the weak area on the kilometer bridge,the large relative displacement between the stock rail of REJ and the main beam can cause poor stability of ballast bed on beam end,small resistance fasteners need to be laid on the sides of stock rail on the main beam to increase the stability of ballast and fasteners on the beam end.To improve the driving safety and comfort of beam end,the Sleeper-Supporting Apparatus(SSA)should be specially designed to ensure the uniform transition of track on beam ends.Temperature and wind loads have a significant impact on track regularity on the kilometer span bridge,the dynamic response of trains and bridges under those loads needs to be attended to.

湿垃圾来源的蚯蚓粪肥对连作障碍土壤质量和黄瓜产量的影响

随着城市化的发展,湿垃圾产量与日俱增,湿垃圾资源化利用迫在眉睫。利用蚯蚓处理湿垃圾制作蚯蚓粪肥用于农田土壤改良,是一项有效的湿垃圾资源化利用途径以及有利于缓解蔬菜连作障碍方面问题。该文以常规有机肥为参照,选取以湿垃圾及其厌氧沼渣为原料制作的蚯蚓粪肥为研究对象,研究连续3年施加蚯蚓粪肥对黄瓜(Cucumis sativus)土壤综合质量和作物产量的影响。结果表明,经过3年的改良后,施加60.0 t/hm^(2)蚯蚓粪肥的黄瓜产量提高了5.60%,土壤有机质含量提高了50.0%,且蚯蚓粪肥的效果要高于常规有机肥;土壤全氮含量达到最高,高于背景值33.0%;土壤的养分含量(硝态氮、速效磷、速效钾)也得到了提高,其中速效钾含量升高了94.0%。经过3年的改良,土壤中的细菌数量在施加了有机肥后明显增加,其中以添加30.0t/hm^(2)蚯蚓粪肥的细菌数量最多;土壤细菌/真菌的比值有所提高,土壤生物性状得到改善。土壤的呼吸强度随着有机肥的施入而升高,以施加60.0t/hm^(2)蚯蚓粪肥的最大;土壤pH略有降低,盐度无明显变化。因此,湿垃圾来源的蚯蚓粪肥能改善土壤的理化和生物学性质,可在一定程度上缓解连作障碍的发生,可作为化肥替代品或与化肥相配合在农业生产中进行推广。

生物质炭和有机肥配施对苹果重茬育苗地土壤理化性质和微生物群落特征的影响

为研究生物质炭和有机肥配施对连作苹果育苗地的改良效果,以连作5年的苹果育苗地为研究对象,采用高通量测序技术结合土壤理化性质分析,探究不同配比生物质炭和有机肥配施对苹果根际土壤理化性质和微生物群落结构的影响。结果表明,生物质炭和有机肥配施处理后土壤中养分含量显著增加,土壤pH和电导率显著上升。其中以600kg·hm^(-2)生物质炭配施有机肥处理土壤的速效养分含量显著增加,其土壤全氮、碱解氮、速效磷、速效钾和有机碳含量分别显著增加15.06%、27.03%、61.32%、51.55%和20.18%。此外,生物质炭和有机肥处理提高了土壤中细菌群落的多样性和丰度,降低了真菌群落的多样性和丰度,使土壤中有益菌属的丰度显著增加。相关性分析表明,土壤有机碳、速效钾和碱解氮含量对土壤中细菌群落特征影响显著;而真菌群落特征主要受土壤全氮、有机碳和速效钾含量的影响。综上,生物质炭和有机肥配施对苹果育苗地连作障碍具有一定的缓解作用,可改善土壤的微环境,提高土壤质量。

TC21合金在不同温度下进行连续多步置氢处理时的显微组织及室温力学性能

利用OM、XRD、TEM以及压缩试验等方法研究TC21钛合金经不同温度连续多步置氢处理后的显微组织及室温力学性能。结果表明:当氢处理温度超过1073 K时,α相的尺寸明显降低,β相成为主要相。随着氢处理温度的升高,δ氢化物的含量呈先增加后逐渐降低的趋势。当氢处理温度超过1073 K时,TC21钛合金在室温压缩变形过程中出现应变软化现象,且该现象随氢处理温度的升高而越来越显著。随着氢处理温度的升高,TC21钛合金的极限变形率呈先降低后增加的趋势。当氢处理温度为1123 K时,TC21钛合金的极限变形率比原始合金增加67.51%。

Ag含量对低合金化Cu-Ag合金拉拔线材组织和性能的影响

采用热型水平连铸技术制备Ag含量分别为0.6%、1.0%、2.0%和4.0%的Cu-Ag合金杆坯,并将d 16.0 mm杆坯拉拔加工成d 1.0 mm的线材,利用透射电镜分析其微细组织,并测试导电和力学性能。结果表明:拉拔线材由平行于拉拔方向的纤维晶组成,Cu-0.6Ag合金线纤维晶平均宽度约为340 nm;随着Ag含量增加,纤维晶尺寸减小,Cu-4.0Ag合金线纤维晶平均宽度为115 nm。纤维晶存在显著的〈111〉取向,纤维晶晶界主要为由位错塞积形成的小角度晶界,晶内存在大量位错,并发现少量的孪晶。随着Ag含量增加,Ag元素分布由局部富集转变为Ag相析出。Cu-0.6Ag和Cu-4.0Ag合金线材导电率随Ag含量的增大而减小,分别为91.2%IACS和79.5%IACS。Cu-0.6Ag和Cu-4.0Ag合金线材抗拉强度随Ag含量的增加而增大,分别为402.6 MPa和702.9 MPa。抗拉强度提高的主要原因是细晶强化和Ag相沉淀强化作用。

3D打印连续纤维复合材料工艺、结构优化研究进展

连续纤维增强复合材料由于优异的比强度、比刚度、可设计性和轻量化特质,日益受到航空航天等高端装备制造领域的青睐.3D打印技术的发展改变了连续纤维复合材料结构的生产制造流程,使复杂结构的自由成型成为可能,为先进结构材料提供了巨大的设计空间.为充分发挥先进材料性能优势和3D打印成型灵活性,研究人员分别从材料性能和结构设计出发,探索与3D打印连续纤维复合材料相适应的设计制造一体化解决方案,实现产品创新设计和性能提升.本文系统性地回顾了面向连续纤维复合材料性能分析、工艺改进和结构优化的研究工作,结合研究实践对连续纤维复合材料的结构多尺度优化方法进行总结分析,并对未来先进材料结构设计实时化、功能化、智能化的发展趋势进行探讨和展望.

微生物菌剂对连作芹菜根际土壤真菌群落多样性与结构的影响

以宁南旱区连作4年芹菜根际土壤为研究对象,采用田间定位试验结合高通量测序技术,以常规施肥(CK)为对照,研究常规施肥+枯草·哈茨复合菌剂(MF),常规施肥+枯草芽孢杆菌(BS),常规施肥+哈茨木霉菌(TH)3个处理对芹菜连作根际土壤真菌多样性及群落组成的影响。结果表明:施用枯草·哈茨复合菌显著提高了土壤有效磷、速效钾含量,增幅分别为34.29%和9.98%。施用微生物菌剂增加了土壤脲酶、蔗糖酶活性,平均增幅分别为43.16%和12.98%,并显著改变了土壤真菌的β-多样性。被孢霉属(Mortierella)、织球壳属(Plectosphaerella)、赤霉菌属(Gibberella)、链格孢属(Alternaria)、镰刀菌属(Fusarium)是各处理优势菌属,施用枯草·哈茨复合菌显著降低了赤霉菌属、链格孢属、镰刀霉属等真菌性病原菌的相对丰度,降幅分别为59.88%、51.63%、36.13%。冗余分析表明土壤蔗糖酶、脲酶、碱性磷酸酶活性、pH值和全磷是影响真菌群落结构组成的主要驱动因子。综合而言,枯草·哈茨复合菌剂的施用不仅降低了连作芹菜根际土壤镰刀菌属、链格孢属、赤霉菌属等病原菌的富集,还通过改变有效磷、速效钾等土壤理化性质,进一步重塑土壤真菌群落结构。

Effects of technical parameters of continuous semisolid rolling on microstructure and mechanical properties of Mg-3Sn-1Mn alloy

A sloping semisolid rheo-rolling process of Mg-3Sn-1Mn alloy was developed, and the effects of process parameters on the microstructure and mechanical properties of Mg-3Sn-lMn alloy strip were studied. The results show that the primary grain average diameter of the strip increases with the increase of the roll speed. The primary grain average diameter decreases firstly and then increases with the increase of the vibration frequency, and the tensile strength and elongation of the strip increase firstly and then decrease with the increase of the vibration frequency. The primary grain average diameter increases with the increase of casting temperature, and the tensile strength and elongation of the strip decrease correspondingly. When the casting temperature is 670℃, the roll speed is 52 mm/s, and the vibration frequency is 60 Hz, Mg-3Sn-1Mn alloy strip with good properties is produced. The mechanical properties of the present product are higher than those of Mg-3Sn-lMn alloy casting with the addition of 0.87% Ce （mass fraction）.

生物质炭调控药用植物连作障碍的研究进展

我国是中药材种植大国,但不合理的栽培方式和管理措施导致中药材连作障碍在种植区普遍存在,造成药材减产变质、道地产区转移、资源保护与利用不协调等,严重影响药用植物生长发育。因此对中药材连作土壤进行修复是解决中药材连作障碍的一个关键措施。生物质炭一般呈碱性,是一种良好的土壤改良剂,能够增加土壤养分、改良酸化土壤、提升植物品质,近年来得到广泛关注与应用,因此利用生物质炭作为调理剂来缓解中药材连作障碍具有一定潜力。本文针对我国中药材连作障碍的可能成因及潜在危害,分析生物质炭在解决药用植物连作造成的土壤理化性质改变、土壤微生物区系改变、化感自毒危害等问题上的作用,并对生物质炭在药用植物生产上的应用潜力进行展望。

利用组合双曲调频信号的目标径向速度测量与测距去偏

为测定有源声呐运动目标的径向速度,提出了利用组合双曲调频信号的目标径向速度测量与测距去偏方法。分析了实数域双曲调频信号的多普勒不变性和目标测距偏差原理,给出了组合双曲调频信号的目标径向速度测量与测距去偏差的实现表示式,并研究了目标回波多亮点强度起伏背景下的组合双曲调频信号目标径向速度测量误差特性。通过对信号组合方式、信号带宽的选择以及对回波强度波形的相关处理,可提升目标径向速度的测量精度。数值仿真与海试数据分析结果表明,该方法可准确地实现对目标径向速度的单帧测定和对目标测距偏差的修正,有效支持了对目标动静的判断。

Surface quality, microstructure and mechanical properties of Cu-Sn alloy plate prepared by two-phase zone continuous casting

Cu-4.7%Sn （mass fraction） alloy plate was prepared by the self-developed two-phase zone continuous casting （TZCC） process. The relationship between process parameters of TZCC and surface quality of the alloy plate was investigated. The microstructure and mechanical properties of the TZCC alloy plate were analyzed. The results show that Cu-4.7%Sn alloy plate with smooth surface can be obtained by means of reasonable matching the entrance temperature of two-phase zone mold and the continuous casting speed. The microstructure of the TZCC alloy is composed of grains-covered grains, small grains with self-closed grain boundaries, columnar grains and equiaxed grains. Compared with cold mold continuous casting Cu-4.7%Sn alloy plate, the room temperature tensile strength and ductility of the TZCC alloy plate are greatly improved.

连续法制备短切石英纤维/酚醛树脂预混料的固化反应动力学及其模压制品性能

采用连续浸胶法,使用自制的压辊式浸胶槽制备了短切石英纤维/酚醛树脂预混料,通过红外光谱法(FT-IR)、热重分析法(TG)和差示扫描量热法(DSC)对预混料进行了表征,并研究了其固化反应动力学。结果表明,溶剂乙醇影响石英纤维的浸胶过程,连续法制备的石英纤维/酚醛树脂预混料能够降低乙醇的影响;预混料的固化工艺参数为:凝胶温度108.40℃,固化温度183.04℃,后处理温度264.47℃;固化反应级数为0.95,固化反应动力学模型为:dα/dt=Aexp(-ΔE/RT)(1-α)n=4.3×10^(12)exp(-140.74/RT)(1-α)0.95。使用模压法对所制备的预混料进行压制,得到石英纤维/酚醛树脂复合材料的模压制品,该模压制品在800℃下的质量残留率为82.3%,拉伸强度为58 MPa,断裂伸长率为0.353%,剪切强度为105 MPa,线烧蚀率为0.088 mm/s,烧蚀表面形貌未见异常,结果表明采用连续法制备的石英纤维/酚醛树脂预混料的模压制品具有较好的耐热性、烧蚀性和力学性能。