高超声速机翼非线性颤振特性分析

采用3阶修正活塞理论推导二元高超声速机翼的非线性气动弹性动力学方程。选取几组系统参数,分别通过求取系统特征值,得到线性颤振速度。以及在考虑非线性效应时,分析系统在不同流速下的动力学响应特性。数值仿真的结果表明系统的非线性效应可以延迟或提前极限环振荡的产生。     

Assessment of the efficiency of Kriging surrogate models for structural reliability analysis

This paper presents an assessment of the efficiency of the Kriging interpolation models as surrogate models for structural reliability problems involving time-consuming numerical models such as nonlinear finite element analysis structural models. The efficiency assessment is performed through a systematic comparison of the accuracy of the failure probability predictions based on the first-order reliability method using the most common first- and second-order polynomial regression models and the Kriging interpolation models as surrogates for the true limit state function. An application problem of practical importance in the field of marine structures that requires the evaluation of a nonlinear finite element structural model is adopted as numerical example. The accuracy of the failure probability predictions is characterised as a function of the number of support points, dispersion of the support points in relation to the so-called design point and order of the Kriging basis functions. It is shown with the application problem considered that the Kriging interpolation models are efficient surrogate models for structural reliability problems and can provide significantly more accurate failure probability predictions as compared with the most common polynomial regression models.     

Limit cycle analysis for electro‐hydraulic systems with friction

Abstract

In this paper, a graphical prediction method is developed to effectively predict the existence of the limit cycles induced by nonlinear friction force in an electro‐hydraulic control system. The friction‐induced nonlinearity is linearized by its corresponding describing function. Then the stability equation method, accompanied by the parameter plane method, provides a useful tool for the establishment of necessary conditions to sustain a limit cycle in the controller coefficient plane. Henceforth, the limit cycles are predicted in a graphical way, and simulations are carried out to verify the accuracy of the prediction method.     

Fatigue limit estimated using finite lives

For metallic material one is interested in estimating the fatigue limit although it is impossible to test if a specimen has infinite life. In this paper two models are compared. One model estimates the fatigue limit and another estimates the endurance limit. The model which estimates the endurance limit is a model which only uses the information that a specimen has broken or not broken at a certain stress level. The model which estimates the fatigue limit also uses the information about when the specimen is broken, i.e., after how many cycles the specimen breaks. The two models are compared, both on real and simulated staircase tests. It is shown that it is possible to estimate the distribution of the fatigue limit although the fatigue limit itself is impossible to observe. When the two models give very different estimates it indicates that the chosen run‐out level is too low.     

海洋浮游生物粒径谱分析技术

提出了一种基于浮游生物粒径组成和数量分布关系的生物粒径谱研究方法。这一方法可最大限度地将粒径分组,形成近乎连续的谱图,并利用自然海水样品验证了该技术在浮游生物粒径结构研究中的应用效果,表明该技术对于海洋生态群落结构研究和环境监测等具有广阔的应用前景。     

Effects of the 65 mph speed limit on injury morbidity and mortality

Effective December 1987 and January 1988, the maximum speed limit on rural limited access highways in Michigan was raised from 55 mph to 65 mph. This study examined the effects of the raised limit on injury morbidity and mortality. A multiple time-series design was used, comparing roads where the speed limit was raised with roads where the limit remained unchanged. Data were collected on numbers and rates of automobile crashes, injuries, and deaths from January 1978 through December 1988. Time-series intervention analyses were conducted to estimate effects associated with the speed limit change while controlling for long-term trends, seasonal cycles, and other patterns. Statistical controls were also included for major factors known to influence crash and injury rates. Results revealed significant increases in casualties on roads where the speed limit was raised, including a 19.2% increase in fatalities, a 39.8% increase in serious injuries, and a 25.4% increase in moderate injuries. Fatalities also increased on 55 mph limited access freeways, suggesting that the 65 mph limit may have spillover effects on segments of freeways where the limit was not changed. No significant changes in fatalities or injuries were found on other types of roads. The increased convenience of reduced travel time with the higher speed limit is obtained at a significant cost in terms of injury morbidity and mortality.     

Permissible crack widths in steel fibre reinforced marine concrete

The paper presents some results from a continuing study of the marine durability of steel fibre reinforced concrete. The overall aim of the investigation is to develop the material for marine applications. The results reported here pertain to pre-cracked specimens of steel fibre reinforced concrete which were exposed to wet-dry cycles of marine spray in the laboratory simulating tidal zone conditions of exposure. Two types of concrete mixes were used in the investigation—one with standard concrete constituents and OPC and the second replacing about 26% of cement with pfa. The cement content of the mixes was 590 and 435 kg m⁻³, respectively. Fibre reinforcement was provided by means of low carbon steel fibres and melt extract steel fibres at a v _f ℓ/d ratio of 100 and 147. Prism specimens were manufactured and these were precracked to induce cracks of width ranging between 0.03 and 1.73 mm. After cracking, both sealed and unsealed specimens were exposed to laboratory marine spray cycles using sea water. Some control specimens were cured in the laboratory air throughout. Tests were carried out after 650 marine cycles (450 days) and 1450 marine cycles (900 days). Based on data on flexural strength, energy absorption capacity, stiffness and state of corrosion of the fibres, recommendations are made regarding suitable permissible crack widths for the design of steel fibre reinforced concrete for marine applications. The results indicate that a permissible crack width of 0.2 mm is satisfactory for concrete reinforced with melt extract fibres. A smaller value is recommended for concrete reinforced with low carbon steel fibres. Complete healing of open cracks of small widths is observed under exposure to marine cycles.     

非线性振动系统极限环振幅与频率的控制

研究非线性振动系统极限环振幅与频率的控制.利用多尺度法,计算了动力系统Hopf分岔点附近的正规型,获得极限环振幅及频率与反馈系数的近似解析关系.通过选择适当的反馈系数,可对极限环的振幅与频率进行控制.选取一类三维系统作为算例,讨论并比较了几类线性、非线性反馈控制器的控制效果,所得的解析结果与数值模拟的结果基本吻合.     

Beitrag niedriger Lastamplituden zur Ermüdungsschädigung von 0,15 %C Stahl

Contribution of low load cycles to fatigue damage in 0.15 %C steel The S‐N curve of 0.15 %C steel shows an endurance limit. Two‐step variable amplitude loading experiments serve to investigate the influence of numerous cycles below the endurance limit on fatigue damage. If high stress amplitudes of the loading sequences are more than approx. 15 % above the endurance limit, low load cycles contribute significantly to fatigue damage. Investigations of fatigue crack propagation under two‐step variable amplitude loading show accelerated crack growth caused by low load cycles. If high stress amplitudes of the two‐step sequences are less than 15 % above the endurance limit, beneficial influences of numerous low load cycles are found. Under these conditions, the material can sustain far greater numbers of load cycles than predicted by Miner damage accumulation calculation. Fatigue crack growth studies show that under these conditions for the high load numerous low load cycles lead to stop of the crack propagation.     

余维4的Duffing-Van der Pol方程全局分岔分析

本文采用级数展开形式的Melnikov函数解决高余维分岔问题。通过研究一类5次项和3次项共存,具有异宿轨的Duffing-Van der Pol方程的余维4全局分岔问题,得到了该系统的分岔方程及全局拓扑结构,说明了该方法的可行性。研究结果表明,该系统有单个极限环、单个异宿轨、异宿轨和极限环共存、两个极限环共存等情况。最后通过数值模拟验正了理论分析结果的正确性。     

Duffing-van der Pol振子的时滞反馈控制研究

本文研究了Duffing-Van der Pol振子在一类时滞反馈控制下零解的稳定性问题以及极限环的振幅和稳定性问题。依平均法和对时滞反馈控制项泰劳展开的截断得到的平均方程表明,零解的稳定性除与原方程中线性项的系数有关外,只与线性反馈有关,与非线性反馈无关。通过调整线性反馈的增益和时滞,可以使不稳定的零解变得稳定。零解发生Hopf 分岔导致的周期解的振幅除与原方程中非线性项的系数有关外,与线性反馈和非线性反馈均有关。通过调整反馈增益和时滞,不仅可以控制极限环的振幅,还可以抑制极限环的产生。此外,根据平均方程还容易发现反馈时滞对系统动力学行为的影响具有周期性。数值仿真的结果验证了理论分析的正确性。     

Non-propagating crack behaviour at giga-cycle fretting fatigue limit

Fretting fatigue fracture of industrial machines is sometimes experienced after a long period of operation. It has been a question whether the fatigue limit which means infinite life really exists in fretting fatigue or not. Fretting fatigue tests in ultra high cycle region up to 10⁹ cycles were performed. Test results showed that the S‐N curve had a knee point around 2 × 10⁷ cycles and a clear fatigue limit was observed in the giga‐cycle regime for partial slip conditions. An electropotential drop technique was applied to detect the crack growth behaviour under the contact pad. The real‐time measurement of crack depth during the fretting fatigue test at the fatigue limit showed that a crack initiated at an early stage and then ceased to grow after 2 × 10⁷ cycles and the crack became a non‐propagating crack. These results indicated that the fatigue limit exists in fretting fatigue and infinite endurance is achieved by the mechanism of forming a non‐propagating crack.     

横向风荷载作用下轴向运动弦线自激振动和稳定性分析

研究了横向定常风荷载作用下轴向运动弦线的非线性自激振动问题。将风荷载模型化为平均风速的非线性函数,建立动力学微分方程。采用Galerkin方法,将运动弦线简化为离散的二维系统并进行线性化,分析弦线平衡构型的稳定性,根据Routh-Hurtwitz判据确定了平衡点的稳定域。确定了多参数下Hopf分岔点及产生稳定极限环的条件。使用增量谐波平衡(IHB)法求解了自激振动的周期响应,按照Floquet理论确定了周期解的稳定性。最后,讨论了运动速度和平均风速稳定性的影响,并给出相应的稳定性条件。     

Assimilating satellite ocean-colour observations into oceanic ecosystem models

The effectiveness of ocean-colour data assimilation in providing robust biological-parameter estimates for basin-scale ecosystem models is investigated for a phytoplankton-zooplankton-nutrient model using North Atlantic satellite chlorophyll data. The model is forced by annual cycles of mixed-layer depth, day length, photosynthetically available radiation and a temperature-dependent phytoplankton maximum growth rate. Although ocean-colour data are potentially limited in their ability to constrain model parameters because they provide information about the phytoplankton component only, this limitation is offset by the volume of data available covering the range of possible biogeochemical responses to similar and widely varying physical conditions. The results are improved by applying wintertime nutrient estimates based on in situ observations as an additional constraint. Repeatability of parameter estimates obtained from independent samples is examined. Results obtained using regional and basin-wide sampling strategies for obtaining the optimization dataset are compared and the geographic applicability of the calibrated models is assessed.     

确定前轮非线性摆振极限环振幅的一种方法

用摄动法给出了当前轮减摆阻尼器含有速度平方阻尼时前轮摆振的极限环振幅表达式，并讨论了极限环的稳定性。在确定极限环振幅时，利用非线性系统所对应的线性系统在临界稳定时特征矩阵的特点，通过对特征矩阵进行三角分解，得到了消除摄动解中奇异项的条件，利用此条件，很方便地获得了飞机前轮非线性摆振的摄动解，并改正了有关文献中的错误。     

The area theorems for two-core nonlinear directional couplers

The area theorems, describing propagation of ultrashort pulses of resonant laser radiation in a two-core nonlinear directional coupler, are formulated for the first time. It is shown that such a system is characterized by a finite, bounded above set of areas of the stationary propagating pulses. We also predict quantization of the limit cycles and possible existence of the regime of periodic complete transfer of the radiation energy from one fiber to another.     

一类三次系统无穷远点的中心条件与赤道极限环分支

本文研究了一类三次系统无穷远点的中心条件与赤道极限环分枝问题。通过将实平面系统转化为复系统研究,给出了计算无穷远点奇点量的递推公式,并在计算机上用Mathematica推导出该系统无穷远点前七个无穷远点奇点量,进一步导出了无穷远点成为中心的条件和七阶细焦点的条件,得到了三次系统无穷远点分支出七个极限环的一个实例。     

一类三次Kolmogorov系统的极限环分支

本文研究一类三次Kolmogorov捕食系统正平衡点(1,1)的极限环分支情况,得出了其极限环的存在唯一性条件,且它在一定条件下还可分支出五个极限环且有3个稳定的极限环的结果,从而推广了前人相关的结果。     

An exothermic chemical reaction with linear feedback control

This paper investigates the effect of linear control as applied to an exothermic Sal?nikov chemical reaction. It will demonstrate how the control reduces the amplitude of the naturally occurring oscillations in temperature. However, in different parameter regions, this is not the case; that is, the reaction has desirable behaviour without control. A mathematical and numerical analysis of the system will be presented. Steady-state solutions are examined, and the emergence of limit cycles will be shown via the Hopf condition. The conditions under which oscillatory behaviour is not observed will be identified. When oscillatory behaviour is detected, the region to which it is confined will be described. Finally, an example is given of a nonlinear control, which ensures that the system will only portray stable behaviour, and under certain parameter constraints can eliminate oscillations entirely.