Implementation of configuration dependent stiffness proportional damping for the dynamics of rigid multi-block systems

The distinct element method(DEM)has been used successfully for the dynamic analysis of rigid block sys- tems.One of many difficulties associated with DEM is modeling of damping.In this paper,new procedures are proposed for the damping modeling and its numerical implementation in distinct element analysis of rigid muhi-block systems.The stiff- ness proportional damping is constructed for the prescribed damping ratio,based on the non-zero fundamental frequency ef- fective during the time interval while the boundary conditions remain essentially constant.At this time interval,the funda- mental frequency can be estimated without complete eigenvalue analysis.The damping coefficients will vary while the damp- ing ratio remains the same throughout the entire analysis.A new numerical procedure is developed to prevent unnecessary energy loss that can occur during the separation phases.These procedures were implemented in the development of the dis- tinet element method for the dynamic analyses of piled multi-block systems.The analysis results |or the single-block and two-block systems were in a good agreement with the analytic predictions.Applications to the seismic analyses of piled four- block systems revealed that the new procedures can make a significant difference and may lead to much-improved results.

Experimental Study on Non-proportional Multiaxial Strain Cyclic Characteristics and Ratcheting of U71Mn Rail Steel

An experimental study was carried out on the strain cyclic characteristics and ratcheting of U71Mn rail steel subjected to non-proportional multiaxial cyclic loading. The strain cyclic characteristics were researched under the strain-controlled circular load path. The ratcheting was investigated for the stress-controlled multiaxial circular, elliptical and rhombic load paths with different mean stresses, stress amplitudes and their histories. The experiment shows that U71Mn rail steel features the cyclic non-hardening/softening, and its strain cyclic characteristics depend greatly on the strain amplitude but slightly on its history. However, the ratcheting of U71Mn rail steel depends greatly not only on the values of mean stress and stress amplitude, but also on their histories. In the meantime, the shape of load path and its history also apparently influence the ratcheting. The ratcheting changes with the different loading paths.

A Statistical Model with Non-Linear Effects and Non-Proportional Hazards for Breast Cancer Survival Analysis

The Cox proportional hazard model is being used extensively in oncology in studying the relationship between survival times and prognostic factors. The main question that needs to be addressed with respect to the applicability of the Cox PH model is whether the proportional hazard assumption is met. Failure to justify the subject assumption will lead to misleading results. In addition, identifying the correct functional form of the continuous covariates is an important aspect in the development of a Cox proportional hazard model. The purpose of this study is to develop an extended Cox regression model for breast cancer survival data which takes non-proportional hazards and non-linear effects that exist in prognostic factors into consideration. Non-proportional hazards and non-linear effects are detected using methods based on residuals. An extended Cox model with non-linear effects and time-varying effects is proposed to adjust the Cox proportional hazard model. Age and tumor size were found to have nonlinear effects. Progesterone receptor assay status and age violated the proportional hazard assumption in the Cox model. Quadratic effect of age and progesterone receptor assay status had hazard ratio that changes with time. We have introduced a statistical model to overcome the presence of the proportional hazard assumption violation for the Cox proportional hazard model for breast cancer data. The proposed extended model considers the time varying nature of the hazard ratio and non-linear effects of the covariates. Our improved Cox model gives a better insight on the hazard rates associated with the breast cancer risk factors.

The Extended Non-Elementary Amplitude Functions as Solutions to the Damped Pendulum Equation, the Van der Pol Equation, the Damped Duffing Equation, the Lienard Equation and the Lorenz Equations

In this paper, we define some non-elementary amplitude functions that are giving solutions to some well-known second-order nonlinear ODEs and the Lorenz equations, but not the chaos case. We are giving the solutions a name, a symbol and putting them into a group of functions and into the context of other functions. These solutions are equal to the amplitude, or upper limit of integration in a non-elementary integral that can be arbitrary. In order to define solutions to some short second-order nonlinear ODEs, we will make an extension to the general amplitude function. The only disadvantage is that the first derivative to these solutions contains an integral that disappear at the second derivation. We will also do a second extension: the two-integral amplitude function. With this extension we have the solution to a system of ODEs having a very strange behavior. Using the extended amplitude functions, we can define solutions to many short second-order nonlinear ODEs.

EFFECT OF NON-PROPORTIONAL OVERLOADING ON FATIGUE CRACK GROWTH

The effect of proportional and non-proportional overloading on mode l fatigue crack growth have been studied,and the influences of crack tip plastic zone,crack tip blunting as well as crack closure were discussed.Proportional(model I)overloading may cause more serious crack growth retardation than non-proportional(mixed mode)overloading.Therefore,for estimating the fatigue life of engineering structures to simplify a real overload which may of- ten be non-proportional as a proportional one is not always safe.

Effect on Landau damping rates for a non-Maxwellian distribution function consisting of two electron populations

In many physical situations where a laser or electron beam passes through a dense plasma,hot low-density electron populations can be generated,resulting in a particle distribution function consisting of a dense cold population and a small hot population.Presence of such low-density electron distributions can alter the wave damping rate.A kinetic model is employed to study the Landau damping of Langmuir waves when a small hot electron population is present in the dense cold electron population with non-Maxwellian distribution functions.Departure of plasma from Maxwellian distributions significantly alters the damping rates as compared to the Maxwellian plasma.Strong damping is found for highly nonMaxwellian distributions as well as plasmas with a higher density and hot electron population.Existence of weak damping is also established when the distribution contains broadened flat tops at the low energies or tends to be Maxwellian.These results may be applied in both experimental and space physics regimes.

Nonlinear Landau damping of high frequency waves in non-Maxwellian plasmas

Space plasmas often possess non-Maxwellian distribution functions which have a significant effect on the plasma waves. When a laser or electron beam passes through a dense plasma, hot low density electron populations can be generated to alter the wave damping/growth rate. In this paper, we present theoretical analysis of the nonlinear Landau damping for Langmuir waves in a plasma where two electron populations are found. The results show a marked difference between the Maxwellian and non-Maxwellian instantaneous damping rates when we employ a non-Maxwellian distribution function called the generalized （r, q） distribution function, which is the generalized form of the kappa and Maxwellian distribution functions. In the limiting case of r = 0 and q→∞, it reduces to the classical Maxwellian distribution function, and when r = 0 and q→k ＋1, it reduces to the kappa distribution function.

Non-Markovian Dynamics of an Open Two-Level System with Amplitude-Phase Damping

By use of the measure, the backflow of information presented recently, we study the non-Markovianity of the dynamics for a two-level system interacting with a zero-temperature structured environment via amplitude-phase coupling. In the limit of weak coupling between the system and its reservoir, the time-local non-Markovian master equation for the reduced state of the system is derived. Under the secular approximation, the exact analytic solution is obtained. Numerical simulations show that the amplitude and phase dampings can produce destructive interference to the backflow of information, leading to the weaker non-Markovianity of the compound dynamics compared with the dynamics of a single amplitude or phase damping model. We also study the characteristics of the initial-state pairs that maximize the backflow of information.

The Harmonic Oscillator with Random Damping in Non-Markovian Thermal Bath

In this paper, we define the harmonic oscillator with random damping in non-Markovian thermal bath. This model represents new version of the random oscillators. In this side, we derive the overdamped harmonic oscillator with multiplicative colored noise and translate it into the additive colored noise by changing the variables. The overdamped harmonic oscillator is stochastic differential equation driving by colored noise. We derive the change in the total entropy production (CTEP) of the model and calculate the mean and variance. We show the fluctuation theorem (FT) which is invalid at any order in the time correlation. The problem of the deriving of the CTEP is studied in two different examples of the harmonic potential. Finally, we give the conclusion and plan for future works.

Active Damping of Milling Vibration Using Operational Amplifier Circuit

The problem of chatter vibration is associated with adverse consequences that often lead to tool impairment and poor surface finished in a workpiece, and thus, controlling or suppressing chatter vibrations is of great significance to improve machining quality. In this paper, a workpiece and an actuator dynamics are considered in modeling and controller design. A proportional-integral controller(PI) is presented to control and actively damp the chatter vibration of a workpiece in the milling process. The controller is chosen on the basis of its highly stable output and a smaller amount of steady-state error. The controller is realized using analog operational amplifier circuit. The work has contributed to planning a novel approach that addresses the problem of chatter vibration in spite of technical hitches in modeling and controller design. The method can also lead to considerable reduction in vibrations and can be beneficial in industries in term of cost reduction and energy saving. The application of this method is verified using active damping device actuator(ADD) in the milling of steel.

THE ANALYTICAL APPROACH FOR LARGE SCALE NON-CLASSICALLY DAMPED DYNAMIC SYSTEM

This paper gives a dynamic decoupling approach for the analysis of large scale non-classically damped system, in which the complex variable computations were completely avoided not only in solving for the eigenvalue problem but also in the calculation of the dynamic response. The analytical approaches for undamped gyroscopic system, non-classically damped system, including the damped gyroscopic system were unified. Very interesting and useful theoretical results, practical algorithms were obtained which are applicable to both non-defective and defective systems.

A method for stochastic seismic response analysis of non-classically damped structures

A method to calculate the stationary random response of a non-classically damped structure is proposed that features clearly-defined physical meaning and simple expression. The method is developed in the frequency domain. The expression of the proposed method consists of three terms, i.e., modal velocity response, modal displacement response, and coupled (between modal velocity and modal displacement response). Numerical results from the parametric study and three example structures reveal that the modal velocity response term and the coupled term are important to structural response estimates only for a dynamic system with a tuned mass damper. In typical cases, the modal displacement term can provide response estimates with satisfactory accuracy by itself, so that the modal velocity term and coupled term may be ignored without loss of accuracy. This is used to simplify the response computation of non-classically damped structures. For the white noise excitation, three modal correlation coefficients in closed form are derived. To consider the modal velocity response term and the coupled term, a simplified approximation based on white noise excitation is developed for the case when the modal velocity response is important to the structural responses. Numerical results show that the approximate expression based on white noise excitation can provide structural responses with satisfactory accuracy.

Accelerated proportional degradation hazards-odds model in accelerated degradation test

An accelerated proportional degradation hazards-odds model is proposed. It is a non-parametric model and thus has path- free and distribution-free properties, avoiding the errors caused by faulty assumptions of degradation paths or distribution of degra- dation measurements. It is established based on a link function which combines the degradation cumulative hazard rate function and the degradation odds function through a transformation pa- rameter, and this makes the accelerated proportional degradation hazards model and the accelerated proportional degradation odds model special cases of it. Hypothesis tests are discussed, and the proposed model is applicable when some model assumptions are satisfied. This model is utilized to estimate the reliability of minia- ture bulbs under low stress levels based on the degradation data obtained under high stress levels to validate the effectiveness of this model.

On precise time integration method for non-classically damped MDOF systems

In the complex mode superposition method, the equations of motion for non-classically damped multiple-degree-of-freedom （MDOF） discrete systems can be transferred into a combination of some generalized SDOF complex oscillators. Based on the state space theory, a precise recurrence relationship for these complex oscillators is set up; then a delicate general solution of non-classically damped MDOF systems, completely in real value form, is presented in this paper. In the proposed method, no calculation of the matrix exponential function is needed and the algorithm is unconditionally stable. A numerical example is given to demonstrate the validity and efficiency of the proposed method.

316L不锈钢非比例循环硬化特性的数值模拟

在等效应变范围为0.7%条件下,对316L不锈钢进行室温应变控制拉-扭疲劳试验,研究了比例应变路径(单轴路径和比例路径)和非比例应变路径(十字路径和圆路径)下的循环硬化特性;采用AF-OW随动硬化模型结合Chaboche各向同性硬化准则以及将非比例度嵌入到各向同性硬化准则中的改进模型对各路径下的循环特性进行模拟,并进行试验验证。结果表明:316L不锈钢在各路径下的循环初期均产生了循环硬化现象,在单轴、比例、十字和圆路径下的硬化率分别为5.2%,4.5%,38.2%,44.6%,在非比例应变路径下,该钢产生明显的附加强化;AF-OW模型结合各向同性硬化准则可以准确地模拟单轴和比例路径下的循环硬化特性,但对十字和圆路径下的模拟效果较差,模拟得到的正应力-正应变滞回环与试验结果之间的最大相对误差均大于20%;改进模型可以准确地描述十字和圆路径下的循环硬化特性,正应力-正应变滞回环的最大相对误差分别为1.3%和3.2%,最大等效峰值应力的相对误差分别为1.9%和1.2%。

清化方治疗湿热蕴结型非酒精性脂肪性肝病临床研究

目的:观察清化方治疗非酒精性脂肪性肝病(NAFLD)的临床疗效。方法:将66例NAFLD患者按随机数字表法分为对照组和观察组各33例,因研究过程中有脱落,对照组、观察组最终完成研究的患者例数分别为30例、32例。两组均给予生活方式干预,观察组在此基础上给予清化方干预。两组均以12周为1个疗程,共治疗2个疗程。观察两组患者干预前、干预12周、干预24周的受控衰减参数(CAP)、血脂代谢指标、肝功能指标、血糖代谢指标及体质量指数(BMI),并评价干预24周的腹部B超疗效和中医证候疗效。结果:①干预12周、24周后,两组CAP较干预前均降低(P<0.05);干预24周后,两组CAP较干预12周均降低(P<0.05)。干预12周、24周后,观察组CAP均低于对照组(P<0.05)。②干预24周后,观察组血清TG水平较干预前及干预12周降低(P<0.05),且低于同时点对照组(P<0.05)。③干预24周后,观察组空腹胰岛素(FINS)水平和HOMA胰岛素抵抗(HOMA-IR)指数较干预前降低(P<0.05),且低于同时点对照组(P<0.05)。④干预12周、24周后,两组BMI较干预前均降低(P<0.05)。干预24周后,观察组BMI较干预12周降低(P<0.05),且低于同时点对照组(P<0.05)。⑤干预24周后,观察组腹部B超疗效和中医证候疗效均优于对照组(P<0.05)。结论:清化方联合生活方式干预有助于改善NAFLD患者肝脏脂肪沉积,并可改善患者中医证候,疗效确切。

非堆积型多颗粒阻尼器等效力学模型及其减振性能分析

为考虑颗粒群碰撞过程中时间效应对非堆积型多颗粒阻尼器(non-packed particle damper, NPPD)减振性能的影响,在现有考虑惯容的等效单颗粒力学模型(equivalent inertia single-particle model, EISM)研究基础上,提出了基于接触单元法的等效单颗粒力学模型(equivalent inertia single-particle model based on contact element method, EISM-CE),并基于Runge-Kutta算法建立了NPPD单自由度结构运动状态求解算法。设计进行附加NPPD单层钢框架结构振动台试验,探究不同填充率对结构顶层位移频响曲线的影响规律,提出了EISM-CE参数取值原则,进而进行力学模型试验验证及模型对比分析。在模型验证合理性基础上,基于EISM-CE依次进行了自由振动、简谐激励及记录强震动下减振性能及能量变化规律分析。研究结果表明,与现有EISM相比,提出的基于接触单元法的EISM-CE模型及参数取值原则更加合理有效。减振性能数值分析结果表明,不同激励下NPPD均具有较好的减振性能;考虑碰撞时间效应后EISM-CE与EISM对应减振性能及机理分析结果存在一定的差异。

基于应力梯度和附加强化的多轴疲劳寿命建模

鉴于Manson-Coffin方程未考虑应力梯度和附加强化的影响,以及缺口附近非均匀应力场和非比例附加强化对疲劳损伤演化过程的影响,建立了适用于多轴缺口件的疲劳寿命预测模型.首先,考虑裂纹萌生和扩展的物理机制,借助坐标变换原理和临界面理论,以最大剪切应变幅为损伤参量确定临界面位置;其次,分别对临界面的正应力和剪应力进行归一化处理,提出了考虑多轴应力集中系数和应力梯度影响指数的等效应力梯度因子;同时,考虑相位差、路径非比例和材料非比例对疲劳寿命的影响,提出了新的非比例附加强化因子;最后,结合Manson-Coffin方程建立了考虑应力梯度和非比例附加强化的多轴疲劳寿命预测模型,并将该模型、Manson-Coffin方程、LV模型和FS模型的预测寿命与实验寿命进行对比,结果表明该模型的预测精度优于其它3种模型的.