Higher-order approximate solutions of fractional stochastic point kinetics equations in nuclear reactor dynamics

Stochastic point kinetics equations(SPKEs) are a system of Ito? stochastic differential equations whose solution has been obtained by higher-order approximation.In this study, a fractional model of SPKEs has been analyzed. The efficiency of the proposed higher-order approximation scheme has been discussed in the results section. The solutions of SPKEs in the presence of Newtonian temperature feedback have also been provided to further discuss the physical behavior of the fractional model.

QUASI-STATIC AND DYNAMICAL ANALYSIS FOR VISCOELASTICTIMOSHENKO BEAM WITH FRACTIONAL DERIVATIVECONSTITUTIVE RELATION

The equations of motion governing the quasi-static and dynamical behavior of a viscoelastic Timoshenko beam are derived. The viscoelastic material is assumed to obey a three-dimensional fractional derivative constitutive relation. ne quasi-static behavior of the viscoelastic Timoshenko beam under step loading is analyzed and the analytical solution is obtained. The influence of material parameters on the deflection is investigated. The dynamical response of the viscoelastic Timoshenko beam subjected to a periodic excitation is studied by means of mode shape functions. And the effect of both transverse shear and rotational inertia on the vibration of the beam is discussed.

DYNAMICAL STABILITY OF VISCOELASTIC COLUMN WITH FRACTIONAL DERIVATIVE CONSTITUTIVE RELATION

The dynamic stability of simple supported viscoelastic column, subjected to a periodic axial force, is investigated. The viscoelastic material was assumed to obey the fractional derivative constitutive relation. The governing equation of motion was derived as a weakly singular Volterra integro-partial-differential equation, and it was simplified into weakly singular Volterra integro-ordinary-differential equation by the Galerkin method. In terms of the averaging method, the dynamical stability was analyzed. A new numerical method is proposed to avoid storing all history data. Numerical examples are presented and the numerical results agree with the analytical ones.

Representation of the constitutive equation of viscoelastic materials by the generalized fractional element networks and its generalized solutions

The generalized fractional element networks are presented in this paper. In order to extend the structure of the model solutions to the generalized function space and make it contain more physical meanings, the restriction on the parameters of the fractional element proposed by Schiessel et al. is eliminated and a 'compatibility equation' is added. The discretization method for solving the inverse Laplace transform is used and developed. The generalized solutions of the model equations are given. At the same time the generalized fractional element network--Zener and Poyinting-Thomson models are discussed in detail. It is shown that all the results obtained previously about the models of single parameter with fractional order and the classical models with integer order can be contained as the special cases of the results of this paper.

Fractional Modeling and Analysis of Coupled MR Damping System

The coupled magnetorheological (MR) damping system addressed in this paper contains rubber spring and magnetorheological damper. The device inherits the damping merits of both the rubber spring and the magnetorheological damper. Here a fractional-order constitutive equation is introduced to study the viscoelasticity of the combined damper. An introduction to the definitions of fractional calculus, and the transfer function representation of a fractional-order system are given. The fractional-order system model of a magnetorheological vibration platform is set up using fractional calculus, and the function of displacement is presented. It is indicated that the fractional-order constitutive equation and the transfer function are feasible and effective means for investigating of magnetorheological vibration device. © 2014 Chinese Association of Automation.

A NUMERICAL METHOD FOR FRACTIONAL INTEGRAL WITH APPLICATIONS

A new numerical method for the fractional integral that only stores part history data is presented, and its discretization error is estimated. The method can be used to solve the integro_differential equation including fractional integral or fractional derivative in a long history. The difficulty of storing all history data is overcome and the error can be controlled. As application,motion equations governing the dynamical behavior of a viscoelastic Timoshenko beam with fractional derivative constitutive relation are given. The dynamical response of the beam subjected to a periodic excitation is studied by using the separation variables method. Then the new numerical method is used to solve a class of weakly singular Volterra integro_differential equations which are applied to describe the dynamical behavior of viscoelastic beams with fractional derivative constitutive relations. The analytical and unmerical results are compared. It is found that they are very close.

Nonclassical constitutive model involving void evolution of casting magnesium alloy

The void evolution equation and the elastoplastic constitutive model of casting magnesium alloy were investigated. The void evolution equation consists of the void growth and the void nucleation equations. The void growth equation was obtained based on the continuous supposition of the material matrix,and the void nucleation equation was derived by assuming that the void nucleation follows a normal distribution. A softening function related to the void evolution was given. After the softening function was embedded to a nonclassical elastoplastic constitutive equation,a constitutive model involving void evolution was obtained. The numerical algorithm and the finite element procedure related to the constitutive model were developed and applied to the analysis of the distributions of the stress and the porosity of the notched cylindrical specimens of casting magnesium alloy ZL305. The computed results show satisfactory agreement with the experimental data.

Mechanical response and simulation for constitutive equations with distributed order derivatives

Mechanical response and simulation for constitutive equation with distributed order derivatives were considered.We investigated the creep compliance,creep recovery,relaxation modulus,stress–strain behavior under harmonic deformation for each case of two constitutive equations.We express these responses and results as easily computable forms and simulate them by using MATHEMATICA 8.The results involve the exponential integral function,convergent improper integrals on the infinite interval(0,+∞)and the numerical integral method for the convolution integral.For both equations,stress responses to harmonic deformation display hysteresis phenomena and energy dissipation.The two constitutive equations characterize viscoelastic models of fluid-like and solid-like,respectively.

基于分数阶导数模型的巷道围岩变形失稳规律研究

巷道在应力长时间作用下会发生蠕变变形,为探究蠕变变形失稳规律,以分数阶导数为基础,将Newton黏壶改进为Abel黏壶,并引入负指数形式的损伤变量,建立了分数阶Nishihara本构模型。根据晋城市锦辰煤业3采区砂岩在不同应力下的蠕变实验,验证了本构模型的有效性,所提出的新模型可以更好到描述巷道围岩在长期力学作用下的变形规律。

液固两相区本构方程的研究

根据液固两相区的微观结构推导了适于分析两相区变形的本构方程。此方程考虑了金属在凝固过程中的各种行为 (相变、温度场与应力场的耦合、固相率的变化等 ) ,并首次将固相率的影响引入本构方程。利用此方程对试样的变形过程进行了有限元模拟 。

具有分数导数本构关系的粘弹性Timoshenko梁的静动力学行为分析

利用粘弹性材料的三维分数导数型本构关系 ,建立粘弹性Timoshenko梁的静、动力学行为研究的数学模型 ;分析Timoshenko梁在阶跃载荷作用下的准静态力学行为 ,得出了问题的解析解 ,考察了一些材料参数对梁的挠度的影响· 基于模态函数讨论了粘弹性Timoshenko梁在横向简谐激励作用下的动力响应 。

具有分数导数型本构关系的粘弹性柱的动力稳定性

研究简支的受轴向周期激励的粘弹性柱动力稳定性 ,柱的材料满足分数导数型本构关系· 建立了描述粘弹性柱动力学行为的弱奇异性Volterra积分_偏微分方程 ,利用Galerkin方法将其化归为弱奇异性Volterra积分_常微分方程· 利用平均化方法的思想给出了粘弹性柱运动稳定状态的存在性条件· 给出一种新的计算方法 ,克服了存储整个响应历史数据的困难 ,并给出了数值算例 。

分数积分的一种数值计算方法及其应用

提出了一种只需要存储部分历史数据的分数积分的数值计算方法,并给出了误差估计。这种方法可对包含分数积分和分数导数的积分-微分方程进行较长时间的数值计算,克服了存储全部历史数据的困难,并能对计算误差进行控制。作为应用,给出了具有分数导数型本构关系的粘弹性Timoshenko梁的动力学行为研究的控制方程,利用分离变量法讨论梁在简谐激励作用下的动力响应,然后用新提出的数值方法对控制方程进行数值计算,数值计算结果和理论结果进行了比较,它们比较吻合。

分数维空间中的损伤力学研究初探

结合损伤力学和分形几何理论，给出分数维空间中分形损伤变量定义ω（ｄ，ζ）及其解析表达式．指出欧氏空间损伤变量ω０实际是分数维空间分形损伤变量ω（ｄ，ζ）当维数取Ｅｕｃｌｉｄｅａｎ维数时的一种特例，将欧氏空间损伤变量定义推广到分数维空间，建立起一种兼顾反映损伤细观结构效应和宏观损伤力学分析需要的损伤定义与描述方法．在此基础上，推导了材料损伤演化律和损伤本构关系的分形表达形式．作为例证，文中分析了单调压缩载荷下混凝土损伤及演化行为．实验对比分析表明：分形损伤模型较好地反映了混凝土实际损伤力学行为．

磁流变阻尼器的分数阶模型及其减振系统分析

研制了一种复合式磁流变阻尼器,它主要由橡胶弹簧、磁流变阻尼两部分组成,其性能兼具橡胶弹簧减振和磁流变阻尼减振的优点。引入了分数阶微积分理论,建立了复合阻尼器的分数阶Zener理论模型,并探讨了在该模型下的粘弹性。为验证该模型的有效性,将分数阶微积分应用到磁流变振动台系统建模上,建立了分数阶系统模型,并给出了分数阶系统传递函数描述,求出了位移函数。实验表明,减振系统的分数阶模型与实验数据能够较好的吻合,从而证明了分数阶模型在磁流变阻尼器的减振模型研究上的有效性。

分数阶在磁流变液性能研究中的应用

将分数阶微积分引入Maxwell粘弹性流体的本构方程中,建立修正的Maxwell模型以描述磁流变液.通过贮能模量和耗能模量曲线,研究磁流变液的阻尼特性.在不同的磁流变液体组成参数实验条件下,理论的贮能模量和耗能模量能够与实验结果很好拟合,且模型阶数有着明显变化.研究表明,分数阶的本构方程能够很好地描述磁流变液的阻尼特性,方程分数阶算子与磁流变液物质参数有关.

液固两相区变形行为的研究及其本构方程的建立

基于两相区微观组织的结构及其力学行为的基础上 ,研究了影响两相区变形行为的主要因素·首次将固相率的影响加入到本构方程中 ,并将塑性应变与蠕变应变统一考虑 ,建立了适合于两相区变形的本构方程·同时包括了凝固过程中相变的影响项 。

一种改进的R-L分数阶导数定义在固体推进剂粘弹性本构模型中的应用

针对Riemann-Liouville分数阶导数定义的不足之处进行了改进,利用改进过的分数阶导数定义,建立了类Kelvin体粘弹性本构模型,并应用于某固体推进剂上,对本构方程中的三个参数进行了求解,与经典的prony级数模型进行比较,采用分数阶导数的类Kelvin体粘弹性本构模型与实验结果能很好地吻合。

一种采用分数阶导数的新流变模型理论

提出了一种采用分数阶导数的新流变模型理论 ,它将分数微积分理论和经典模型理论的方法统一起来 ,使得模型的物理概念更明确 .使已有分散的分数阶导数模型工作系统化 ,使问题的解法系统化 .它克服了经典模型理论与实验结果吻合不好的严重缺点 ,仅采用很少几个元件组合就可获得很好的效果 .利用这种模型理论 ,可望构造出各种与实验结果吻合得很好的新固体和流体模型 .这种新模型理论可以满意地描述物体的瞬时弹性、延迟弹性、粘性流、塑性等性能 .

孔隙率对气凝胶力学性能的影响(英文)

建立了考虑孔隙率影响的气凝胶的本构方程,分析了孔隙率对其有效弹性模量、体积模量和气凝胶固体网络骨 架上应力的影响.结果表明孔隙率越大,固体骨架承受的应力越大;有效弹性模量、体积模量随孔隙率的变化而变化;同 时气凝胶干燥过程中,由于蒸发,孔中的液体不断被气体取代,导致作用在固体和液体上应力重新分布.容易造成干裂.