砂岩脆性变形破坏过程中声发射信息试验研究

针对砂岩试样进行了单轴刚性加载试验，并测试整个过程的声发射信息。根据试验情况，可将砂岩在整个变形阶段的声发射信号特征划分为压密、弹性、稳定破裂、非稳定破裂和峰后情况五个阶段。通过对稳定破裂和非稳定破裂分界点对应的临界点处的应力和应变值与峰值应力及其对应的应变比值分析发现，大部分应变比在74%与78%之间；应力比则相对具有较大的离散性，均值在73%左右。上述研究，通过对砂岩脆性破坏过程中声发射信息与应力比和应变比之间的关系分析，增进了对岩石破裂过程中生发现象的认识，为相应岩石脆性破坏导致的地质灾害分析提供了新的研究思路。     

三种红层岩石常规三轴压缩下的强度与变形特性研究

利用MTS815Teststar程控伺服岩石力学试验系统研究了川东地区一红层边坡中的砂岩、粉砂岩和泥岩围压为0³MPa的应力-应变全过程曲线,建立了峰值强度、峰值强度前弹性模量以及峰值强度后的弹性模量和围压的关系。将低围压下红层的全应力-应变曲线概化成5个阶段,分别为压密段、弹性段、屈服段、应变软化段和塑性流动阶段。试验结果得出,红层弹性模量随围压的增加而提高且变化明显,砂岩和粉砂岩在此围压内为脆性破坏,泥岩为塑性破坏的规律。     

基于元件组合理论的砂岩动态损伤本构模型

采用分离式霍普金森压杆（SHPB）系统，对砂岩进行不同速度下的冲击试验，得到砂岩的应变率效应特征以及典型的动态本构曲线。该曲线分为近似线弹性阶段、塑性阶段、塑性增强阶段和正向卸载阶段。通过组合模型的方法，构建了砂岩含损伤的动态本构模型，借助LS-DYNA软件中的用户材料子程序UMAT接口实现对本构模型的二次开发，并对砂岩在冲击速度为7.5、9.5、11.5和13.5 m/s 4种情况下的SHPB动态冲击压缩试验进行模拟。结果表明:所构建的模型可以很好地描述砂岩的应变率效应和应力-应变曲线弹性段，并且动态峰值强度、最大应变均与试验结果一致，应变率、峰值强度、最大应变与试验结果的相对误差不超过10%。所构建的砂岩动态本构模型能够准确地描述砂岩在冲击作用下的动态力学特性。     

经历不同高温后砂岩的动态力学特性实验研究

运用RX3 -20 -12型箱式电阻炉将砂岩试样分别加热至100、200、400、600、800和1 000℃,然后自然冷却至常温,制成经历不同温度的砂岩试件。运用直径为100mm的分离式Hopkinson压杆装置,用薄圆形紫铜片作为波形整形器,以不同弹速轴向冲击砂岩试样,测试经历不同温度后砂岩试样在不同冲击荷载下的动态力学性能,得出了砂岩的应力-应变曲线及各自的破坏形态。结果表明:常温下砂岩的动态压缩破坏的应力-应变曲线具有明显的4阶段特征,但经历100~400℃作用的砂岩应力-应变曲线的平台段消失,温度继续升高时平台段又重新出现;砂岩的峰值应变随温度升高而升高,动态压缩强度也随温度升高而升高,但在800℃以后陡然下降;砂岩的动态压缩破坏形态受温度和冲击荷载的共同影响,冲击荷载越大破碎程度越大,而且破坏过程总是由外层向内芯发展。     

分级加卸载硬岩短时蠕变特性实验研究

由单向抗压强度实验及8级加卸载短时蠕变实验,得到蠕变下限为27MPa的细砂岩试样典型的坚硬岩石脆性断裂特征.应力-应变等时曲线线性回归函数的相关系数均高于0.92,长期强度与瞬时强度之比达94.39%,证明细砂岩试样的整体蠕变特性不强.应力-轴向应变等时曲线线性回归函数的平均相关系数高出应力-径向应变等时曲线线性回归函数的平均相关系数3.92%,因此其轴向非线性蠕变特性相对于径向非线性蠕变特性更弱.随着时间延续,细砂岩试样的非线性蠕变特性总体服从负Gauss分布规律,具有明显的时间效应.随加载应力水平的提高,应力-轴向应变等时曲线和应力-径向应变等时曲线线性拟合函数的平均相关系数下降幅度分别为0.97%和0.67%,线性相关性普遍降低.所以细砂岩试样的非线性蠕变程度随加载应力水平的提高而提高,载荷效应明显.     

高应力区峰后红砂岩蠕变特性及模型分析

在实验室通过RLW-2000型岩石三轴流变仪,对2组9个红砂岩样进行高应力区峰后单轴压缩蠕变试验,研究了红砂岩峰后瞬时应变、蠕变应变与应力水平的关系,分析了红砂岩峰后/峰前蠕变关联特性,探讨了红砂岩蠕变破坏机制,确定了峰后红砂岩高应力区蠕变本构模型。结果表明:随着蠕变应力水平提高,峰后岩样瞬时应变呈减小趋势,蠕变应变与蠕变应变速率呈增加趋势,峰后岩样同样具有瞬时加载四阶段与蠕变水平三阶段特征;相同应力水平下,岩样峰后/峰前状态对瞬时应变比影响大于蠕变应变比;应力水平越高,岩样瞬时应变比与蠕变应变比越大,但应力水平对岩样蠕变应变比影响大于瞬时应变比;峰后破坏岩样主控破裂面形态复杂,高径比越小,岩样内部破坏越充分,高径比越大,越易产生压剪破坏;Burgers-Kelvin模型能够表征峰后红砂岩高应力区蠕变特性。     

一种新的岩石非线性黏弹塑性蠕变模型研究

为了克服传统元件组合模型不能描述岩石蠕变过程中非线性特征的缺陷，首先根据加速蠕变阶段的应变和应变率随蠕变时间急剧增大的特点，建立黏塑性应变与蠕变时间的指数函数关系并提出非线性黏塑性体．将该非线性黏塑性体与广义Burgers蠕变模型串联，建立可以描述岩石全蠕变过程的非线性黏弹塑性蠕变模型，根据叠加原理得到一维应力状态下的轴向蠕变方程．然后基于塑性力学理论指出岩石三维蠕变本构方程建立过程中的不足之处，并给出非线性黏弹塑性蠕变模型合理的三维蠕变方程．最后采用不同应力水平下砂岩轴向蠕变试验对模型合理性进行验证，结果表明：拟合曲线与试验曲线吻合度较高，所建蠕变模型能够很好地描述砂岩在不同应力水平下的蠕变变形规律，尤其对加速蠕变阶段的非线性特征描述效果很好，验证了模型的合理性．     

砂岩峰后卸除围压过程的渗透性试验研究

为了探讨煤层开采引起的围岩卸除围压过程中砂岩渗透性的变化规律,本文用数控瞬态渗透法在电液伺服岩石力学试验系统MTS815.02上进行了砂岩试样的渗透特性试验。得出了试样峰前渗透系数-应变与应力-应变的关系曲线,以及在峰后保持轴向应变一定卸除围压过程中试样的渗透系数-围压与主应力差-围压的关系曲线;对试验砂岩在变形破坏过程中渗透性变化规律进行了总结,重点分析了其峰后卸除围压过程中渗透性的变化规律;并对试验砂岩峰后渗透系数与有效围压关系进行了拟合,得出了拟合方程式,为煤层开采引起的围岩体应力场与渗流场耦合问题提供参考。     

粉砂岩峰后破坏区应力脆性跌落的试验和本构方程研究

对粉砂岩试样进行常规三轴压缩试验,得到了其在不同围压下的应力-应变全程曲线.结果表明,岩样应力-应变曲线峰前(破坏前区)部分的力学性质较为稳定,其力学行为可用经典强度理论进行描述;应力-应变曲线峰后(破坏后区)部分,岩样处于非稳定状态,其力学行为难以用经典强度理论来描述,而脆塑性模型恰好可以描述试验岩样的应力非连续变化特征.岩石的应力脆性跌落是有条件发生的,应力脆性跌落系数是围压的函数,并给出应力脆性跌落系数与围压的关系.对完整岩样而言,使用弹性-线性软化-残余塑性三线性非理想脆塑性模型可以描述岩样的本构特征,而对含有节理岩样而言,采用双线性弹性-线性软化-残余塑性四线型非理想脆塑性模型与试验更为相符.     

岩石压缩过程应力-应变-磁感强度效应的实验研究

为了弄清岩石挤压产生的磁感强度效应,将钕铁硼Nd-Fe-B磁芯分别植入圆柱形大理岩、石灰岩中,在其周围产生磁场.借助断裂使岩石导磁回路与磁强发生的改变,进行挤压过程中应力、应变和磁感强度三变量测试.研究结果表明:岩石裂隙变化能够引起磁感强度的改变,应力-应变-磁强存在一一对应的数值关系；达到最大应力前,大理岩、石灰岩周围磁感强度出现增大异常的破坏预兆；在岩石裂解阶段,应力-应变曲线与磁强-应变曲线的变化规律具有明确的反对称性.最后还建立了分段表达岩石应力-磁感强度拟合关系式.     

Dimension-reduction of FPK equation via equivalent drift coefficient

The Fokker—Planck—Kolmogorov (FPK) equation plays an essential role in nonlinear stochastic dynamics. However, neither analytical nor numerical solution is available as yet to FPK equations for high-dimensional systems. In the present paper, the dimension reduction of FPK equation for systems excited by additive white noise is studied. In the proposed method, probability density evolution method (PDEM), in which a decoupled generalized density evolution equation is solved, is employed to reproduce the equivalent flux of probability for the marginalized FPK equation. A further step of constructing an equivalent coefficient finally completes the dimension-reduction of FPK equation. Examples are illustrated to verify the proposed method.     

A two-body continuous-discrete filter

In the theory of classical mechanics, the two-body central forcing problem is formulated as a system of the coupled nonlinear second-order deterministic differential equations. The uncertainty introduced by the small, unmodeled stochastic acceleration is not assumed in the particle dynamics. The small, unmodeled stochastic acceleration produces an additional random force on a particle. Estimation algorithms for a two-body dynamics, without introducing the stochastic perturbation, may cause inaccurate estimation of a particle trajectory. Specifically, this paper examines the effect of the stochastic acceleration on the motion of the orbiting particle, and subsequently, the stochastic estimation algorithm is developed by deriving the evolutions of conditional means and conditional variances for estimating the states of the particle-earth system. The theory of the nonlinear filter of this paper is developed using the Kolmogorov forward equation “between the observations" and a functional difference equation for the conditional probability density “at the observation." The effectiveness of the nonlinear filter is examined on the basis of its ability to preserve perturbation effect felt by the orbiting particle and the signal-to-noise ratio. The Kolmogorov forward equation, however, is not appropriate for the numerical simulations, since it is the equation for the evolution of “the conditional probability density." Instead of the Kolmogorov equation, one derives the evolutions for the moments of the state vector, which in our case consists of positions and velocities of the orbiting body. Even these equations are not appropriate for the numerical implementations, since they are not closed in the sense that computing the evolution of a given moment involves the knowledge of higher order moments. Hence, we consider the approximations to these moment evolution equations. This paper makes a connection between classical mechanics, statistical mechanics and the theory of the nonlinear stochastic filtering. The results of this paper will be of use to astrophysicists, engineers and applied mathematicians, who are interested in applications of the nonlinear filtering theory to the problems of celestial and satellite mechanics. Simulation results are introduced to demonstrate the usefulness of an analytic theory developed, in this paper.     

Nonlinear stochastic exclusion financial dynamics modeling and complexity behaviors

In attempt to reproduce and investigate nonlinear dynamics of financial markets, a new random agent-based financial price dynamics is developed and investigated by stochastic exclusion process. The exclusion process, one of Markov interacting processes, is firstly introduced to imitate the trading interactions among the investing agents in this work and to explain various statistical facts found in financial data. To better understand the fluctuation complexity properties of the proposed model, the complex analyses of random logarithmic price return series are preformed, including power-law distribution, Lempel–Ziv complexity, correlation dimension analysis, maximum Lyapunov exponent, mean Lyapunov exponents and Kolmogorov–Sinai entropy density. In order to verify the rationality of the model, the corresponding analyses of real return series are also studied for comparison. The empirical research reveals that this financial model can reproduce similar statistical behaviors, power-law distribution of returns, complexity and chaotic features of returns for real stock markets.     

A study of the chaotic behaviour of the elastic-plastic Euler arch

This paper deals with the dynamics of a truss structure, the Euler arch. The bars are made of elastic-plastic material, and the structure can exhibit large displacements. The aim of this paper is to give evidence of the possible chaotic behavior of this structure, even in the presence of a hardening plastic branch. The tools used are the diagrams of bifurcation, the measure of the dimension of the attractor, the Kolmogorov entropy, and the maximum Lyapunov exponent. This study emphasizes the sensitivity to the initial conditions by means of generalized basins of attraction.     

Direct numerical simulation of driven cavity flows

Direct numerical simulations of 2D driven cavity flows have been performed. The simulations exhibit that the flow converges to a periodically oscillating state at Re=11,000, and reveal that the dynamics is chaotic at Re=22,000. The dimension of the attractor and the Kolmogorov entropy have been computed. Explicit time-integration techniques are discussed.     

Stochastic averaging of energy harvesting systems

A stochastic averaging method is proposed for nonlinear energy harvesters subjected to external white Gaussian noise and parametric excitations. The Fokker–Planck–Kolmogorov equation of the coupled electromechanical system of energy harvesting is a three variables nonlinear parabolic partial differential equation whose exact stationary solutions are generally hard to find. In order to overcome difficulties in solving higher dimensional nonlinear partial differential equations, a transformation scheme is applied to decouple the electromechanical equations. The averaged Itô equations are derived via the standard stochastic averaging method, then the FPK equations of the decoupled system are obtained. The exact stationary solution of the averaged FPK equation is used to determine the probability densities of the displacement, the velocity, the amplitude, the joint probability densities of the displacement and velocity, and the power of the stationary response. The effects of the system parameters on the output power are examined. The approximate analytical outcomes are qualitatively and quantitatively supported by the Monte Carlo simulations.     

Stochastic averaging for nonlinear vibration energy harvesting system

A stochastic averaging technique for the nonlinear vibration energy harvesting system to Gaussian white noise excitation is developed to analytically evaluate the mean-square electric voltage and mean output power. By introducing the generalized harmonic transformation, the influence of the external circuit on the mechanical system is equivalent to a quasi-linear stiffness and a quasi-linear damping with energy-dependent coefficients, and then the equivalent nonlinear system with respect to the mechanical states is completely established. The Itô stochastic differential equation with respect to the mechanical energy of the equivalent nonlinear system is derived through the stochastic averaging technique. Solving the associated Fokker–Plank–Kolmogorov equation yields the stationary probability density of the mechanical states, and then the mean-square electric voltage and mean output power are analytically obtained through the approximate relation between the electric quantity and the mechanical states. The agreements between the analytical results and those from the moment method and from Monte Carlo simulations validate the effectiveness of the proposed technique.     

动力系统的复杂性刻划

本文扼要地综述了近年来提出的刻划动力系统复杂性的各种度量．着重点在于将复杂性同随机性区分开．由此对于过去为刻划混沌而提出的度量，其中包括Ｌｙａｐｕｎｏｖ指数、拓扑熵、测度熵和Ｋｏｌｍｏｇｏｒｏｖ复杂性等，作了简单回顾．从自动机和信息论的观点对于包括ＡＣ、ＳＣ、ＥＭＣ在内的新提出的复杂性度量作了阐述．通过单峰映射和一维元胞自动机等例子对上述复杂性度量进行了比较，并较详细地介绍了利用形式语言和自动机来分析动力系统的方法．     

基于FPK方程的减摆器的非线性阻尼测试方法

受高斯白噪声外激的一阶非线性动力学方程能通过求解对应的FPK方程得到精确稳态解．本文基于这一结果导出减摆器非线性阻尼力与系统速度输出的概率结构的关系,将动力学系统中非线性阻尼力参数的测试问题转化测量系统的概率结构,并通过仿真进行了验证．