实验数据反演识别分析方法与力学表征

本文给出了两类基于实验(实测)数据的反演识别方法,简述了其在界面力学性能及工程实测数据分析中的应用.在粘接界面力学性能的反演识别实验研究中,基于不同加载速率的实验曲线,结合参数化界面力学模型,通过反演识别给出粘接界面力学性能参数,并对识别结果的适定性进行独立的实验验证;在基于工程实测数据的反演识别与力学建模方面,在分析盾构装备载荷特点的基础上,对海量的实测数据统计分类,提出了力学量纲分析的建模方法,并应用于盾构掘进载荷的反演识别研究.     

三维液体非线性晃动动力学特性的数值模拟

主要讨论圆筒形贮腔中三维液体非线性晃动问题,将任意的拉格朗日-欧拉（即ArbitraryLagrangian-Eulerian,简称ALE）运动学描述引入到Navies-Stokes方程中,在时间域上采用一种速度和压力的分步计算格式进行时间离散;在空间域上利用Galerkin加权余量法对系统方程进行数值离散;得到了数值计算粘性不可压液体非线性晃动的ALE分步有限元法的计算格式,推导了三维液体自由液面上结点法向矢量的数值计算方法,模拟了圆筒形贮腔（包括带圆环形隔板的圆筒形贮腔）中三维液体的非线性晃动;并得到了一些重要的非线必不知所云 性,通过数值模拟结果与实验结果的比较,证明实了本文方法的可靠性与有效性。     

Fractional plasticity for over-consolidated soft soil

The stress–strain response of over-consolidated soft soil, e.g., clay, is dependent on its pre-consolidation history and material state. In this study, a state-dependent constitutive model for over-consolidated soft soils is proposed by extending the fractional plasticity originally developed for granular soil. The state-dependent stress-dilatancy and peak failure behaviour of over-consolidated soft soil are analytically captured through stress-fractional gradient of the current yielding surface. In addition, a reference yielding surface describing the pre-consolidation history of soft soil is proposed. A combined hardening rule expressed as a function of both the incremental plastic volumetric and shear strains is suggested. To validate the proposed model, a series of drained and undrained test results of different soft soils with a wide range of over-consolidation ratios are simulated and compared. It is found that without using additional plastic potentials and state parameters, the developed fractional model can capture the state-dependent hardening and softening responses of soft soils subjected to different over-consolidation states.

     

Fractional central pattern generators for bipedal locomotion

Locomotion has been a major research issue in the last few years. Many models for the locomotion rhythms of quadrupeds, hexapods, bipeds and other animals have been proposed. This study has also been extended to the control of rhythmic movements of adaptive legged robots. In this paper, we consider a fractional version of a central pattern generator (CPG) model for locomotion in bipeds. A fractional derivative D ^α f(x), with α non-integer, is a generalization of the concept of an integer derivative, where α=1. The integer CPG model has been proposed by Golubitsky, Stewart, Buono and Collins, and studied later by Pinto and Golubitsky. It is a network of four coupled identical oscillators which has dihedral symmetry. We study parameter regions where periodic solutions, identified with legs’ rhythms in bipeds, occur, for 0<α≤1. We find that the amplitude and the period of the periodic solutions, identified with biped rhythms, increase as α varies from near 0 to values close to unity.     

Fractional Diffusion Limit for Collisional Kinetic Equations

This paper is devoted to diffusion limits of linear Boltzmann equations. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate time scale, the small mean free path limit gives rise to a diffusion equation. In this paper, we consider situations in which the equilibrium distribution function is a heavy-tailed distribution with infinite variance. We then show that for an appropriate time scale, the small mean free path limit gives rise to a fractional diffusion equation.     

The Pohozaev Identity for the Fractional Laplacian

In this paper we prove the Pohozaev identity for the semilinear Dirichlet problem \({(-\Delta)^s u =f(u)}\) in \({\Omega, u\equiv0}\) in \({{\mathbb R}^n\backslash\Omega}\) . Here, \({s\in(0,1)}\) , (?Δ) ^s is the fractional Laplacian in \({\mathbb{R}^n}\) , and Ω is a bounded C ^1,1 domain. To establish the identity we use, among other things, that if u is a bounded solution then \({u/\delta^s|_{\Omega}}\) is C ^α up to the boundary ?Ω, where δ(x) = dist(x,?Ω). In the fractional Pohozaev identity, the function \({u/\delta^s|_{\partial\Omega}}\) plays the role that ?u/?ν plays in the classical one. Surprisingly, from a nonlocal problem we obtain an identity with a boundary term (an integral over ?Ω) which is completely local. As an application of our identity, we deduce the nonexistence of nontrivial solutions in star-shaped domains for supercritical nonlinearities.     

Fractional step algorithm for estuarine mass transport

A successful and economical fractional step algorithm for the convection-dispersion-reaction equation is described. Exact solutions are adopted for the reaction and convection steps, the latter by the introduction of a moving co-ordinate system. The dispersion step uses an optimized finite difference algorithm which specifically accommodates the grid non-uniformity. The excellent performance of the algorithm is confirmed by numerical experiments together with computations of the Fourier response and integrated square error characteristics.     

力学的反演、反演的力学

１地震发生了,是怎么造成的？１９７６年７月２８日唐山发生了一次７．８级的大地震,在没有警告的情形下,一座工业大城市顷刻之间夷为平地,死亡人数超过２４万,成为２０世纪伤亡最重的一次自然灾害．全国为之震惊．华北地区的人民尤为惊慌,希望知道这个地区是否还有发大震（这时随后发过好几次五、六级的余震）的危险,下次将在何处发震,特别是北京发震的危险程度如何．既然地震是一个力学过程,这个问题对我们力学工作者是一个严肃的挑战．从力学问题来看,我们所知道的是地震时得到的记录,地震后的遗迹（见图１,图２）所想寻找的…     

Fractional diffusion equations for open quantum system

To describe non-local interactions of quantum systems with environment we consider a fractional generalization of the quantum Markovian equation. Quantum analogs of fractional Laplacian operator for coordinate and momentum spaces are suggested. In phase-space form of quantum mechanics we obtain fractional equations for Wigner distribution function, where fractional Laplacian operators of the Grünvald–Letnikov type are used.     

Fractional Order Disturbance Observer for Robust Vibration Suppression

For the first time, the fractional order disturbance observer (FO-DOB) is proposed for vibration suppression applications such as hard disk drive servo control. It has been discovered in a recently published US patent application (US20010036026) that there is a tradeoff between phase margin loss and strength of the low frequency vibration suppression. Given the required cutoff frequency of the low pass filter, also known as the Q-filter, it turns out that the relative degree of the Q-filter is the major tuning knob for this tradeoff. The solution in US20010036026 was based on an integer order Q-filter with a variable relative degree. This actually motivated the use of a fractional order Q-filter. The fractional order disturbance observer is based on the fractional order Q-filter. The implementation issue is also discussed. The nice point of this paper is that the traditional DOB is extended to the fractional order DOB with the advantage that the FO-DOB design is now no longer conservative nor aggressive, i.e., given the cutoff frequency and the desired phase margin, we can uniquely determine the fractional order of the low pass filter.     

Dispersion Relations for the Linearized Fokker-Planck Equation

We analyze the spectral properties and dispersion relations for the linearized Fokker-Planck operator in the case of hard potentials, as in Ellis & Pinsky's work [7] on the Boltzmann equation. Results similar to those in [7] are obtained for the Fokker-Planck operator although the presence of a diffusion operator instead of a multiplication operator introduces many additional technical difficulties. (Accepted December 7, 1995)     

Fractional Order Disturbance Observer for Robust Vibration Suppression

For the first time, the fractional order disturbance observer (FO-DOB) is proposed for vibration suppression applications such as hard disk drive servo control. It has been discovered in a recently published US patent application (US20010036026) that there is a tradeoff between phase margin loss and strength of the low frequency vibration suppression. Given the required cutoff frequency of the low pass filter, also known as the Q-filter, it turns out that the relative degree of the Q-filter is the major tuning knob for this tradeoff. The solution in US20010036026 was based on an integer order Q-filter with a variable relative degree. This actually motivated the use of a fractional order Q-filter. The fractional order disturbance observer is based on the fractional order Q-filter. The implementation issue is also discussed. The nice point of this paper is that the traditional DOB is extended to the fractional order DOB with the advantage that the FO-DOB design is now no longer conservative nor aggressive, i.e., given the cutoff frequency and the desired phase margin, we can uniquely determine the fractional order of the low pass filter.     

A Fractional Linear System View of the Fractional Brownian Motion

A definition of the fractional Brownian motion based on the fractional differintegrator characteristics is proposed and studied. It is shown that the model enjoys the usually required properties. A discrete-time version based in the backward difference and in the bilinear transformation is considered. Some results are presented.     

Inversion for weak triclinic anisotropy from acoustic axes

Acoustic axes are directions in anisotropic elastic media, in which phase velocities of two or three plane waves (P$P$, S1$S1$ or S2$S2$ waves) coincide. Acoustic axes are important, because they can cause singularities in the field of polarization vectors and anomalies in the shape of the slowness surface. The maximum number of acoustic axes in triclinic anisotropy is 16, and their directions depend on anisotropy parameters in a complicate way. Under weak anisotropy approximation this dependence simplifies and the directions of acoustic axes can be used for the inversion for anisotropy parameters. The maximum acoustic axes under weak anisotropy is 16, the minimum number of acoustic axes is zero. In the inversion, we can retrieve 13 combinations of anisotropy parameters provided we use directions of 7 acoustic axes at least. Under weak anisotropy approximation, the directions of acoustic axes are insensitive to strength of anisotropy; hence we cannot invert for absolute values of weak anisotropy parameters, but only for their relative values. Numerical tests have shown that the inversion is applicable only to very weak anisotropy with strength of less than 5%, provided that the acoustic axes used in the inversion are determined with an accuracy of 0.1^°$0.1^{°}$ or better. In this case the inversion yields an average error for elastic parameters of less than 10%. In order to invert for the total set of 21 anisotropy parameters it is necessary to combine the measurements of the directions of the acoustic axes with measurements of other attributes of elastic waves in anisotropic media.     

平面SH波传递算子反演方法

讨论了弹性水平层状介质中ＳＨ波的反演问题,在平面脉动ＳＨ波激励和反射模式下利用的传递算子方法逐层反演了介质的速度,密度和厚度,反演过程转化为线性回归,并且进行了数值模拟这种逐层反演方法简化了方程的阶数和计算量。     

Fractional WKB approximation

Wentzel–Kramer–Brillouin (WKB) approximation for fractional systems is investigated in this paper using the fractional calculus. In the fractional case, the wave function is constructed such that the phase factor is the same as the Hamilton’s principle function S. To demonstrate our proposed approach, two examples are investigated in detail.     

An Improved Weighting Method for Inversely Determining Elastic Constants of Coating Layers from Dispersion Curves of Surface Acoustic Waves

This paper investigates the inversion of elastic constants of a coating layer from measured dispersion curves of a layered half-space sample. A systematic analysis on the sensitivity of dispersion curves is performed and the results provide important information in constructing a better inversion process. Numerical simulation has been given to demonstrate several possibilities for obtaining accurate elastic constants from the measured dispersion data over different frequency domains. Experiments have also been carried out using broadband Poly(vinylidene fluoride-trifluoroethylene) [P(VDF-TrFE)] focusing transducers and their surface wave measurement system over a wide frequency range of 4?~?120 MHz. Nickel coating layers electroplated on thick glass substrates are tested for the inversion. It is observed that the proposed inversion method, which carefully chooses the dispersion data at specific frequency ranges as well as adding some weightings to them, is indeed significantly improve the accuracy and convergence of the obtained elastic constants of the coated nickel layers. Young’s modulus of the coated nickel layers is also measured by a nano-indentation system and the results show good agreement with the data determined by the proposed inversion method.     

Optimal Continuous Dependence Estimates for Fractional Degenerate Parabolic Equations

We derive continuous dependence estimates for weak entropy solutions of degenerate parabolic equations with nonlinear fractional diffusion. The diffusion term involves the fractional Laplace operator, \({\triangle^{\alpha/2}}\) for \({\alpha \in (0,2)}\) . Our results are quantitative and we exhibit an example for which they are optimal. We cover the dependence on the nonlinearities, and for the first time, the Lipschitz dependence on α in the BV-framework. The former estimate (dependence on nonlinearity) is robust in the sense that it is stable in the limits \({\alpha \downarrow 0}\) and \({\alpha \uparrow 2}\) . In the limit \({\alpha \uparrow 2}\) , \({\triangle^{\alpha/2}}\) converges to the usual Laplacian, and we show rigorously that we recover the optimal continuous dependence result of Cockburn and Gripenberg (J Differ Equ 151(2):231–251, 1999) for local degenerate parabolic equations (thus providing an alternative proof).     

An Analytical Solution for an Exponential-Type Dispersion Process

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