A New Approach to Asymptotic Diagonalization of Linear Differential Systems

We study the asymptotic diagonalization of a system consisting of an -matrix plus a finite number of -perturbations on an interval I ₀=[t ₀, ), where p, m _i[1, ). Using linear skew-product flows and spectral theory, we show that if the unperturbed system has full spectrum over its omega-limit set, then the entire system is asymptotically diagonalizable almost everywhere.     

Applications of Nonlinear Dynamical Systems Theory in Developmental Psychology: Motor and Cognitive Development

Applications of nonlinear dynamical systems theory to psychology have led to recent advances in understanding neuromotor development and advances in theories of cognitive development. This article reviews published findings associated with a specific coherent and influential application from which a theory of adaptive, self-organized cognition has been derived and related to a theory of developmental dynamics of the neuromotor system. The review focuses on implications of the two theories for quantifying developmental phenomena, and suggests a method for quantifying the cognitive theory.     

Invariant Manifold Approach for the Stabilization of Nonholonomic Chained Systems: Application to a Mobile Robot

In this paper it is shown that a class ofn-dimensional nonholonomic chained systems can bestabilized using the invariant manifold approach. First, we derive aninvariant manifold for this class of systems and we show that, once onit, all the closed-loop trajectories tend to the origin under a linearsmooth time-invariant state feedback. Thereafter, it is shown that thismanifold can be made attractive by means of a discontinuoustime-invariant state feedback. Finally, a mobile robot is taken as anexample demonstrating the effectiveness of our study.     

Application of Nonlinear Normal Mode Analysis to the Nonlinear and Coupled Dynamics of a Floating Offshore Platform with Damping

The nonlinear dynamics of ships and floating offshore platforms hasattracted much attention over the last several years. However the topicof multiple-degrees-of-freedom systems has almost been completely ignoredwith very few exceptions. This is probably due to the complexity ofanalyzing strongly nonlinear and coupled systems. It turns out thatcoupling may be particularly important for certain critical dynamicssuch as the dynamics of a floating offshore platform about its diagonalaxis. In a previous work, Kota et al. [1] applied the recently developed nonlinearnormal mode technique to analyze the coupled nonlinear dynamics of afloating offshore platform. Although this previous work was restrictedto unforced and undamped systems, in this work a comparison of the twoalternative nonlinear normal mode analysis techniques was completed.Considering the relative practical importance of damping versus externalforcing for this system, in the present work, we utilize just one of thetwo major techniques available [2] to analyze damped multiple-degrees-of-freedom nonlinear dynamics. Specifically, we investigate the effect ofnonlinearity, and non-proportionate damping. Our results show that thistechnique allows one to simply consider the effect of nonlinearity andgeneral damping on the resulting normal modes. This technique isparticularly powerful because it allows one to visualize the modes in ageometric fashion using the invariant manifold concept from dynamicalsystems.     

刚柔耦合约束多体系统的动力分析

本文提出了描述柔性多体系统的牵连坐标系统。该系统由惯性参考系,牵连坐标系,物体坐标系及单元坐标系组成,实现了对刚体平动,刚体转动及弹性运动的连续分解,最大限度地消除了由于刚体大角度转动导致的非线性特性。以有限元法为基础,应用拉格朗日方程建立了在该坐标下的刚柔耦合约束多体系统的动力学控制方程。该方程具有耦合程度小、易于推导、编程及求解等优点,为大规模约束多体系统的动力分析提供了新的途径。本文还讨论了平面铰链约束的约束形式及约束方程,最后给出了一个典型多体系统的数值算例。     

A General Data-Based Approach for Developing Reduced-Order Models of Nonlinear MDOF Systems

A general procedure is presented for analyzing dynamic response measurements from complex multi-degree-of-freedom nonlinear systems incorporating arbitrary types of nonlinear elements. The analysis procedure develops a reduced-order, nonlinear model whose format is convenient for numerical simulation studies. No information about the systems mass properties is needed, and only the applied excitations and corresponding response are needed to develop the model whose dimension is compatible with the number of available sensors. The utility of the approach is demonstrated by means of a three-degree-of-freedom system incorporating polynomial-type nonlinear features with hardening as well as softening characteristics.     

Invariant Manifolds for Random Dynamical Systems with Slow and Fast Variables

We consider random dynamical systems with slow and fast variables driven by two independent metric dynamical systems modeling stochastic noise. We establish the existence of a random inertial manifold eliminating the fast variables. If the scaling parameter tends to zero, the inertial manifold tends to another manifold which is called the slow manifold. We achieve our results by means of a fixed point technique based on a random graph transform. To apply this technique we need an asymptotic gap condition.      

分数因子与分数阶完整力学系统的运动方程和循环积分

引入分数因子和分数增量,给出了分数阶微积分的定义和性质;基于分数阶导数的定义,证明了含有分数因子的等时变分与分数阶算子的交换关系;提出了分数阶完整保守和非保守系统的Hamilton原理;建立了分数阶完整保守系统和非保守系统的运动微分方程;得到了分数阶完整保守系统的循环积分;并利用分数阶循环积分导出分数阶罗兹方程．最后给出了两个例子．研究表明利用分数因子给出的分数阶微分方程是一个含有分数因子的通常的微分方程,那么分数阶系统运动微分方程的求解都可以采用通常微分方程的求解方法．     

Modeling and Dynamic Analysis of Telescopic Systems of Structural Members with Clearance

The dynamic behavior of multi-section constructions with clearance during extending and retracting motion of the sections is analyzed. First, an appropriate physical modeling is introduced before next, the governing boundary value problem is derived by applying Hamilton's principle. Then, a classical discretization procedure is used to generate a coupled system of nonlinear ordinary differential equations as the corresponding truncated mathematical model. Performing appropriate simulations to be verified by results of an alternative software package and partly validated by some preliminary experiments, the vibrational behavior of the suggested type of multi-section telescoping systems can be studied in detail.     

A Frequency-Domain Approach to Optimal Fractional-Order Damping

In this paper, we will consider the single term optimal fractional-order damper for an otherwise undamped oscillator. First, we will find the single term damper that minimizes the time domain integral of the squared step error (2-norm) and the integral of the time-weighted squared error (Hilbert–Schmidt–Hankel norm). Next we will consider a more intuitive frequency domain approach that insures the maximally flat magnitude response. Time and frequency domain plots are given for comparison with the integer-order solutions. Further improvements in performance are shown to be possible using multiple active fractional-order dampers.     

Invariant Set and Attractor of Nonautonomous Functional Differential Systems: A Decomposition Approach

In this paper, the invariant set and attractor are addressed for the nonautonomous functional differential systems. An estimation of the existence range of the invariant set and attractor are given by using a decomposition approach and the properties of nonnegative matrices. In addition, an example is given to denote the application of the new results.     

Analytical Stability Bound for a Class of Delayed Fractional-Order Dynamic Systems

Delayed Linear Time-Invariant (LTI) fractional-order dynamic systems areconsidered. The analytical stability bound is obtained by using Lambertfunction. Two examples are presented to illustrate the obtainedanalytical results.     

A Unified Approach to Dynamic Contact Problems in Viscoelasticity

In this paper we consider mathematical models describing dynamic viscoelastic contact problems with the Kelvin–Voigt constitutive law and subdifferential boundary conditions. We treat evolution hemivariational inequalities which are weak formulations of contact problems. We establish the existence of solutions to hemivariational inequalities with different types of non-monotone multivalued boundary relations. These results are consequences of an existence theorem for second order evolution inclusions. In a particular case we deliver sufficient conditions under which the solution to a hemivariational inequality is unique. Finally, applications to several unilateral and bilateral problems in contact mechanics are provided.*Research supported in part by the State Committee for Scientific Research of the Republic of Poland (KBN) under Grants no. 2 P03A 003 25 and 4 T07A 027 26.     

A Sedimentological Approach to Upscaling

Optimised upscaling in reservoir simulations requires the construction of realistic petrophysical properties that are representative of the heterogeneity in the sedimentary deposits. Reservoir heterogeneities are controlled by the arrangement of various hierarchies of sedimentary facies and their internal bounding surfaces. The conventional sedimentological approach to reservoir upscaling involves subdivision and ranking of various hierarchies of architectural units and associated bounding surfaces of the reservoir sequence according to their geological significance. This global upscaling approach produces realistic scaled up models that retain both the structural and non-structural heterogeneities of the original sedimentological models. Analyses of sedimentary sequences from various depositional environments indicate that the fractional Levy model can adequately describe the heterogeneity and scaling characteristics of individual genetic sediment sequences in the clastic sedimentary system without further subdividing and ranking of the heterogeneous sequences. The heterogeneous nature of each sedimentary system can be quantified by the Levy index parameter, whereas the maximum upscaling magnitude (or upscaling index) for a particular sequence can be determined from the Levy width parameter plot. Depositional modelling mimics the sedimentary processes in a range of scales and honours hierarchies of sedimentary facies and their bounding surfaces. It can be used effectively for upgridding and upscaling in accordance with the stratigraphic framework and sedimentological models. Both the fractional Levy model and the depositional modelling provide quantitative alternatives to the conventional global sedimentological upscaling approach.     

计及二阶效应的门座起重机变幅工况动力学分析

对门座起重机的变幅工况进行了计及二阶效应的大范围运动弹性动力分析。使用柔性多体系统动力学方法描述柔性体的变形和运动,结合非线性有限元理论推导了一般运动柔性单元在局部坐标系下的计及二阶效应的动力学方程,进而使用三结点Euler-Bernoulli梁单元的形函数,推导了柔性梁单元的动力学方程。对该方程进行静力凝聚并使用随动坐标法,得到便于系统动力学方程组集的整体坐标系下的两结点梁单元动力学方程。对某型门座起重机臂架系统的变幅工况进行了计及二阶效应的弹性动力分析,结果表明:二阶弹性位移和内力均为相应线性解上的波动,且波动幅值较大,因此对大柔度重载机械应进行考虑二阶效应的弹性动力分析。     

Formulation and Solution of Dynamic Problems of Elastic Rod Systems Subjected to Boundary Conditions Described by Multivalued Relations

The dynamic behavior of rod systems under the action of external force factors described by multivalued (subdifferential) relations is studied. The mathematical formulation of the problem is given in the form of a dynamic quasivariational inequality. With the use of the Newmark difference scheme, successive approximations, and finite-element discretization, the problem is reduced to minimization of a convex nonsmooth finite-dimensional functional with respect to velocities at each time step. Introduction of auxiliary variables by the method of a modified Lagrangian reduces the problem of minimization of this functional to a sequence of smooth problems of nonlinear programming. The algorithm is verified using the numerical solution for a problem with one degree of freedom. The algorithm proposed is used to calculate the rods of deep-well pumps.     

Some aspects of destabilization in reversible dynamical systems with application to follower forces

This paper examines the destabilization of the equilibria of reversible dynamical systems which is induced by the addition of irreversible perturbations. Attention is restricted to reversible dynamical systems which have frequently appeared in the literature on elastic stability. There they are often referred to as follower force problems. The destabilization phenomenon is linear in nature and explicit criteria are established to determine the particular eigenvalue splittings. The post-destabilization dynamics are also examined using the appropriate normal forms for two specific cases, one where the eigenvalues are non-resonant and the other where the eigenvalues are in a strong one-to-one resonance. Finally, the destabilization criteria and certain features of the post-destabilization dynamics are illustrated using two examples of follower force systems.     

Complexity Versus Complex Systems: A New Approach to Scientific Discovery

Extraction of quantitative features from observations via suitable measuring devices M means that the words of science are coded as numbers, and the syntaxis is a set of mathematical rules. Once general premises are available all consequences can be worked in a purely deductive way. This characteristic of science displays two orders of drawbacks, namely, undecidability of deductive procedures, and intractability of computer modelings of complex situations. The way out of such a crisis consists in an adaptive strategy, that is, in a frequent readjustment of M suggested by the observed events. As a consequence, M provides different data streams (words) for the same observed events, as it is tuned to different resolutions. The adaptive strategy here introduced should by no means be confused with the adaptivity of a learning machine, which—inputted by a data stream—readjusts itself over a class of theoretical explanations in order to select the optimal one, thus providing knowledge conditional on the assigned input. On the contrary, physics aims at extracting regular patterns out of things, by a trial and error procedure which includes not only modifications of the explanations for fixed data sets, but also exploring different data sets via modified M's. This M-adjustment is a pre-linguistic endeavour, not expressible by a formal language. Such an essential characteristic of the physical program means that physics can not be performed by a machine.