A linear stability approach to vortex-induced vibrations and waves

The motion induced by vortex shedding on slender flexible structures subjected to cross-flow is considered here. This phenomenon of vortex-induced vibration (VIV) is analysed by considering the linear stability of a coupled system that includes the structure dynamics and the wake dynamics. The latter is modelled by a continuum of wake oscillators, distributed along the span of the structure. In the case of uniform flows over a straight tensioned cable, VIV are found to arise as an instability related to the merging of two waves. In the case of a cable of finite length, the selection of modes that experience lock-in with the wake is found using the same stability argument. In non-uniform flows, several unstable wave systems are identified, and competition between them is discussed. Comparison is then made with existing experimental and computational data of VIV of slender structures under uniform and non-uniform flows. Phenomena previously identified in these systems, such as mode switching when the flow velocity is varied, time sharing of the response between two frequencies, or the coexistence of several regions of VIV with different dynamics in the same structure, are discussed with the help of the proposed model.     

Responses to Constrained Stimulus Sequences in Nonlinear Psychophysics

Generic models used in nonlinear psychophysical dynamics (NPD) have been extensively explored for their capacity to simulate both local singular phenomena and non-monotonic response functions. Internal parameters representing a form of system sensitivity and secondary recursive activity can interact when very low stimulation operates on the gain controlling the evolution of response trajectories, when these trajectories evolve either singly or when chained. Ways in which an existing NPD model can, without change of structure, incorporate naturalistic processes of feedback and stimulus constraint are illustrated. Stimuli-response pairs presented in long closely spaced sequences may appear to be created by a diversity of cognitive strategies, but this assumption is not necessary if nonlinear dynamics are involved. The total system may then resemble the convolution of two fast/slow trajectories. Cusp catastrophe-like sequences can be induced. Nonparametric bases for making statistical comparisons between theory and data, when both are in time series form, are given.     

A conditional sampling method based on fuzzy clustering for the analysis of large-scale dynamics in turbulent flows

A conditional sampling technique, based on fuzzy clustering, is used to educe the organization of the secondary flow motions observed in the large-eddy simulation of a turbulent square channel flow. The data analysed are the multi-valued time series obtained from sampling the secondary velocity components at a fixed cross-section of the channel, over consecutive time steps. The mean values of the secondary flow motion velocities are one order of magnitude lower than their r.m.s values. The purpose of the conditional sampling scheme used is to replace the picture of the secondary flow motions provided by the unconditional time mean with several ensemble averages. In this way the whole variability of the instantaneous data can be split in two parts: one for the difference between the observed ensemble averages, and the other for the variability within each ensemble. Unlike other conditional sampling schemes which sort only part of the data into one or more families depending on an externally fixed condition, the fuzzy clustering approach used here first determines the optimum number of families or clusters and then classifies all the recorded time steps. The results show that the local turbulence intensities of the ensemble averages obtained from fuzzy clustering can be reduced by one order of magnitude. In addition, the classification of all the time steps into several clusters or families enables the large scale dynamics of the educed structures to be analysed.     

Determination of corrective local compliances of structures for use in vibration computations

Usually, thin-walled structures, in particular, aircraft, launchers, and space structures, are irregular compound systems. In structure dynamics, they are usually represented as separate mutually interacting substructures [1–3]. Very often, different substructures are connected at separate nodes. This is typical of separable blocks, suspensions, and transformable details [4]. At such nodes, considerable local strains and compliances may arise in connected substructures, which significantly affects the dynamic characteristics of the entire structure. In engineering practice, the local compliances of a structure at connection nodes are often modeled by equivalent springs whose characteristics are determined by approximate methods [5] and expeirents.The substructure synthesis method, the methods for calculating the dynamic characteristics of compound structures, and the methods for their refinement have been considered in numerous papers; here we note the publications [6–10].In the present paper, we propose a method for calculating additional (corrective) local compliances at the connection nodes of compound structures on the basis of quasistatic strain equations and for taking these compliances into account in the equations of dynamics of compound structures obtained by expanding the displacements with respect to lower vibration modes of the substructures.     

Detecting causal relations in time series with the new cross Markov Matrix technique

Nowadays, scientists are increasingly asked to investigate problems, which require the analysis of irregular, chaotic, non-stationary and corrupted time series. Assessing the causal relations between such signals is particularly challenging and, in many instances, interventions and experiments are impossible or impractical. The present work is a contribution to the development of indicators to quantify the mutual influences between time series. The criterion is called Cross Markov Matrix and belongs to the strand of techniques based on the conversion of time series into complex networks and the subsequent analysis of their topological properties. The proposed indicator is quite competitive with the available tools and can complement them very effectively. Indeed, all techniques have their strong and weak points and therefore corroborating the conclusions with mathematically independent methods is a recommended practice. The properties of the Cross Markov Matrix have been investigated with the help of a systematic series of numerical tests using synthetic data. The potential of the approach is then substantiated by the analysis of various real-life examples, ranging from environmental and global climate problems to the mutual influence between media coverage of Brexit and the pound-euro exchange rate.

     

Unsteady flow diagnostics using weak perturbations

The examination of the motion of very weak waves generated from small sources on the boundary of a flow domain gives information on how the domain shape influences the flow, both from spatial and temporal perspectives. In the study of shock wave dynamics the shock itself generates a weak wave when passing over a small step, or surface irregularity. The basic principle is that if a particle produces a series of point disturbances in a flow field, the induced perturbations will propagate outwards at the local sonic velocity whilst at the same time being convected along with the local flow velocity. A number of issues may be identified for an unsteady flow. Firstly, the flow field at later times may be influenced by perturbations produced at earlier times. Secondly, if the positions of the perturbations can be monitored as a function of time, then the trajectory and velocity of the particle may be deduced. Thirdly, if a perturbation arises from a point on a boundary, then its influence, if any, on any particular part of the flow can be established. A number of examples are presented to illustrate the value of the technique and its potential to uncover the mechanisms responsible for the formation of certain flow patterns in high-speed compressible flows.     

多稳态串联折纸结构的非线性动力学特性

折纸结构和折纸力学超材料由于其无穷的设计空间、出色的变形能力、超常规力学特性和广泛的应用前景,最近受到了学术界和工程界的 广泛关注.特别地,某些折纸结构单胞由于具有独特的双稳态特性而获得深入研究.注意到折纸结构和折纸超材料通常由多胞构成,但多胞 结构的多稳态特性及其诱发的动力学行为尚不清晰,相关的研究还较少.本文在双稳态Miura-ori堆叠结构单胞的基础上,研究由两个异构 双稳态单胞基于力平衡串联而成的结构.静力学分析指出,双胞串联结构具有4个定性不同的稳定构型,呈现出多稳态特征.动力学分析指 出,双胞串联结构在4个稳定构型处具有显著不同的固有频率特征. 逐渐增大激励幅值,双胞串联结构的多稳态特性诱发出类型丰富的复杂 非线性动力学响应,包括亚谐、超谐甚至混沌的阱内和阱间振动. 根据幅值特征,我们将稳态动力学响应分为九类,并开展了动力学响应的 吸引盆和吸引盆稳定性分析.结果表明,不同类型动力学响应的吸引盆稳定性(即出现概率)显著不同,且与激励幅值密切相关.本文得到的 多稳态双胞串联结构的静力学特性、动力学响应的分类,以及吸引盆稳定性相对于激励幅值的演化规律,对深入认识多稳态折纸结构的非 线性动力学特性,调控非线性动力学响应具有参考价值和指导意义.      

Orbital decomposition for ill-behaved event sequences: transients and superordinate structures

Time series analysis is often challenged by the presence of transient functions. We examined some types of transients found in time series of events that lend themselves to symbolic dynamics analysis through the method of orbital decomposition, which is based on the principle that chaotic series arise from coupled oscillators. Synthetic data sets were constructed to study the impact of intrusive events, intrusive series, merged functions, non-coupled oscillators, and driving oscillations on the patterns of final statistics obtained from orbital decomposition analysis. Two real-world data sets - a logbook of the ritual behaviors of a patient with obsessive compulsive disorder and a time series of kill dates from an infamous serial murderer - were examined for non-ergodic properties similar to those found in the synthetic data.     

Rich dynamics caused by diffusion

It is an awfully difficult task to design an efficient numerical method for bifurcation diagrams, the graphs of Lyapunov exponents, or the topological entropy about discrete dynamical systems by linear/nonlinear diffusion with the Direchlet/Neumann- boundary conditions. Until now there are less works concerned with such a problem. In this paper, we propose a scheme about bifurcating analysis in a series of discrete-time dynamical systems with linear/nonlinear diffusion terms under the periodic boundary conditions. The complexity of dynamical behaviors caused by the diffusion term are to be determined. Bifurcation diagrams are shown by numerical simulation and chaotic behavior (chaotic Turing patterns) is demonstrated by computing the largest Lyapunov exponent. Our theoretical model can give an interesting case study about the phenomenon: the individuals exhibit a very simple dynamics but the groups with linear/nonlinear coupling can own a complex dynamics including fluctuation, periodicity and even chaotic behavior. We find that diffusion can trigger chaotic behavior in the present system and there exist multiple Turing patterns. It is interesting as regular or chaotic patterns can be reported in this study. Chaotic orbits emerge when exploring further in the diffusion coefficient space, and such a behavior is entirely absent in the corresponding continuous time-space system. The method proposed in the present paper is innovative and the conclusion is novel.

     

The effects of the irregular sample and missing data in time series analysis

Human self-report time series data are typically marked by irregularities in sampling rates; furthermore, these irregularities are typically natural outcomes of the data generation process. Relatively little has been published to assist the analysis of irregularly sampled data. We report the results of a series of computational experiments on synthetic data sets designed to assess the utility of techniques for handling irregular time series data. The behavior of a conservative quasiperiodic, a dissipative chaotic, and a self-organized critical dynamics were sampled regularly in time and the regular sampling was disrupted by data point removal or by stochastic shifts in time. Missing data segments were then patched by means of segment concatenation, by segment filling with average data values, or by local interpolation in phase space. We compared results of nonlinear analytical tools such as autocorrelations and correlation dimensions using complete and patched sets, as well as power spectra with Lomb periodograms of the decimated sets. Local interpolation in phase space was particularly successful at preserving key features of the original data, but required potentially impractical quantities of intact data as a primer. While the other patching methods are not limited by the need for intact data, they distort results relative to the intact series. We conclude that irregularly sampled data sets with as much as 15 percent missing data can potentially be re-sampled or repaired for analysis with techniques that assume regular sampling without introducing substantial errors.     

Wave patterns in a nonclassic nonlinearly-elastic bar under Riemann data

Recently there has been interest in studying a new class of elastic materials, which is described by implicit constitutive relations. Under some basic assumption for elasticity constants, the system of governing equations of motion for this elastic material is strictly hyperbolic but without the convexity property. In this paper, all wave patterns for the nonclassic nonlinearly elastic materials under Riemann data are established completely by separating the phase plane into twelve disjoint regions and by using a nonnegative dissipation rate assumption and the maximally dissipative kinetics at any stress discontinuity. Depending on the initial data, a variety of wave patterns can arise, and in particular there exist composite waves composed of a rarefaction wave and a shock wave. The solutions for a physically realizable case are presented in detail, which may be used to test whether the material belongs to the class of classical elastic bodies or the one wherein the stretch is expressed as a function of the stress.     

Similarity of apparently random structures in the outer region of wall turbulence

Structural similarities between samples of individual, apparently random structures in various wall-bounded turbulent flows are examined using a template-matching technique. Two-dimensional structural patterns obtained by particle image velocimetry in a turbulent boundary layer are sampled along streamwise lines to extract one-dimensional spatial series that are used as templates. These templates are correlated with time series data obtained in turbulent pipe flow, turbulent channel flow, and atmospheric boundary layer flow in order to determine the frequency and coherency with which similar structures occur. The results indicate that a small ensemble of templates from one flow can be concatenated to represent a large fraction of the entire velocity-time history of each of the other flows by using episodes during which the various templates correlate well. Thus, within the pipe flow, channel flow, and atmospheric boundary layer, one frequently finds detailed time series segments that coincide closely, i.e., in fine detail, with a handful of templates found in a laboratory boundary layer. This type of similarity, which includes seemingly random, fine details at large and small scales, is much stronger than similarity based on statistical comparisons. The individual templates that work best, i.e., those that most frequently yield episodes of high correlation, are segments of hairpin-vortex packets. The high frequency with which these particular structures occur suggests that they are common features of all wall-bounded turbulent flows, including turbulent flows at very high Reynolds number such as the atmospheric boundary layer.     

Understanding neuromotor strategy during functional upper extremity tasks using symbolic dynamics

The ability to model and quantify brain activation patterns that pertain to natural neuromotor strategy of the upper extremities during functional task performance is critical to the development of therapeutic interventions such as neuroprosthetic devices. The mechanisms of information flow, activation sequence and patterns, and the interaction between anatomical regions of the brain that are specific to movement planning, intention and execution of voluntary upper extremity motor tasks were investigated here. This paper presents a novel method using symbolic dynamics (orbital decomposition) and nonlinear dynamic tools of entropy, self-organization and chaos to describe the underlying structure of activation shifts in regions of the brain that are involved with the cognitive aspects of functional upper extremity task performance. Several questions were addressed: (a) How is it possible to distinguish deterministic or causal patterns of activity in brain fMRI from those that are really random or non-contributory to the neuromotor control process? (b) Can the complexity of activation patterns over time be quantified? (c) What are the optimal ways of organizing fMRI data to preserve patterns of activation, activation levels, and extract meaningful temporal patterns as they evolve over time? Analysis was performed using data from a custom developed time resolved fMRI paradigm involving human subjects (N=18) who performed functional upper extremity motor tasks with varying time delays between the onset of intention and onset of actual movements. The results indicate that there is structure in the data that can be quantified through entropy and dimensional complexity metrics and statistical inference, and furthermore, orbital decomposition is sensitive in capturing the transition of states that correlate with the cognitive aspects of functional task performance.     

Nonlinear normal modes in multi-mode models of an inertially coupled elastic structure

Nonlinear normal modes for elastic structures have been studied extensively in the literature. Most studies have been limited to small nonlinear motions and to structures with geometric nonlinearities. This work investigates the nonlinear normal modes in elastic structures that contain essential inertial nonlinearities. For such structures, based on the works of Crespo da Silva and Meirovitch, a general methodology is developed for obtaining multi-degree-of-freedom discretized models for structures in planar motion. The motion of each substructure is represented by a finite number of substructure admissible functions in a way that the geometric compatibility conditions are automatically assured. The multi degree-of-freedom reduced-order models capture the essential dynamics of the system and also retain explicit dependence on important physical parameters such that parametric studies can be conducted. The specific structure considered is a 3-beam elastic structure with a tip mass. Internal resonance conditions between different linear modes of the structure are identified. For the case of 1:2 internal resonance between two global modes of the structure, a two-mode nonlinear model is then developed and nonlinear normal modes for the structure are studied by the method of multiple time scales as well as by a numerical shooting technique. Bifurcations in the nonlinear normal modes are shown to arise as a function of the internal mistuning that represents variations in the tip mass in the structure. The results of the two techniques are also compared.     

Flow Partitioning in Fully Saturated Soil Aggregates

Microbes play an important role in facilitating organic matter decomposition in soils, which is a major component of the global carbon cycle. Microbial dynamics are intimately coupled to environmental transport processes, which control access to labile organic matter and other nutrients that are needed for the growth and maintenance of microorganisms. Transport of soluble nutrients in the soil system is arguably most strongly impacted by preferential flow pathways in the soil. Since the physical structure of soils can be characterized as being formed from constituent micro-aggregates which contain internal porosity, one pressing question is the partitioning of the flow among the “inter-aggregate” and “intra-aggregate” pores and how this may impact overall solute transport within heterogeneous soil structures. The answer to this question is particularly important in evaluating assumptions to be used in developing upscaled simulations based on highly resolved mechanistic models. In our synthetic model of soils, firstly we statistically generated a number of micro-aggregates containing internal pores. Then we constructed a group of diverse multi-aggregate structures with different packing ratios by stacking those micro-aggregates and varying the size and shape of inter-aggregate pore spacing between them. We then performed pore-scale flow simulations using computational fluid dynamics methods to determine the flow patterns in these aggregate-of-aggregates structures and computed the partitioning of the flow through intra- and inter-aggregate pores as a function of the spacing between the aggregates. The results of these numerical experiments demonstrate that soluble nutrients are largely transported via flows through inter-aggregate pores. Although this result is consistent with intuition, we have also been able to quantify the relative flow capacity of the two domains under various conditions. For example, in our simulations, the flow capacity through the aggregates (intra-aggregate flow) was less than 2 % of the total flow when the spacing between the aggregates was larger than $18\,\upmu \hbox {m}$ . Inter-aggregate pores continued to be the dominant flow pathways even at much smaller spacing; intra-aggregate flow was less than 10 % of the total flow when the inter- and intra-aggregate pore sizes were comparable. Although the results may not be exactly the same as those obtained from actual soil systems, such studies are making it possible to identify which model upscaling assumptions are realistic and what computational methods are required for detailed numerical investigation of hydrodynamics and microbial carbon cycling dynamics in soil systems.     

Multi-scaled analysis of the damped dynamics of an elastic rod with an essentially nonlinear end attachment

We study multi-frequency transitions in the transient dynamics of a viscously damped dispersive finite rod with an essentially nonlinear end attachment. The attachment consists of a small mass connected to the rod by means of an essentially nonlinear stiffness in parallel to a viscous damper. First, the periodic orbits of the underlying hamiltonian system with no damping are computed, and depicted in a frequency–energy plot (FEP). This representation enables one to clearly distinguish between the different types of periodic motions, forming back bone curves and subharmonic tongues. Then the damped dynamics of the system is computed; the rod and attachment responses are initially analyzed by the numerical Morlet wavelet transform (WT), and then by the empirical mode decomposition (EMD) or Hilbert–Huang transform (HTT), whereby, the time series are decomposed in terms of intrinsic mode functions (IMFs) at different characteristic time scales (or, equivalently, frequency scales). Comparisons of the evolutions of the instantaneous frequencies of the IMFs to the WT spectra of the time series enables one to identify the dominant IMFs of the signals, as well as, the time scales at which the dominant dynamics evolve at different time windows of the responses; hence, it is possible to reconstruct complex transient responses as superposition of the dominant IMFs involving different time scales of the dynamical response. Moreover, by superimposing the WT spectra and the instantaneous frequencies of the IMFs to the FEPs of the underlying hamiltonian system, one is able to clearly identify the multi-scaled transitions that occur in the transient damped dynamics, and to interpret them as ‘jumps’ between different branches of periodic orbits of the underlying hamiltonian system. As a result, this work develops a physics-based, multi-scaled framework and provides the necessary computational tools for multi-scaled analysis of complex multi-frequency transitions of essentially nonlinear dynamical systems.     

Fourier-based incremental homogenisation of coupled unilateral damage–plasticity model for masonry structures

In structural analysis of large masonry structures, nondemanding computation effort, numerical stability and simplified model assembly and meshing often have a higher priority over precise details of local stress or strain responses. This paper presents the development of a Fourier-based incremental homogenisation technique, where the macro–micro transformations of mechanical variables are derived by incremental variational problems to minimise the potential energy in representative volume elements (RVEs) with respect to local fluctuating displacement fields expanded in Fourier series. In addition to the proposed homogenisation technique, a unilateral damage–plasticity constitutive model for mortar joints in the RVE is developed within the framework of thermomechanics, which accounts for the stiffness and strength degradation (or recovery) due to the transverse crack opening/closing in the mortar joints. The numerical solution for the homogenisation problem and the performances of the proposed coupled-damage plastic mode and Fourier-based homogenisation scheme verified by detailed case studies are presented. It has been shown that the computational effort of the analysis with the proposed modelling technique can be considerably reduced by more than 20% as compared with that of the discrete modelling technique.     

壁湍流相干结构的辨识

本文评价了辨识湍流边界层近壁区域相干结构的条件采样法、自相关函数法、数字滤波法和子波分析法。结果表明：条件采样方法对门限值和平均窗宽等检测参数具有较强的依赖性，可以通过调整这些参数来选择最佳的参数值使得相干结构的误判概率达到最小。自相关函数法不需要任何参数就能够得出确定的结论，因此是一种比较客观的方法。但是，这种方法只能从统计上确定平均猝发周期，并不能实时地辨识相干结构。数字滤波法能够将湍流脉动信号分解为大尺度涡和近似各向同性的小尺度涡两部分，但是如何去掉大尺度信号中的非相干部分是仍然需要解决的问题。子波分析是分解湍流信号辨识湍流相干结构的有效手段，它能够将湍流信号在时域空间和频域空间进行双局部化分解，用能量最大准则确定相干结构对应的时间尺度参数，用子波逆变换提取相干结构对应的速度信号波形     

变质量密度简支梁横向振动的模态局部化

结构动力学领域的模态局部化现象最早由Hodges发现，主要发生在周期结构中．例如螺旋桨之类的循环对称结构、连续梁以及通信天线等大型空间桁架结构。发生摸态局部化现象时．振动能量集中于结构局部，容易造成结构破坏。实际上．模态局部化现象已经造成了一些损害．特别是在航宅航天领域。目前研究模态局部化现象时主要采用简单模型，例如周期分布的弹簧质量系统、均匀连续粱，O．O．Bendiksen研究了密度周期分布杆的纵向和扭转振动，求解了该问题的控制方程Mauthieu方程。本文基于Floquet解用Fourier级数法求解了变质量密度简支梁的横向振动问题，得到了固有频率和模态、并观察到了固有频率分组现象和模态局部化现象。求解特征值问题的过程中应用了连分式技术，有效的提高了计算精度。     

LOW-FREQUENCY RESPONSES OF NONLINEARLY MOORED VESSELS IN RANDOM WAVES: COUPLED SURGE,PITCH AND HEAVE MOTIONS

The responses of a multi-degree-of-freedom model of a moored vessel are analysed, accounting for the hydroelastic interaction between the nonlinear wave hydrodynamics and the nonlinear mooring stiffness. A two-scale perturbation method developed by Sarkar & Eatock Taylor to determine low-frequency hydrodynamic forces on a single-degree-of-freedom model of a nonlinearly moored vessel has been extended to analyse the nonlinear multi-degree-of-freedom dynamics of the system. Surge, heave and pitch motions are considered. The perturbation equations of successive orders are derived. To illustrate the approach, semi-analytical expressions for the higher-order hydrodynamic force components have been obtained for a truncated circular cylinder in finite water depth. In addition to conventional quadratic force transfer functions, a new type of higher-order force transfer function is introduced. This is used to characterize the hydrodynamic forces on the vessel which arise due to nonlinearity of the mooring stiffness. These are a type of radiation force, generated by the nonlinear interaction of the fluid–structure coupled system. Based on a Volterra series model, the power spectral densities of the new higher-order forces are then derived for the case of Gaussian random seas. It is shown that the additional response arising due to nonlinear dynamics of the mooring system can significantly contribute to low-frequency drift forces and responses of the vessel. Unlike conventional non-Gaussian second-order forces which are quadratic transformations of a Gaussian random process, the new higher-order forces arising due to the nonlinear mooring stiffness are polynomials of a Gaussian random process (up to fourth order for a Duffing oscillator model). This may significantly influence the extreme responses.