Dynamics of a semi-infinite beam on unilateral springs: Touch-down points motion and detached bubbles propagation

The dynamics of a semi-infinite Bernoulli-Euler beam laid on a bed of unilateral elastic springs is governed by a moving-boundary problem, since the positions of the touch-down points, those points which separate the detached beam parts from the laid ones, are unknown. This problem is solved numerically by means of a self-made finite element code and some numerical results are shown and discussed. The nonlinear and non-smooth effects of the touch-down points motion on the beams dynamics are analyzed. The presence of detached bubbles, which appear, propagate and disappear in the beam, is investigated, and new complex motions are highlighted.     

基于断面形状优化的地铁车轮减振降噪研究

以降低地铁车辆在运行中产生的轮轨接触噪声为目的,将结构动力优化方法运用于地铁车轮断面外形设计,建立了地铁车轮振动噪声最优化设计的数学模型,编制了相应的算法程序.以我国某地铁车轮为例,给出了以车轮断面外形几何参数为设计变量、车轮结构振动辐射噪声值最小为目标函数的优化计算实例,得到了车轮断面外形几何参数在可行域内的最优解.结果表明,该优化设计方法是成功的,可以有效地降低车轮因振动而产生的噪声.     

Nonlinear Dynamics of Shells: Theory,Finite Element Formulation,and Integration Schemes

The paper is concerned with a dynamical formulation of a recently established shell theory capable to catch finite deformations and falls within the class of geometrically exact shell theories. A basic aspect is the design of time integration schemes which preserve specific features of the continuous system such as conservation of momentum, angular momentum, and energy when the applied forces allow to. The integration method differs from the one recently proposed by Simo and Tarnow in being applicable without modifications to shell formulations with linear as well as nonlinear configuration spaces and in being independent of the nonlinearities involved in the strain-displacement relations. A finite element formulation is presented and various examples of nonlinear shell dynamics including large overall and chaotic motions are considered.     

Wavelet Analysis of Structures: Statics, Dynamics and Damage Identification

Applications of the wavelet transform in solid mechanics are presented herein. The analysis problem is addressed first where the objective is to derive an adaptive wavelet-based method for the static and dynamic analysis of structures. This is done via a collocation scheme. The damage identification problem is investigated next making use of the space-localized properties of the wavelet transform: the regularity of the solution is detected by looking at the amplitude of the coefficients of the wavelet decomposition of the response. Open problems are finally outlined that will be the object of future work.     

某调距导管桨系泊工况水力性能和流激直发声预报

采用经验证的计算流体力学方法,对某艏辅推调距导管桨设计螺距和系泊工况螺距的水动力性能进行了有效预报,并对系泊工况装船桨流激噪声进行了分析。系泊工况下,由于导管桨的抽吸作用在导管外壁近壁面区域存在与导管内部流动方向相反的逆向流动,且导管桨尾流场速度梯度分布不均匀、流动紊乱,此时桨叶与导管的推力之比约为1.2∶1。系泊工况船+桨的瞬态流场脉动信息表明,导管桨各部件噪声源强度均表现出从1倍到4倍叶频依次下降的规律,最强幅值集中在桨叶导边和导管内壁;在远场声源级频谱曲线中轴向测点线谱较高峰值位置体现出导管桨进流流场的流动特性。对比分析该艏辅推整体和各部件宽带声源级指向性,可知旋转部件(桨叶、桨榖)对总噪声级的贡献较大,静止部件是径向测点噪声的主要贡献源。     

Dynamics modeling and robotic-assist,leader-follower control of tractor convoys

This paper proposes a generalized dynamics model and a leader-follower control architecture for skid-steered tracked vehicles towing polar sleds. The model couples existing formulations in the literature for the powertrain components with the vehicle-terrain interaction to capture the salient features of terrain trafficability and predict the vehicles response. This coupling is essential for making realistic predictions of the vehicles traversing capabilities due to the power-load relationship at the engine output. The objective of the model is to capture adequate fidelity of the powertrain and off-road vehicle dynamics while minimizing the computational cost for model based design of leader-follower control algorithms. The leader-follower control architecture presented proposes maintaining a flexible formation by using a look-ahead technique along with a way point following strategy. Results simulate one leader-follower tractor pair where the leader is forced to take an abrupt turn and experiences large oscillations of its drawbar arm indicating potential payload instability. However, the follower tractor maintains the flexible formation but keeps its payload stable. This highlights the robustness of the proposed approach where the follower vehicle can reject errors in human leader driving.     

Modelling, Dynamics and Control of Tethered Satellite Systems

Tethered satellite systems (TSS) pose quite challenging problems concerning their modelling, derivation of the equations of motion, numerical simulation of their dynamics, deciding on stability of relative equilibria provided the system moves on a circular orbit around the Earth and the occurrence of chaotic dynamics. Moreover, for the processes of deployment or retrieval of one satellite from or to another satellite certain control strategies, for example time or energy optimal control, are necessary. All these problems are considered in this paper.     

Atomistic simulation of free transverse vibration of graphene,hexagonal SiC,and BN nanosheets

Free transverse vibration of monolayer graphene, boron nitride (BN), and silicon carbide (SiC) sheets is inves-tigated by using molecular dynamics finite element method. Eigenfrequencies and eigenmodes of these three sheets in rectangular shape are studied with different aspect ratios with respect to various boundary conditions. It is found that aspect ratios and boundary conditions affect in a similar way on nat-ural frequencies of graphene, BN, and SiC sheets. Natural frequencies in all modes decrease with an increase of the sheet's size. Graphene exhibits the highest natural frequen-cies, and SiC sheet possesses the lowest ones. Missing atoms have minor effects on natural frequencies in this study.     

A Framework and Methodology for the Study of Nonlinear,Self-Organizing Family Dynamics

Family systems theories have emerged over the past 30 to 40 years primarily through clinical observations, resulting in diverse and internally inconsistent views of family structures, development, dynamics, and pathology; as well as a separation from more empirically based small group research. The 5-R's model is intended to unify the various family systems theories and render them more empirically testable using concepts and methodologies from non-linear dynamical systems theory. The conversation of one family was analyzed using orbital decomposition as a pilot test of the most basic assumptions of the 5-R's model. An optimal string length of three was found along with evidence of coherent complexity (chaos), with Lyapunov dimensionality equal to 1.7 and Shannon's entropy equal to 8.68. Results are discussed with respect to further empirical validation of the 5-R's model and clinical uses of the model and orbital decomposition methodology in conjoint therapy.     

Study on Dynamics, Stability and Control of Multi-Body Flexible Structure System in Functional Space

ＩｎｔｒｏｄｕｃｔｉｏｎＷｉｔｈｔｈｅｄｅｖｅｌｏｐｍｅｎｔｏｆｔｈｅｍｏｄｅｒｎｓｃｉｅｎｃｅａｎｄｅｎｇｉｎｅｅｒｉｎｇｔｅｃｈｎｏｌｏｇｙ ,ｅｓｐｅｃｉａｌｌｙａｓｔｒｏｎ ａｖｉｇａｔｉｏｎｈａｖｉｎｇｂｅｃｏｍｅｐｒａｃｔｉｃａｌｌｙ ,ｔｈｅｐｒｏｂｌｅｍｄｉｓｃｕｓｓｉｎｇｄｙｎａｍｉｃｓ,ｓｔａｂｉｌｉｔｙａｎｄｃｏｎｔｒｏｌｏｆｓｙｓｔｅｍｏｆｔｈｅｌａｒｇｅｆｌｅｘｉｂｌｅｓｐａｃｅｓｔｒｕｃｔｕｒｅ (ＬＦＳＳ)ｈａｓｂｅｅｎａａｃｔｉｖｅｒｅｓｅａｒｃｈｆｉｅｌｄａｔｈｏｍｅａ…     

Dynamics of a mass–spring–beam with 0:1:1 internal resonance using the analytical and continuation method

The nonlinear harmonic response of an autoparametric system comprised of a linear oscillator with a vertically attached flexural beam is investigated and the capability of the beam as a vibration absorber is assessed. A weak torsional spring is used for constraining the rotation of the beam giving rise to an almost non-flexural rotational mode with a low frequency. The system parameters are also tuned to enforce the zero-to-one-to-one internal resonance condition. The Lagrange’s formulation accompanied by the assumed-mode method is used to derive the discretized equations based on the order three nonlinear Euler–Bernoulli beam theory. An analytical solution is developed based on the method of multiple scales where the generalized coordinate corresponding to the non-flexural rotational mode is approximated by higher order perturbation expansion than the other coordinates, due to much larger contribution of the non-flexural rotation to the response. Comprehensive response and bifurcation analysis are performed using analytical and direct numerical solutions. The results are obtained for vertically-aligned and also initially inclined beams and various interesting behaviors are recognized for different non-dimensional system parameters. Different types of bifurcations such as the Pitch-fork, Hopf, Period-doubling and symmetry breaking bifurcations are observed in the solution of slow-flow equations and some of them are found to be beneficial for vibration absorption in a limited range of excitation amplitudes and frequencies.     

Dynamics of Geometrically Nonlinear Rods: I. Mechanical Models and Equations of Motion

Slender thread like bodies (like cables, ropes, textilethreads or belts) are often used in technical applications. Becauseof their dimensions the one-dimensional continuum is the appropriatemechanical model for bodies of this type. Making use of the basicrelations of three-dimensional continua as a starting point the paperdevelops the general kinematic and kinetic relations of one-dimensionalcontinua for the case that the cross-sections will remain plane (Bernoullihypothesis), that large deflections are possible but the strains remainsmall and that the material is homogeneous and isotropic and behaveslinearly elastic. This results in the equations of motion of shearableand extensible rods (Timoshenko-beams). By neglection of shear deformationand of the rotational inertia of the cross-sections (assumptions thatcan be done in most technical applications) the equations of motionof Euler–Bernoulli-beams are derived in standard and concentratedform. The Euler–Bernoulli-beam equations contain the equations ofmotion of threads with zero bending and torsional stiffness. It isshown that the neglection of bending and torsional stiffness is onlyvalid if the tension is always positive. The second part of this paper[1] selects and develops appropriate numerical solution methods.The derived algorithms are used to solve problems from space and marineengineering.     

Common Dynamic Properties of Biosignals During Cognition: Self-Similarity and Chaotic Dynamics of Both Response Times and EEG During Movement Imagery

This study was undertaken to verify whether different output variables or biosignals, measured during performance of a cognitive task, manifest common dynamical properties. Nonlinear properties of both response times (RTs) and electroercephalograms (EEG) were tested. We asked subjects to generate mental images of actions following of auditorily presentation simple phrases suggesting the action. Analysis of RT series combined from many subjects and of EEG records from single subjects clearly manifested self-similarity and chaotic dynamics that provide insights into the self-organization of the brain/behavioral system.     

Prediction of Friction and Wear of Sliding Contacts,Based on Generalizational Theory of Thermal Dynamics and Modelling of Friction and Wear of Tribosystems

On the basis of electrofriction interaction analysis of high current sliding electric contacts and experimental verification of the theoretical prerequisites, a method, has been elaborated to assess the tribotechnica characteristics which allows one to make an optimal choice of materials for contact pairs in high-current sliding electric contacts at the designing stage.     

Dynamics of martensitic phase boundaries: discreteness, dissipation and inertia

We study a fully inertial model of a martensitic phase transition in a one-dimensional crystal lattice with long-range interactions. The model allows one to represent a broad range of dynamic regimes, from underdamped to overdamped. We systematically compare the discrete model with its various continuum counterparts including elastic, viscoelastic and viscosity-capillarity models. Each of these models generates a particular kinetic relation which links the driving force with the phase boundary velocity. We find that the viscoelastic model provides an upper bound for the critical driving force predicted by the discrete model, while the viscosity-capillarity model delivers a lower bound. We show that at near-sonic velocities, where inertia dominates dispersion, both discrete and continuum models behave qualitatively similarly. At small velocities, and in particular near the depinning threshold, the discreteness prevails and predictions of the continuum models cannot be trusted.      

Recent advancement of flow-induced piezoelectric vibration energy harvesting techniques: principles,structures, and nonlinear designs

Energy harvesting induced from flowing fluids (e.g., air and water flows) is a well-known process, which can be regarded as a sustainable and renewable energy source. In addition to traditional high-efficiency devices (e.g., turbines and watermills), the micro-power extracting technologies based on the flow-induced vibration (FIV) effect have sparked great concerns by virtue of their prospective applications as a self-power source for the microelectronic devices in recent years. This article aims to conduct a comprehensive review for the FIV working principle and their potential applications for energy harvesting. First, various classifications of the FIV effect for energy harvesting are briefly introduced, such as vortex-induced vibration (VIV), galloping, flutter, and wake-induced vibration (WIV). Next, the development of FIV energy harvesting techniques is reviewed to discuss the research works in the past three years. The application of hybrid FIV energy harvesting techniques that can enhance the harvesting performance is also presented. Furthermore, the nonlinear designs of FIV-based energy harvesters are reported in this study, e.g., multi-stability and limit-cycle oscillation (LCO) phenomena. Moreover, advanced FIV-based energy harvesting studies for fluid engineering applications are briefly mentioned. Finally, conclusions and future outlook are summarized.

     

Dynamic interaction of various beams with the underlying soil – finite and infinite, half-space and Winkler models

Various beams lying on the elastic half-space and subjected to a harmonic load are analyzed by a double numerical integration in wavenumber domain. The compliances of the beam–soil systems are presented for a wide frequency range and for a number of realistic parameter sets. Generally, the soil stiffness G has a strong influence on the low-frequency beam compliance whereas the beam parameters EI and m^′ are more important for the high-frequency compliance. An important parameter is the elastic length l=(EI/G)^1/4 of the beam–soil system. Around the corresponding frequency ω_l=v_S/l, the wave velocity of the combined beam–soil system changes from the Rayleigh wave v_R≈v_S to the bending wave velocity v_B and the combined beam–soil wave has typically a strong damping. The interaction frequency ω_l is found not far from the characteristic frequency ω₀=(G/m^′)^1/2 where an amplification compared to the static compliance is observed for special parameter constellations. In contrast, real foundation beams show no resonance effects as they are highly damped by the radiation into the soil. At medium and high frequencies, asymptotes for the compliance of the beam–soil system are found, u/P(ρv_Paiω)^−3/4 in case of the dominating damping and u/P(−m^′ω²)^−3/4 for high frequencies. The low-frequency compliance of the coupled beam–soil system can be approximated by u/P1/Gl, but it also depends weakly on the width a of the foundation. All numerical results of different beam–soil systems are evaluated to yield a unique relation u/P₀=f(a/l). The integral transform method is also applied to ballasted and slab tracks of railway lines, showing the influence of train speed on the deformation of the track beam. The presented results of infinite beams on half-space are compared with results of finite beams and with infinite beams on a Winkler support. Approximating Winkler parameters are given for realistic foundation-soil systems which are useful when vehicle-track interaction is analyzed for the prediction of railway induced vibration.     

Two-to-one resonant multi-modal dynamics of horizontal/inclined cables. Part I: Theoretical formulation and model validation

This paper is first of the two papers dealing with analytical investigation of resonant multi-modal dynamics due to 2:1 internal resonances in the finite-amplitude free vibrations of horizontal/inclined cables. Part I deals with theoretical formulation and validation of the general cable model. Approximate nonlinear partial differential equations of 3-D coupled motion of small sagged cables – which account for both spatio-temporal variation of nonlinear dynamic tension and system asymmetry due to inclined sagged configurations – are presented. A multi-dimensional Galerkin expansion of the solution of nonplanar/planar motion is performed, yielding a complete set of system quadratic/cubic coefficients. With the aim of parametrically studying the behavior of horizontal/inclined cables in Part II [25], a second-order asymptotic analysis under planar 2:1 resonance is accomplished by the method of multiple scales. On accounting for higher-order effects of quadratic/cubic nonlinearities, approximate closed-form solutions of nonlinear amplitudes, frequencies and dynamic configurations of resonant nonlinear normal modes reveal the dependence of cable response on resonant/nonresonant modal contributions. Depending on simplifying kinematic modeling and assigned system parameters, approximate horizontal/inclined cable models are thoroughly validated by numerically evaluating statics and non-planar/planar linear/non-linear dynamics against those of the exact model. Moreover, the modal coupling role and contribution of system longitudinal dynamics are discussed for horizontal cables, showing some meaningful effects due to kinematic condensation.     

Dynamics of firing patterns, synchronization and resonances in neuronal electrical activities： experiments and analysis

Recent advances in the experimental and theoretical study of dynamics of neuronal electrical firing activities are reviewed. Firstly, some experimental phenomena of neuronal irregular firing patterns, especially chaotic and stochastic firing patterns, are presented, and practical nonlinear time analysis methods are introduced to distinguish deterministic and stochastic mechanism in time series. Secondly, the dynamics of electrical firing activities in a single neuron is concerned, namely, fast-slow dynamics analysis for classification and mechanism of various bursting patterns, one- or two-parameter bifurcation analysis for transitions of firing patterns, and stochastic dynamics of firing activities （stochastic and coherence resonances, integer multiple and other firing patterns induced by noise, etc.）. Thirdly, different types of synchronization of coupled neurons with electrical and chemical synapses are discussed. As noise and time delay are inevitable in nervous systems, it is found that noise and time delay may induce or enhance synchronization and change firing patterns of coupled neurons. Noise-induced resonance and spatiotemporal patterns in coupled neuronal networks are also demonstrated. Finally, some prospects are presented for future research. In consequence, the idea and methods of nonlinear dynamics are of great significance in exploration of dynamic processes and physiological functions of nervous systems.