Response of multiple layered media

A recently developed method for estimating the response of multiple coupled one-dimensional dynamic systems can be adapted to deal with the response of multiple layered media. This paper discusses this adaptation. The purpose is to bring this method to bear on this important subject, on the one hand, and to expand the range of applicability of the method on the other. In the method the interactions between the one-dimensional dynamic systems are defined in terms of reflection and transmission coefficients at junctions at which the dynamic systems terminate. In that sense the formalism is cast in terms of standard procedures in the investigations of the response of multiple layered media and, therefore, the adaptation is straightforward. Once the adaptation is instituted, the procedures are extended so that the formalism can treat situations in which steady flows are present in the layers. This extension has previously received only meager analytical attention. It is argued that in certain situations of this kind, the flows may introduce significant modifications in the response. The conditions and the nature of such modifications are defined and examined.     

A perturbation technique for gyroscopic systems with small internal and external damping

The response of linear damped gyroscopic systems can be obtained by means of techniques of linear systems theory, which involves the computation of the transition matrix. The response is in terms of complex quantities, which is likely to cause computational difficulties as the order of the system increases. In the absence of damping, it is possible to derive the response of a linear gyroscopic system with relative ease by working with real quantities alone. When damping is small, one can use a perturbation approach to produce the response by regarding the undamped gyroscopic system as the unperturbed system. In a previous paper, a perturbation analysis was used to derive the response of a gyroscopic system with small internal damping. This paper extends the approach to the case of external damping, which is characterized not only by symmetric coefficients multiplying velocities but also by skew symmetric coefficients multiplying displacements, where the latter terms are known as circulatory. A numerical example is presented.     

Pole assignment of friction-induced vibration for stabilisation through state-feedback control

Friction-induced self-excited linear vibration is often governed by a second-order matrix differential equation of motion with an asymmetric stiffness matrix. The asymmetric terms are product of friction coefficient and the normal stiffness at the contact interface. When the friction coefficient becomes high enough, the resultant vibration becomes unstable as frequencies of two conjugate pairs of complex eigenvalues (poles) coalesce (when viscous damping is low).This short paper presents a receptance-based inverse method for assigning complex poles to second-order asymmetric systems through (active) state-feedback control of a combination of active stiffness, active damping and active mass, which is capable of assigning negative real parts to stabilise an unstable system.     

Numerical simulation and analysis of complex patterns in a two-layer coupled reaction diffusion system

The resonance interaction between two modes is investigated using a two-layer coupled Brusselator model. When two different wavelength modes satisfy resonance conditions, new modes will appear, and a variety of superlattice patterns can be obtained in a short wavelength mode subsystem. We find that even though the wavenumbers of two Turing modes are fixed, the parameter changes have influences on wave intensity and pattern selection. When a hexagon pattern occurs in the short wavelength mode layer and a stripe pattern appears in the long wavelength mode layer, the Hopf instability may happen in a nonlinearly coupled model, and twinkling-eye hexagon and travelling hexagon patterns will be obtained. The symmetries of patterns resulting from the coupled modes may be different from those of their parents, such as the cluster hexagon pattern and square pattern. With the increase of perturbation and coupling intensity, the nonlinear system will convert between a static pattern and a dynamic pattern when the Turing instability and Hopf instability happen in the nonlinear system. Besides the wavenumber ratio and intensity ratio of the two different wavelength Turing modes, perturbation and coupling intensity play an important role in the pattern formation and selection. According to the simulation results, we find that two modes with different symmetries can also be in the spatial resonance under certain conditions, and complex patterns appear in the two-layer coupled reaction diffusion systems.     

Instability of parametric dynamic systems with non-uniform damping

A unified way of looking at parametric and combination resonances in systems with periodic coefficients and different amounts of damping in the various modes of vibration is presented. The stability boundaries of the coupled Mathieu equations are determined by the harmonic balance method, Fourier series with periods 2T and T being assumed. The basic characteristics of the solution are discussed and the method is applied to multiple-degree-of-freedom dynamic systems. The destabilizing effect on the combination resonances is obtained by the present method.     

损耗型变形耦合电机系统的混沌参数特性

提出一种考虑两种损耗特性的耦合发电机模型. 与原来的耦合发电机模型相比, 该模型更能反映实际情况. 通过数值计算Lypunov指数谱、分岔图、Poincaré映射等, 分析了系统在各种参数空间的性态变化. 结果显示考虑机械阻尼损耗的耦合发电机模型具有双吸引子, 机械阻尼损耗一方面可以抑制系统混沌, 另一方面却使系统在参数空间具有更复杂的混沌特性, 表征这两种损耗特性的参数对系统动力学行为都有显著的影响.     

Quantification of non-viscous damping in discrete linear systems

The damping forces in a multiple-degree-of-freedom engineering dynamic system may not be accurately described by the familiar ‘viscous damping model’. The purpose of this paper is to develop indices to quantify the extent of any departures from this model, in other words the amount of ‘non-viscosity’ of damping in discrete linear systems. Four indices are proposed. Two of these indices are based on the non-viscous damping matrix of the system. A third index is based on the residue matrices of the system transfer functions and the fourth is based on the (measured) complex modes of the system. The performance of the proposed indices is examined by considering numerical examples.     

On the added mass and radiation damping of rod bundles oscillating in compressible fluids

This paper presents a theoretical analysis as well as numerical results for the added mass and radiation damping coefficients of a group of two-dimensional circular cylinders oscillating harmonically in an infinite compressible fluid. The fluid reaction force on these vibrating cylinders is obtained by solving the two-dimensional acoustic wave equation with Neumann conditions on the cylinders and the radiation condition at infinity. Numerical results show that when the acoustic wavelength is large compared with the cylinder radius, the added mass predominates over the radiation damping, and both are independent of the dimensionless wavenumber. On the other hand, when the acoustic wavelength is small compared with the cylinder radius, the radiation damping predominates over the added mass, and both are small.     

Coupled nonlinear Schrödinger equations including growth and damping

We give an analytical and numerical analysis of a system of coupled nonlinear Schrödinger equations with complex coefficients describing wave-wave interaction in the presence of a linear and non-linear damping (growth). An exact solitary solution is found for arbitrary damping rate for one of the waves when the linear damping of the second wave is zero. In general, the wave envelopes are composed of dispersive shock waves which are explosively unstable.     

Distinguishing the transition to chaos in a spherical pendulum

Complex responses are studied for a spherical pendulum whose support is excited with a translational periodic motion. Governing equations are studied analytically to allow prediction of responses under various excitation conditions. Stability for certain cases of damping is predicted by means of existing analysis and compared with experimental data. Numerical time-step integration of the governing equations is developed to predict responses for various types of excitation and damping conditions. Predicted results are compared with corresponding motions measured in an experimental spherical pendulum system. A data acquisition system is included whereby detailed digitized time histories of the pendulum motion can be established and various parameters can be computed to characterize the type of motion present. Two new vector spaces are defined for describing complex responses which occur for certain specified excitation conditions. It is shown in these parameter spaces that the transition from quasiperiodic to chaotic motions can be carefully quantified in systems with very light damping. This discovery provides a convenient means for comparison of complex motions in the numerical and experimental air pendulum systems. The implications of the results are important for dynamic response in various applications, including fluid motions in satellite tanks and other nonlinear time-dependent physical processes which include very light damping. (c) 1995 American Institute of Physics.     

Metacognition as a Consequence of Competing Evolutionary Time Scales

Evolution is full of coevolving systems characterized by complex spatio-temporal interactions that lead to intertwined processes of adaptation. Yet, how adaptation across multiple levels of temporal scales and biological complexity is achieved remains unclear. Here, we formalize how evolutionary multi-scale processing underlying adaptation constitutes a form of metacognition flowing from definitions of metaprocessing in machine learning. We show (1) how the evolution of metacognitive systems can be expected when fitness landscapes vary on multiple time scales, and (2) how multiple time scales emerge during coevolutionary processes of sufficiently complex interactions. After defining a metaprocessor as a regulator with local memory, we prove that metacognition is more energetically efficient than purely object-level cognition when selection operates at multiple timescales in evolution. Furthermore, we show that existing modeling approaches to coadaptation and coevolution—here active inference networks, predator–prey interactions, coupled genetic algorithms, and generative adversarial networks—lead to multiple emergent timescales underlying forms of metacognition. Lastly, we show how coarse-grained structures emerge naturally in any resource-limited system, providing sufficient evidence for metacognitive systems to be a prevalent and vital component of (co-)evolution. Therefore, multi-scale processing is a necessary requirement for many evolutionary scenarios, leading to de facto metacognitive evolutionary outcomes.     

Modulational instability in asymmetric coupled wave functions

The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schr?dinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and the group velocity dispersion terms) and the nonlinearity and coupling coefficients, on which no assumption is made. A generalized dispersion relation is obtained, relating the frequency and wave-number of a small perturbation around a coupled monochromatic (Stokes') wave solution. Explicitly stability criteria are obtained. The analysis reveals a number of possibilities. Two (individually) stable systems may be destabilized due to coupling. Unstable systems may, when coupled, present an enhanced instability growth rate, for an extended wave number range of values. Distinct unstable wavenumber windows may arise simultaneously.     

Chaotic torsional vibration of imbalanced shaft driven by a limited power supply

In this paper, torsional vibrations of imbalanced shaft driven by a limited power supply are studied. It is shown that mutual interaction of shaft and power supply may in particular result in chaotic self-oscillations that correspond to the strange attractors in the phase space of the coupled dynamical system “shaft–power supply”. In this particular model, strange attractors represent classical Lorenz and Feigenbaum attractors. Rotation characteristic of the power supply and resonance characteristic of the shaft rotational motion in one of the resonance zones are studied. It is shown that at certain intervals, these characteristics may be non-unique, which corresponds to the case of chaotic dynamics. Such non-trivial properties of the coupled system “shaft–power supply” could be used for a better understanding of complex vibrational phenomena in real applied systems such as problems related to the damping of the torsional vibrations.     

Functional Interdependence in Coupled Dissipative Structures: Physical Foundations of Biological Coordination

Coordination within and between organisms is one of the most complex abilities of living systems, requiring the concerted regulation of many physiological constituents, and this complexity can be particularly difficult to explain by appealing to physics. A valuable framework for understanding biological coordination is the coordinative structure, a self-organized assembly of physiological elements that collectively performs a specific function. Coordinative structures are characterized by three properties: (1) multiple coupled components, (2) soft-assembly, and (3) functional organization. Coordinative structures have been hypothesized to be specific instantiations of dissipative structures, non-equilibrium, self-organized, physical systems exhibiting complex pattern formation in structure and behaviors. We pursued this hypothesis by testing for these three properties of coordinative structures in an electrically-driven dissipative structure. Our system demonstrates dynamic reorganization in response to functional perturbation, a behavior of coordinative structures called reciprocal compensation. Reciprocal compensation is corroborated by a dynamical systems model of the underlying physics. This coordinated activity of the system appears to derive from the system’s intrinsic end-directed behavior to maximize the rate of entropy production. The paper includes three primary components: (1) empirical data on emergent coordinated phenomena in a physical system, (2) computational simulations of this physical system, and (3) theoretical evaluation of the empirical and simulated results in the context of physics and the life sciences. This study reveals similarities between an electrically-driven dissipative structure that exhibits end-directed behavior and the goal-oriented behaviors of more complex living systems.     

On the non-linear dynamic behavior of elastohydrodynamic lubricated point contact

The complex dynamic concepts of mechanical systems are regarded each day as new barriers to be overcome. One of the most complex systems, despite its common construction design, is the rolling element bearings. The interactive dynamic interfaces of such bearings are normally disregarded by engineering analysis on the day to day basis due to its complexities. This paper intends to propose a new approach to the characterization of the elastohydrodynamic lubricated point contacts on such components, in order to fully depict its non-linear dynamic behavior, avoiding the use of rough hypothesis on a systemic procedure. A multi-level method was used to solve the coupled lubrication-deformation problem, alongside a Newmark-ß integrator of the motion equation for the contact system. A range of dynamically similar contacts were evaluated, so as to characterize its nonlinear dynamic behavior. A least-squares method was applied to the multi-level algorithm results, fitting the displacements-force relation to a linear and also to a third order polynomial stiffness. The fitting results were compared, clearly showing the nonlinear behavior of such contacts. Also, the oil film damping was regarded as viscous, leading to good overall response. Some peculiarities of the proposed adjust method are also considered.     

A real decoupled method and free interface component mode synthesis methods for generally damped systems

This paper reports on the development of a new transformation method. In contrast to most existing mode transformation methods in which the first-order state-space equation of the damped vibration system is transformed into a decoupled form with complex coefficient matrices, using the decoupled method presented in this paper, the equation of the damped system can be decomposed into a decoupled equation with real coefficient matrices. Two new free interface component mode synthesis methods are also presented. The equivalent full-mode matrix of the damped structure is used to capture the effects of the higher-order modes. Additionally, this work modifies the compatibility conditions at the junctions that are employed in most of the previous component mode synthesis methods for generally damped systems. The first component mode synthesis method is performed in complex space, whereas the second method can be applied in real space. Because the coefficient matrices of the coupled equation constructed by the second component mode synthesis method are all real-valued, the solution of the eigenproblem for this coupled equation can be performed in real space as well. Additionally, numerical examples demonstrate the accuracy and validity of these two component mode synthesis methods.     

Instabilities in Yukawa Liquids

A strongly coupled Yukawa liquid is a system of charged particles which interact via a screened Coulomb interaction and in which the electrostatic energy between neighboring particles is larger than their thermal energy but not large enough for crystallization. Various plasma systems including ultracold neutral plasmas and complex (dusty) plasmas can exist in this strongly coupled liquid phase.Here we investigate instabilities driven by the relative streaming of plasma components in three‐dimensional Yukawa liquids with a focus on complex plasmas. This includes a dust acoustic instability driven by weakly coupled ions streaming through the dust liquid, and a dust‐dust instability driven by the counter‐streaming of strongly coupled dust grains. Compared to the Vlasov behavior we find there can be a substantial modification of the unstable wavenumber spectrum due to strong coupling effects (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental characterization and modeling of microsliding on a small cantilever quartz beam

The design of mechanical systems requires various studies in order to ensure an optimal behavior during operation. In particular, the study of its dynamic behavior makes it possible to evaluate the role of a connection in the energy dissipation mechanisms. In this context, an experimental setup dedicated to small structures has been developed to quantify damping due to microsliding at the beam–clamp interface. The mechanical characterization of the clamped connection is carried out by experimental dynamic tests on a free-clamped structure. The instantaneous frequencies and damping are identified by the wavelet transform technique of a slightly nonlinear system. In parallel, numerical prediction of the equivalent damping is achieved thanks to the implementation of the regularized Coulomb law in a finite element model. A genetic algorithm and artificial neural networks are used to update the stiffness parameter and the friction coefficient. The optimized model is in good agreement with experimental results. It allows for determining the spatial distribution of microsliding and tangential force along the contact interface. The dissipated energy and equivalent damping are finally deduced according to the dynamic deflection of the free part of the beam.