Arbitrary Damping Research Articles

Flutter instability characteristics and mechanisms of Ziegler double pendulum with arbitrary masses, stiffness and damping

Flutter instability characteristics and mechanisms of Ziegler double pendulum with arbitrary masses, stiffness and damping

Implicit-explicit Runge-Kutta methods for Landau-Lifshitz equation with arbitrary damping

Implicit-explicit Runge-Kutta methods for Landau-Lifshitz equation with arbitrary damping

Tailored nonlinear stiffness and geometric damping: Applied to a bistable vibration absorber

A novel device is proposed to obtain arbitrary restoring force characteristics and nonlinear geometric damping. It consists of linear springs and dampers that are compressed along a track. The obtained nonlinear damping and stiffness law depend on the track’s shape. The device is then applied to obtain a nonlinear energy sink (NES) to damp the vibrations of a host system. Both the case of transient vibrations, induced by shock loads, and sustained vibrations, induced by harmonic loads, are studied. For arbitrary stiffness and damping, slow flow dynamics and slow invariant manifolds (SIMs) are derived by applying harmonic balancing and multiple timescales techniques. Under transient vibrations, two performance measures are derived from the SIM, the relative residual energy and the pumping time, and are found for generic nonlinear spring force and nonlinear geometric damping. For sustained vibrations, a load-dependent frequency response (FR) is derived from the SIMs. This FR predicts the occurrence of the efficient strongly modulated responses but also the occurrence of the unfavorable detached responses called isolas, where the NES fails to mitigate and even amplifies vibrations.This research investigates the performance of a conventional cubic NES and a bistable NES (BNES) with nonlinear damping obtained from the proposed device. Especially the BNES with nonlinear damping shows attractive properties, with a high degree of robustness over a wide energy range and a low vibration threshold under transient loading. Under harmonic loads, the nonlinear damping helps reduce the effect of isolas. A novel tuning methodology is proposed to avoid isolas for a range of load magnitudes. The new device opens up a whole range of possibilities regarding energy dissipation through nonlinear damping.

Double-wall carbon nanotubes model with nonlinear localized damping: Asymptotic stability

We consider the one-dimensional equations for the double-wall carbon nanotubes modeled by coupled Timoshenko elastic beam system with nonlinear arbitrary localized damping. We prove that the damping placed on an arbitrary small support, unquantized at the origin, leads to uniform decay rates (asymptotic in time) for the energy function. This study generalizes and improves previous literature outcomes.

A method to accurately define arbitrary algorithmic damping character as viscous damping

Undesired oscillations often emerge in numerical solutions, especially in the case of dynamic problems. These are mainly spurious oscillations which must be eliminated or reduced at least to provide accurate results. Numerical methods with damping effect are especially useful to achieve this goal. However, the concrete shape of the damping characteristics has a great impact on the effectiveness. Dissipative numerical methods mostly have a specific damping character with very limited alteration possibility. In this article, a novel numerical method has been introduced where the dissipative effect is exerted via viscous damping. Using the proposed method, a great variety of damping curves can be defined accurately, straight through the determination of the algorithmic damping ratio. The newly developed technique is mainly useful for applications where the shape of the damping characteristics significantly affects the accuracy.

Tunable topological interface states in one-dimensional inerter-based locally resonant lattices with damping

Wave dispersion and topology of phononic crystals in classical mechanical systems are well understood and extensively studied subjects. However, the topological properties of acoustic metamaterials with more complex unit cells having several masses, internal resonators, and inerter elements is an insufficiently investigated topic. In this work, we study a class of locally resonant acoustic systems having diatomic- and triatomic-like mass-in-mass unit cells with inerter elements and different springs connecting outer masses. Winding numbers and signs of band gaps are investigated to assess the topological characteristics of a lattice band structure that support edge/interface modes and whether that property is affected when inerter elements are embedded into the system. The dynamics of finite undamped and damped chains constituted of two connected sub-lattices are investigated to demonstrate the existence of interface modes and their localization in space. We reveal that the presented diatomic-like and triatomic-like mass-in-mass chains can generate several interface modes that reside within both lower and higher frequency band gaps. The concept is illustrated through the investigation of the eigenvalue spectrum for varying and fixed stiffness of outer springs and frequency response function. The effect of arbitrary viscous damping is explored based on steady-state responses of the lattice interface mass points. Numerical analysis reveals that the introduction of inerters in combination with local resonators can significantly shift the band gaps and corresponding interface modes to lower frequency values while keeping the main topological properties of the initial configuration without inerters. The effect of damping is shown to be significant and capable to attenuate both lower and higher frequency interface mode amplitudes. We anticipate that this study will pave the wave for future works on the topic that include more reliable models of inerters in the topological mechanical metamaterial design.

Data-driven modeling of general damping systems by [formula omitted]-means clustering and two-stage regression

Damping is one of the most complicated phenomena in structural analysis and design. In principle, damping arises with energy dissipation in the vibration and therefore, friction, plasticity and viscosity etc are common sources of damping. Though various damping models have been proposed, they are only applicable to some certain damping phenomena and there is no unified way to model an arbitrary damping system. To the end, this paper presents a data-driven framework for modeling of general damping systems. There are three key ingredients in establishing this framework. At first, pre-defined dictionaries of basis functions are built to describe the hysteretic and viscous behaviors of a general damping model. Secondly, the k-means clustering technique is applied to separate the two datasets corresponding to respective hysteretic and viscous parts of the damping model from the measured data. Thirdly, a two-stage regression procedure is invoked where the viscous and hysteretic parts of the damping model are identified sequentially from the readily separated two datasets. Such identification proceeds by means of linear least-squares regression and sparse regularization. As a consequence, if a new damping system whose hysteretic and viscous behaviors are totally reflected in the dictionary, the underlying model equation can be directly and quickly recovered through the proposed data-driven approach. Numerical examples as well as an experimental test are studied to demonstrate the effectiveness and efficiency of the proposed data-driven modeling approach for general damping systems.

Green's function method for dynamic contact calculations.

Resolving atomic scale details while capturing long-range elastic deformation is the principal difficulty when solving contact mechanics problems with computer simulations. Fully atomistic simulations must consider large blocks of atoms to support long-wavelength deformation modes, meaning that most atoms are far removed from the region of interest. Building on earlier methods that used elastic surface Green's functions to compute static substrate deformation, we present a numerically efficient dynamic Green's function technique to treat realistic, time-evolving, elastic solids. Our method solves substrate dynamics in reciprocal space and utilizes precomputed Green's functions that exactly reproduce elastic interactions without retaining the atomic degrees of freedom in the bulk. We invoke physical insights to determine the necessary number of explicit substrate layers required to capture the attenuation of subsurface waves as a function of surface wave vector. We observe that truncating substrate dynamics at depths that fall as a power of wave vector allows us to accurately model wave propagation without implementing arbitrary damping. The framework we have developed substantially accelerates molecular dynamics simulations of large elastic substrates. We apply the method to single asperity contact, impact, and sliding friction problems and present our preliminary findings.

Optimum and performance of absorber with zero damping

This paper considers optimum parameters tuned mass damper (TMD) as a vibration absorber with zero damping. Generally, tuned absorbers with damping have been considered to be applied to the structures. While adjusting damping constant produces additional complexity in real applications, this paper investigates the use of absorber with zero damping. The properties of the absorber to be designed then is reduced to only its spring constant, while the damping is set to zero throughout the design process. To optimize its spring constant, genetic algorithm (GA) with real coding is utilized. With the optimized spring properties obtained from the optimization, the performance of structures is then investigated under several earthquake excitations. The performance of the optimum absorber with zero damping is also compared with the one when arbitrary damping presents in the absorber. The simulation results show that the performance of the absorber with zero damping is smaller compared to the one of absorber with damping. However, the response of absorber with damping tends to decrease when time increases.

Sound radiation of a vibrating elastically supported circular plate embedded into a flat screen revisited using the Zernike circle polynomials

This study deals with the problem of sound radiation by an elastically supported thin circular plate. The plate is excited asymmetrically. In such cases, usually different approximate methods are used to calculate the acoustic power. These methods are time-consuming, and some of them are applicable only to axisymmetric problems. They work only for the lowest and the highest frequencies. Consequently, their applications are limited. Another shortcoming of such methods is that they work only for either clamped circular plates or simply supported plates. In practical applications, the boundary conditions of circular plates are often required. Therefore, the model of an elastically supported plate is of a great interest in this regard. Finally, the methods presented in the literature are time-consuming and not highly accurate. They often incorporate numerical integration to calculate the acoustic pressure and the acoustic power. The use of the radial polynomials leads to much more accurate and efficient results. The acoustic power is expressed in terms of the modal impedance coefficients. The coefficients are calculated without numerical integration and with arbitrary precision in a wide low-frequency band. They are expressed in terms of a rapidly converging expansion series. The formulas presented are useful to solve the problem of vibration of a plate including arbitrary excitation, material damping, and fluid-structure interactions. This results in a system of three coupled differential equations. The first one is the Helmholtz equation governing the fluid vibrations in the upper half-space, the second one is also the Helmholtz equation governing the fluid vibrations in the lower half-space, and the third one deals with the motion of the plate. Consequently, it leads to a system of algebraic equations. Finally, the effects of the plate's boundary conditions on the acoustic power, the far field, and the near field are analyzed numerically.

Dual Craig-Bampton component mode synthesis method for model order reduction of nonclassically damped linear systems

The original dual Craig-Bampton method for reducing and successively coupling undamped substructured systems is extended to the case of arbitrary viscous damping. The reduction is based on the equations of motion in state-space representation and uses complex free interface normal modes, residual flexibility modes, and state-space rigid body modes. To couple the substructures in state-space representation, a dual coupling procedure based on the interface forces between adjacent substructures is used, which is novel compared to other methods commonly applying primal coupling procedures in state-space representation. The very good arbitrary viscous damping of the dual Craig-Bampton approach is demonstrated on a beam structure with localized dampers. The results are compared to a classical Craig-Bampton approach for damped systems showing the potential of the proposed method.

Exact steady states of the periodically forced and damped Duffing oscillator

We present an analytical methodology to compute the exact steady states of the strongly nonlinear Duffing oscillator with arbitrary viscous damping and under the action of a time-periodic excitation. In contrast to current analytical approaches that consider harmonic excitations to produce approximate steady-state solutions, the excitations considered in this work are multi-harmonic and are computed in closed form. We consider the exact fundamental resonance plot of this strongly nonlinear system and present an exact depiction of the dynamic balance between the internal and external forces leading to it in terms of rotating vectors in the complex plane with modulated amplitudes and modulated frequencies of rotation. Moreover, an infinity of exact steady-state solutions seems to be possible, each corresponding to a different time-periodic excitation. Generalization of the presented methodology to systems with other type of nonlinearities or with many degrees of freedom is presumably straightforward.

Probabilistic characteristics of noisy Van der Pol type oscillator with nonlinear damping

The exact Fokker–Planck equation for the joint probability distribution of amplitude and phase of a Van der Pol oscillator perturbed by both additive and multiplicative noise sources with arbitrary nonlinear damping is first derived by the method of functional splitting of averages. We truncate this equation in the usual manner using the smallness of the damping parameter and obtain a general expression for the stationary probability density function of oscillation amplitude, which is valid for any nonlinearity in the feedback loop of the oscillator. We analyze the dependence of this stationary solution on system parameters and intensities of noise sources for two different situations: (i) Van der Pol generator with soft and hard excitation regimes; (ii) Van der Pol oscillator with negative nonlinear damping. As shown, in the first case the probability distribution of amplitude demonstrates one characteristic maximum, which indicates the presence of a stable limit cycle in the system. The non-monotonic dependence of stationary probability density function on oscillation frequency is also detected. In the second case we examine separately three situations: linear oscillator with two noise sources, nonlinear oscillator with additive noise and nonlinear oscillator with frequency fluctuations. For the last two situations, noise-induced transitions in the system under consideration are found.

OS1216 減衰比向上が可能な複数の前方注視点を用いた車線追従制御の研究

OS1216 減衰比向上が可能な複数の前方注視点を用いた車線追従制御の研究

Boundary Backstepping Control of Flow-Induced Vibrations of a Membrane at High Mach Numbers

We design a controller for flow-induced vibrations of an infinite-band membrane, with flow running across the band and only above it, and with actuation only on the trailing edge of the membrane. Due to the infinite length of the membrane, the dynamics of the membrane in the spanwise direction are neglected, namely, we employ a one-dimensional (1D) model that focuses on streamwise vibrations. This framework is inspired by a flow along an airplane wing with actuation on the trailing edge. The model of the flow-induced vibration is given by a wave partial differential equation (PDE) with an antidamping term throughout the 1D domain. Such a model is based on linear aeroelastic theory for Mach numbers above 0.8. To design a controller, we introduce a three-stage backstepping transformation. The first stage gets the system to a critically antidamped wave equation, changing the stiffness coefficient's value but not its sign. The second stage changes the system from a critically antidamped to a critically damped equation with an arbitrary damping coefficient. The third stage adjusts stiffness arbitrarily. The controller and backstepping transformation map the original system into a target system given by a wave equation with arbitrary positive damping and stiffness.

Large amplitude flow-induced oscillations and energy harvesting using a cyber-physical pitching plate

The dynamics of an elastically mounted flat plate in a uniform stream undergoing flow-induced pitching oscillations is studied with the aid of a cyber-physical system which is capable of simulating arbitrary structural dynamics. The system measures the angular position and velocity, and combines them with appropriate gains to provide a torque to a computer-controlled servomotor that emulates arbitrary torsional stiffness and damping. A series of experiments were carried out over a wide range of parameter space and the results demonstrate that inertial scaling of the stiffness and damping effectively captures the system behavior. As the torsional stiffness decreases, the system exhibits several bifurcations in its dynamical behavior. Firstly, a subcritical transition through a saddle-node bifurcation results in small-amplitude asymmetric limit-cycle oscillations and later, a subcritical transition through a Hopf bifurcation gives rise to large-amplitude symmetric limit-cycle oscillations. At very low stiffness the plate does not oscillate. Energy harvesting from the flow is only ~1% efficient, but is found to be optimized at a non-dimensional stiffness close to unity while increasing the Reynolds number is found to extend the range of damping over which large scale oscillations and energy harvesting can be sustained. Although velocity measurements are not made, the details of torque-position phase plane are used to infer the details of the formation time and stability of the leading-edge vortex associated with the rapidly pitching plate.

Longitudinal and Transverse Single File Diffusion in Quasi-1D Systems

We review our recent results on Single File Diffusion (SFD) of a chain of particles that cannot cross each other, in a thermal bath, with long ranged interactions, and arbitrary damping. We exhibit new behaviors specifically associated to small systems and to small damping. The fluctuation dynamics is explained by the decomposition of the particles' motion in the normal modes of the chain. For longitudinal fluctuations, we emphasize the relevance of the soft mode linked to the translational invariance of the system to the long time SFD behavior. We show that close to the zigzag threshold, the transverse fluctuations also exhibit the SFD behavior, characterized by a mean square displacement that increases as the square root of time. This cannot be explained by the single file ordering, and the SFD behavior results from the strong correlation of the transverse displacements of neighbouring particles near the bifurcation. Extending our analytical modelization, we demonstrate the existence of this subdiffusive regime near the zigzag transition, in the thermodynamic limit. The zigzag transition is a supercritical pitchfork bifurcation, and we show that the transverse SFD behavior is closely linked to the vanishing of the frequency of the zigzag transverse mode at the bifurcation threshold. [Formula: see text] Special Issue Comments: This article presents mathematical results on the dynamics in files with longitudinal movements. This article is connected to the Special Issue articles about advanced statistical properties in single file dynamics,28 expanding files,63 and files with force and advanced formulations.29

Decay rates for Timoshenko system with nonlinear arbitrary localized damping

We consider the Timoshenko model for vibrating beams under the localized effect of both nonlinear frictional damping acting on the transverse displacement equation and on the rotation angle equation. We have obtained the exponential stability behavior for solutions, using an observability result, which allows us to consider different speeds of propagation for the waves.

D03 時間軸変換による厳密な線形化を用いたAcrobotシステムの安定化制御実験(M-OS14-1:非線形制御理論とその応用I,M-OS14 非線形制御理論とその応用,「海を越え,国を越え,世代を超えて!」)

This paper reports series of experimental studies for Acrobot System by applying modified Linearization Method, which is an extension of the previous study conducted by Saito who used Exact Linearization by Time Scale Transformation. Saito derived the algorithm formation for a system without viscous damping factor, while author reports simulation data that indicate the aforementioned method is applicable to highly nonlinear system with arbitrary damping factor.

Single-file diffusion of particles with long-range interactions: Damping and finite-size effects

We study the single file diffusion of a cyclic chain of particles that cannot cross each other, in a thermal bath, with long-ranged interactions and arbitrary damping. We present simulations that exhibit new behaviors specifically associated with systems of small numbers of particles and with small damping. In order to understand those results, we present an original analysis based on the decomposition of the particles' motion in the normal modes of the chain. Our model explains all dynamic regimes observed in our simulations and provides convincing estimates of the crossover times between those regimes.