Effect Of Nonlinear Damping Research Articles

Modulational Collapsing and Adjusting with External Potential in a Complex Nonlinear Plasma

Modulational collapse of a wave pulse in a complex nonlinear plasma described by a complex nonlinear Schrodinger equation (CNSE) including the effects of viscous heating and nonlinear damping, and the adjusting by an external potential are investigated. Theoretical and numerical results reveal that the original pulse first suffers modulational instability, the growth rate of the modulational instability increases with the increase of viscous heating, but it is not sensitive to the nonlinear damping. The instability induces the self-similar collapsing, then the fields rapidly transform into a turbulent state with short-wavelength modes. The results are explained in terms of the evolution of the total energy, which can become invariant during the evolution even though the system is nonconservative. The external potential can delay the self-defocusing process of the pulse. Those results can apply to the phenomena described by the CNSE.

Finite element modeling of one-dimensional nonreciprocal acoustic metamaterial with anti-parallel diodes.

A class of passive nonreciprocal acoustic metamaterials is developed to control the flow and distribution of acoustic energy in acoustic cavities and systems. Such development departs radically from present methods that favor the transmission direction by using hardwired arrangements of the hardware and hence, it cannot be reversed. The proposed nonreciprocal acoustic metamaterial (NAMM) cell consists of a cylindrical acoustic cavity with piezoelectric flexible boundaries that provide control in one-dimension. These boundaries are connected to an array of anti-parallel diodes to introduce simultaneous nonlinear damping and stiffness effects that break the reciprocity of energy flow through the NAMM cell. A finite element model of the NAMM cell is developed to investigate the nonreciprocal characteristics of the cell by optimizing the parameters that influence the nonlinear damping and stiffness effects introduced by the diodes. Numerical examples are presented to demonstrate the effectiveness of the proposed NAMM in tuning the directivity, flow, and distribution of acoustic energy propagating though the metamaterial.

Nonlinear damping and mass effects of electromagnetic shunt damping for enhanced nonlinear vibration isolation

This paper investigates the nonlinear mass and damping effects of nonlinear electromagnetic shunt damping (N-EMSD) for vibration isolation performance enhancement of a permanent magnets (PMs) based nonlinear vibration isolator (NVI). An electromagnetic structure composing of two coils and two PMs is designed to realize equivalent nonlinear damping and mass. The nonlinear mechanic-electromagnetic coupling coefficient is analyzed and modeled. The voltage frequency of the circuit is twice the displacement frequency that is totally different with that of the linear electromagnetic shunt damping (L-EMSD). The amplitude frequency response function of the NVI with N-EMSD is theoretically derived via the harmonic balance method (HBM) and the stability is judged with Jacobian matrix. Then the equivalent nonlinear damping and nonlinear mass of the N-EMSD is derived. The numerical predictions agree with the experimental results, which demonstrate that the use of inductance in shunt circuit can change the equivalent nonlinear mass and the “jump” frequency of the NVI. Large value of inductance deteriorates the vibration isolation performance and the optimal inductance is slightly smaller than zero. Furthermore, N-EMSD can realize nonlinear damping to achieve wide band vibration isolation of the NVI. The optimal negative resistance is discussed.

A novel two-degree-of-freedom model of nonlinear self-excited force for coupled flutter instability of bridge decks

This paper aims to propose a novel model for predicting the nonlinear heave-torsion coupled flutter instability of flat bridge decks. The nonlinear oscillatory system during coupled post-flutter instabilities was modeled as a weak perturbation of the classical linear flutter theory. A novel nonlinear self-excited force model was then proposed by introducing extra nonlinear terms in classical linear model to consider the effects of nonlinear aerodynamic damping, amplitude-dependent vibration mode and the coupling of aerostatic deformation. An efficient algorithm for parameters identification and solving of the nonlinear coupled oscillator was also developed. The effectiveness of the proposed analytical framework was validated through an elastically-supported sectional model test in estimating the self-sustained vibrations during post-critical states of a typical closed-box bridge deck.

Optimal design and seismic performance of tuned fluid inerter applied to structures with friction pendulum isolators

The hydraulic realization of the inerter, called fluid inerter, is a piston-cylinder device designed to convey a fluid through an external helical channel, thus producing rotational inertia of a fluid mass. This paper proposes a novel base-isolation scheme that combines friction pendulum isolators with a Tuned Fluid Inerter (TFI), wherein a grounded fluid inerter benefits from the interaction with an auxiliary set of low-damping rubber isolators as tuning elements. Based on experiments on a small-scale prototype, the fluid inerter is modeled as a linear inerter in parallel with a nonlinear dashpot, whose power-law damping term is related to the pressure drops in the helical channel. Instead, the hysteretic behavior of friction pendulum isolators is described by a standard Coulomb-type frictional model. Optimal design of the fluid inerter is performed within a probabilistic framework, by modeling the base acceleration as a Kanai-Tajimi filtered random process and handling the nonlinearities of fluid inerter and friction isolators through statistical linearization. An extensive parametric study is conducted to assess the influence of different characteristics of isolators and earthquake excitation and, above all, of the nonlinearity of the fluid inerter. The effectiveness of the TFI is demonstrated through nonlinear response history analysis under a suite of 100 ground-motion records. The proposed isolation scheme not only significantly reduces the displacement demand of the isolators, but also mitigates the acceleration and interstory drift response of the superstructure. Moreover, the benefits of the inherent nonlinear damping effect produced by the fluid inerter proves to be particularly effective to reduce the peak response under pulse-like ground motions that may occur in near-field earthquake events, which indeed represent critical excitations for structures with friction isolators.

Hamiltonian Formalism for Bose Excitations in a Plasma with a Non-Abelian Interaction

We have developed the Hamiltonian theory for collective longitudinally polarized colorless excitations (plasmons) in a high-temperature gluon plasma using the general formalism for constructing the wave theory in nonlinear media with dispersion, which was developed by V.E. Zakharov. In this approach, we have explicitly obtained a special canonical transformation that makes it possible to simplify the Hamiltonian of interaction of soft gluon excitations and, hence, to derive a new effective Hamiltonian. The approach developed here is used for constructing a Boltzmann-type kinetic equation describing elastic scattering of collective longitudinally polarized excitations in a gluon plasma as well as the effect of the so-called nonlinear Landau damping. We have performed detailed comparison of the effective amplitude of the plasmon-plasmon interaction, which is determined using the classical Hamilton theory, with the corresponding matrix element calculated in the framework of high-temperature quantum chromodynamics; this has enabled us to determine applicability limits for the purely classical approach described in this study.

Nonlinear Effect of Dead Time in Small-Signal Modeling of Power-Electronic System Under Low-Load Conditions

Dead time is required to ensure that the switches of a synchronous switching inverter leg never conduct at the same time. During dead time, the current commutates to an antiparallel diode that can cause a voltage error depending on the instantaneous current direction. To measure a frequency response from a system, external injections are commonly required to perturb the system. The perturbation can change the current direction at the frequency of the injection, causing a voltage error at the injection frequency due to the dead time. The error depends on the perturbation amplitude, inductor current ripple, and fundamental current amplitude. This article proposes a describing-function method to model the dead-time effect under low-load conditions. It is shown that a nonlinear damping effect from the dead time can occur under low-load conditions and cannot be modeled with a resistor-like element. Real-time hardware-in-the-loop-simulation results are presented and used to demonstrate the effectiveness of the proposed method. Experimental measurements are used to verify the nonlinear dead-time effect.

Local dynamic analysis of imperfect fluid-conveying nanotubes with large deformations incorporating nonlinear damping

An attempt is made in this article to analyse the large-amplitude local dynamics of nanofluid-conveying nanotubes with geometrical imperfections. Each element of the nanotube can have displacements along both longitudinal and transverse directions. A nonlinear damping model is also taken into account utilising the Kelvin–Voigt approach. The stress nonlocality and strain gradient influences are modelled using an advanced scale-dependent theory. Moreover, the Beskok–Karniadakis approach is applied for relative motions at the nanotube wall. To present the coupled motion equations of the coupled nanotube, Hamilton’s approach is used. Moreover, to develop a reliable solution procedure, Galerkin’s method along with continuation technique is utilised. The effects of nonlinear damping, geometrical imperfection, being at nanoscales, fluid velocity and relative motion at the wall on the large-amplitude local dynamics are investigated.

Output Power of Piezoelectric MEMS Vibration Energy Harvesters Under Random Oscillation

The output characteristics of MEMS piezoelectric vibration energy harvesters (PVEHs) under random oscillations are analysed. We fabricated cantilever-type MEMS-PVEHs using Pb(Zr,Ti)O3 films. The autocorrelation function of the transient displacement of the cantilever tip under random oscillations features a narrow-band random vibration. From the power spectral density (PSD) of the output voltage of the PVEHs, the resonance frequency decreases and the full-width at half-maximum increases with increasing vibration acceleration. By comparing output properties under various sinusoidal oscillations, nonlinear effects including the soft-spring effect and nonlinear damping effect clearly influence the output characteristics under random oscillations. The power generation is proportional to the square of the vibration acceleration even in the acceleration region where nonlinear effects become conspicuous.

Reformative translation model for probability density functions of amplitude processes of crosswind-excited super-tall buildings

At the vicinity of vortex lock-in wind speed, the nonlinear aerodynamic damping effect of super-tall buildings is significant, which can greatly promote the surge of vortex-induced vibration in the crosswind direction, where the crosswind response characterized by harmonic amplitude shows narrow-band hardening non-Gaussian characteristic with the kurtosis well below 3, and the corresponding probability distribution of amplitude process distinctly differs from that of typical random buffeting response. Although the moment-based Hermite translation model has been widely used for estimating the extreme value distribution of non-Gaussian process, it fails to represent the probability distribution of hardening non-Gaussian amplitude process, notably for the response with a kurtosis close to 1.5. In this study, a new translation model based on orthogonal expansion of random processes is developed for obtaining the non-Gaussian amplitude process from an underlying Gaussian amplitude process, and the probability density function of the non-Gaussian amplitude process is derived by mapping the cumulative distribution function. The coefficients of translation model are determined by minimizing the errors between the estimated probability density functions and target values through nonlinear optimization, and the closed-form semi-empirical formulations, which connect the model coefficients with response kurtosis, are also proposed using least-square curve fitting. Moreover, the effectiveness and monotonicity of the proposed translation model are examined. This model can be readily incorporated into the extreme value analysis of crosswind response and facilitate the evaluation of wind-induced fatigue of super-tall buildings.

The study of nonlinear dust acoustic wave propagation in a Lorentzian dusty Vlasov plasma in the presence of negative ions

Applying a reductive perturbation analysis in the Vlasov–Poisson model, a Korteweg–de Vries (KdV) equation has been derived for small amplitude dust acoustic waves in a Lorentzian dusty plasma composed of electrons, positive ions, negative ions and charged dust particles. In this paper, two models have been considered, one containing negative and the other containing positive grain charges. Nonlinear propagation of dust acoustic waves in both cases of negative and positive grain charges is governed by KdV equation which gives dust acoustic soliton solution. This dust acoustic soliton solution is rarefied for negative equilibrium dust charge and compressive for positive equilibrium dust charge. Our investigation also shows that the amplitude of dust acoustic soliton in both cases is less than their amplitudes if they are obtained by fluid theory. Thus, our kinetic model captures the nonlinear damping effect of dust acoustic soliton which is absent in fluid theory. The effect of kappa index and dust temperature on the soliton amplitude and width are also studied.

Decay rates for second order evolution equations in Hilbert spaces with nonlinear time-dependent damping

The paper is concerned with the Cauchy problem for second order hyperbolic evolution equations with nonlinear source in a Hilbert space, under the effect of nonlinear time-dependent damping. With the help of the method of weighted energy integral, we obtain explicit decay rate estimates for the solutions of the equation in terms of the damping coefficient and two nonlinear exponents. Specialized to the case of linear, time-independent damping, we recover the corresponding decay rates originally obtained in [ 3 ] via a different way. Moreover, examples are given to show how to apply our abstract results to concrete problems concerning damped wave equations, integro-differential damped equations, as well as damped plate equations.

Some Features of Geometric Nonlinear Damping on Isolation Performance

The addition of nonlinear characteristics to improve the dynamic performance of isolation systems and vibration absorbers has been extensively investigated in the past decades. Both nonlinear stiffness and nonlinear damping have been largely analysed. A common way in which this can be achieved in practice, is by arranging linear elements (springs and viscous dampers) in a specific geometrical configuration. This paper focuses on the fundamental effect of geometrical nonlinear damping in a vibration isolation system, and briefly revises two of the classical implementation mechanisms. They can achieve a better performance than linear systems, by assuring lower damping force at lower displacements, and higher damping force at higher displacements. However, strong nonlinear effects can manifest around resonances, causing non-negligible higher-order harmonics to appear, and making the approximate frequency response obtained by the harmonic balance, unuseful. This paper proposes a new strategy to limit such undesired dynamic effects. For this aim, a coupling is introduced on purpose in the damping mechanism, which allows tailoring the damping force for the specific need.

Nonlocal nonlinear mechanics of imperfect carbon nanotubes

In this article, for the first time, a coupled nonlinear model incorporating scale influences is presented to simultaneously investigate the influences of viscoelasticity and geometrical imperfections on the nonlocal coupled mechanics of carbon nanotubes; large deformations, stress nonlocality and strain gradients are captured in the model. The Kelvin-Voigt model is also applied in order to ascertain the viscoelasticity effects on the mechanics of the initially imperfect nanoscale system. The modified coupled equations of motion are then derived via the Hamilton principle. A solution approach for the derived coupled equations is finally developed applying a decomposition-based procedure in conjunction with a continuation-based scheme. The significance of many parameters such as size parameters, initial imperfections, excitation parameters and linear and nonlinear damping effects in the nonlinear mechanical response of the initially imperfect viscoelastic carbon nanotube is assessed. The present results can be useful for nanoscale devices using carbon nanotubes since the viscoelasticity and geometrical imperfection are simultaneously included in the proposed model.

A Study of the Hydrodynamic Performance of a Pitch-type Wave Energy Converter–Rotor

The effect of hydrodynamic performance of the wave energy converter (WEC)–rotor based on linear potential flow theory due to nonlinear viscous damping was investigated. Free decay tests were conducted using computational fluid dynamics (CFD) to obtain the viscous damping moment. The commonly used procedure for obtaining the damping moment is based on peak amplitudes which normally require a long time history records. Such long free decay records may not be possible in nodding WEC rotor due high damping. The energy method proposed by Bass and Haddara requires only the short and full range of the recorded data. This method provides sufficiently good results when the bodies have high damping. The method equates the rate of change of the total energy of a body undergoing free rolling/pitching to the rate of energy dissipated by the damping. The present study adopts a similar methodology for estimating the linear and linear plus quadratic damping. To incorporate the nonlinear viscous damping moment in the linear equation of motion, an equivalent linearization concept is used without neglecting the nonlinear damping effects. The hydrodynamic coefficients obtained from the linear potential flow theory, nonlinear viscous damping moment from the energy method and estimated PTO damping are used to solve the equation of motion of the WEC rotor. The estimated pitch free decay data shows good agreement with the simulated CFD results when compared to the linear viscous damping moment and better agreement is obtained with linear plus quadratic viscous damping moment. The regular and irregular wave analyses show that a considerable effect on the hydrodynamic performance of the WEC rotor is observed when the linear and linear plus quadratic viscous damping are included.

Nonreciprocal metamaterial with programmable nonlinear virtual resistors

Emphasis is placed on the development of a class of active acoustic diodes and metamaterials in an attempt to control the flow and distribution of acoustic energy in acoustic cavities and systems. The proposed active nonreciprocal acoustic metamaterial (ANAM) cell consists of only one-dimensional acoustic cavity provided with active flexible boundaries. These boundaries are made from piezoelectric bimorphs with the inner layers which interact directly with cavity acting as sensors for monitoring the pressures of the propagating acoustic waves. The outer layers of the bimorphs provide the necessary control actions to an array of programmable nonlinear shunted resistors. These resistors are programmable and are designed in such a manner to introduce simultaneous nonlinear damping and cubic hardening stiffness effects. A lumped-parameter model of the ANAM cell is developed to control the nonreciprocal characteristics of the cell by the selection of the proper balance between the nonlinear damping and stiffness effects. Lyapunov stability criterion is used to generate the structure of such a balanced control strategy. The Harmonic Balance Method is used to predict the limit cycle behavior of the ANAM, the backbone characteristics and the stable limits of the control gains. Numerical examples are presented to demonstrate the effectiveness of the proposed ANAM in tuning and programming the directivity, flow, and distribution of acoustic energy propagating though the metamaterial.

Effect of Fractional Damping in Double-Well Duffing–Vander Pol Oscillator Driven by Different Sinusoidal Forces

Abstract The effect of nonlinear damping including fractional damping on the onset of horseshoe chaos is studied both analytically and numerically in the double-well Duffing–Vander Pol (DVP) oscillator driven by various sinusoidal forces. The sinusoidal type periodic forces of our interest are sine wave, rectified sine wave, and modulus of sine wave. Using the Melnikov analytical method, the threshold condition for the onset of horseshoe chaos is obtained for each sinusoidal force. Melnikov threshold curves are drawn in (f,\;ω) parameters space for each force. When the damping component (p) increases from a small value, the Melnikov threshold value ( f M ) $(f_{M})$ is decreased for each force. Suppression of horseshoe chaos is predicted due to the effect of weak periodic perturbation and nonlinear fractional damping. Analytical predictions are demonstrated through direct numerical simulations.

Investigation of mechanical nonlinear effect in piezoelectric MEMS vibration energy harvesters

Nonlinear resonance in piezoelectric vibration energy harvesters (pVEHs) has a large effect on the characteristics of power generation. In this study, the origin of nonlinearity was investigated on MEMS pVEHs using a 3-µm-thick-Pb(Zr,Ti)O3 film. The resonant frequency and mass of the pVEHs were 180.6 Hz and 3.63 mg, respectively. From the resonance curves of the output voltage and tip displacement measured at a low acceleration, where linear resonance was obtained, the electromechanical coupling and mechanical quality factors of the pVEHs were determined to be 0.3% and 430, respectively. Although the high output power density of 4.1 µW·mg−1·G−2 was obtained at the acceleration of 0.024 G, the effect of nonlinear resonance appeared and suppressed the output power density at the acceleration of 0.07 G and more (G is the gravitational acceleration). The comparison between the results of experiment and numerical analysis using an equivalent circuit model revealed that the nonlinear damping effect has a larger contribution than a nonlinear spring on the suppression of the output power density at a high acceleration.

Relativistic charge solitons created due to non-linear Landau damping: a candidate for explaining coherent radio emission in pulsars

A potential resolution for the generation of coherent radio emission in pulsar plasma is the existence of relativistic charge solitons, which are solutions of nonlinear Schr\"{o}dinger equation (NLSE). In an earlier study, Melikidze et al. (2000) investigated the nature of these charge solitons; however, their analysis ignored the effect of nonlinear Landau damping, which is inherent in the derivation of the NLSE in the pulsar pair plasma. In this paper we include the effect of nonlinear Landau damping and obtain solutions of the NLSE by applying a suitable numerical scheme. We find that for reasonable parameters of the cubic nonlinearity and nonlinear Landau damping, soliton-like intense pulses emerge from an initial disordered state of Langmuir waves and subsequently propagate stably over sufficiently long times, during which they are capable of exciting the coherent curvature radiation in pulsars. We emphasize that this emergence of {\em stable} intense solitons from a disordered state does not occur in a purely cubic NLSE; thus, it is {\em caused} by the nonlinear Landau damping.

Theoretical and experimental study on dynamic characteristics of V-shaped beams immersed in viscous fluids: From small to finite amplitude

In this paper, an underwater vibration model is developed to depict the dynamic characteristic of V-shaped beams for both small and finite amplitude vibrations by considering the fluid–structure interactions between the complicated geometry and viscous fluids. The gap to width ratio in beam’s cross-section is introduced to describe the geometry of the V-shaped beam. For small amplitude vibrations, a complex hydrodynamic function in terms of the gap to width ratio and the frequency parameter is presented to characterize the fluid–structure interactions according to the 2-D fluid dynamics simulations. Besides, a 3-D numerical simulation is performed to verify the proposed computational approach and hydrodynamic function in the 2-D analysis. As the vibration amplitude increases, the 2-D fluid dynamics simulations are further conducted to investigate the effects of amplitude parameter on the flow physics. Therefore, a revised hydrodynamic function governed by the interplay of the frequency parameter, the gap to width ratio and the amplitude parameter is presented to model the hydrodynamic force for finite vibration amplitude accounting for nonlinear damping effects. Moreover, the experimental verifications on both small and finite amplitude vibrations of several V-shaped beams with different geometrical sizes are carried out. It illustrates that the presented model is capable of capturing the nonlinear damping phenomenon occurred at finite oscillation amplitudes and is generally able to predict the underwater vibrations of V-shaped beams with both small and finite amplitude.