Weak Damping Research Articles

Experimental and numerical study of pile foundations subjected to rotating machine-induced coupled excitations

ABSTRACT Dynamic response characteristics of a hollow steel single-pile and three-pile group are investigated under coupled vibration. Forced coupled vibration tests are conducted on the piles for static loads of 12 kN and 14 kN under different eccentric moments. The time-acceleration responses are measured for different frequencies for both horizontal and rocking modes and finally the frequency-amplitude responses are determined for horizontal and rocking components separately. The dynamic frequency-amplitude responses of piles are analysed by continuum approach method with two different soil-pile models: (i) a linear visco-elastic composed medium with the consideration of reduced shear modulus and (ii) a boundary zone model with non-reflective interface of shear modulus with parabolic variation. The variation of stiffness and damping of the soil-pile system are also determined. The analytical results are compared with the dynamic test results to verify the applicability of those soil models for predicting the non-linear response of soil-pile system under coupled vibration. It is observed from the comparison curves that the results obtained from the first soil model are found reasonably close to the dynamic test data. However in the case of second soil model, the resonant amplitude values are found much higher than the test data. Based on the analytical results, the boundary zone parameters like modulus reduction ratio, thickness ratio, weak zone soil damping and separation lengths of pile under different eccentric moments are predicted in present field condition. The variations of group efficiency ratio of the pile group with frequency are also determined form the analysis.

Quantum properties of a strongly driven Josephson junction

A Josephson junction embedded in a dissipative circuit can be externally driven to induce nonlinear dynamics of its phase. Classically, under sufficiently strong driving and weak damping, dynamic multi-stability emerges associated with dynamical bifurcations so that the often used modeling as a Duffing oscillator, which can exhibit bi-stability at the most, is insufficient. The present work analyzes in this regime corresponding quantum properties by mapping the problem onto a highly-nonlinear quasi-energy operator in a rotating frame. This allows us to identify in detail parameter regions where simplifications such as the Duffing approximation are valid, to explore classical-quantum correspondences, and to study how quantum fluctuations impact the effective junction parameters as well as the dynamics around higher amplitude classical fixed points.

Adjustable virtual inertia control of supercapacitors in PV-based AC microgrid cluster

This paper investigates a novel control strategy of supercapacitors to improve the dynamic stability of the interconnected PV-based AC microgrid clusters in standalone operation. An emerging definition of supercapacitors is proposed to emulate the dynamic inertia response. This definition establishes the dynamic connections between the state-of-charge (SOC), the frequency of the standalone AC microgrid clusters and the power of supercapacitors. Then this paper presents a theoretical analysis of dynamic stability on two-area PV microgrid clusters. According to the type of AC microgrid, the dynamic inertia constant is also analyzed. Based on the dynamic stability analysis of two-area PV microgrid clusters and the dynamic inertia constant analysis of supercapacitors, the adjustable virtual inertia control method of supercapacitors is proposed to extract the stored energy for the dynamic inertia response. The aim of the proposed control scheme is to solve the low inertia and weak damping of the standalone interconnected PV microgrid clusters. The effectiveness of the proposed control scheme is validated by Matlab/Simulink platform.

Influence Mechanism of Electromechanical Parameters on Transient Vibration of Electric Wheel System

<div class="section abstract"><div class="htmlview paragraph">Electric wheel systems of in-wheel motor driven vehicles consist of the motor controller, in-wheel motor and tire-suspension assembly. The coupling between the electromagnetic excitation and elastic structure gives rise to electromechanical dynamic issues. As for the structural layout of the electric wheel system, the driving motor is directly connected to the wheel without torsion dampers or transmission in the driveline, thus making the electric wheel structure a weak damping system. Moreover, the driving torque of electric wheel can change rapidly in various conditions of vehicle. As a result, the transient vibration problem becomes one of the key electromechanical dynamic issues in the electric wheel system. To investigate this problem, the electromechanical coupling model of the electric wheel system is established first. Then the transient responses of the electric wheel under abrupt changes of the driving torque are simulated. The results indicate that the tire mainly suffers from longitudinal shocks in the anti-phase rotational mode at 95 Hz and vibration in the in-phase rotational mode at 44Hz successively, while the motor vibrates in the in-phase rotational mode at 44Hz. As the electric wheel system is electromechanically coupled, the influence mechanism and rules of electromechanical parameters on the transient vibration are studied. The results show that the permanent magnet flux linkage increases damping ratio of the in-phase rotational mode in virtue of the electromagnetic stiffness and damping, thus further weakening transient vibration of motor. The anti-phase rotational mode is sensitive to tire’s stiffness. It is effective to optimize tire’s shock by adjusting tire’s stiffness. This paper reveals the electromechanical coupling mechanism of the electric wheel system, and provides reference for parameter design from the perspective of improvement in dynamic characteristics.</div></div>

Optical Excitation of Single- and Multimode Magnetization Precession in Fe - Ga Nanolayers

We demonstrate a variety of precessional responses of the magnetization to ultrafast optical excitation in nanolayers of Galfenol (Fe,Ga), which is a ferromagnetic material with large saturation magnetization and enhanced magnetostriction. The particular properties of Galfenol, including cubic magnetic anisotropy and weak damping, allow us to detect up to 6 magnon modes in a 120-nm layer, and a single mode with effective damping ${\alpha}_{eff}$ = 0.005 and frequency up to 100 GHz in a 4-nm layer. This is the highest frequency observed to date in time-resolved experiments with metallic ferromagnets. We predict that detection of magnetization precession approaching THz frequencies should be possible with Galfenol nanolayers.

A survey of the Szegő equation

We survey the main properties of the cubic Szegő equation from the PDE viewpoint, emphasising global existence of smooth solutions, analytic regularity, growth of high Sobolev norms and the effects of weak damping.

Dispersion surface and electromagnetic responses of the magnetosonic/whistler mode in the high-β collisionless plasmas

Near-parallel and highly oblique magnetosonic/whistler (M/W) mode waves are frequently observed in solar wind and interplanetary shocks. These observed waves are usually analyzed by the plasma kinetic and fluid theories. This study compares the dispersion surface and electromagnetic responses of the M/W mode wave under both kinetic and fluid theories in the plasmas with βp = βe ≃ 1 in detail. In comparison with the kinetic theory, it proposes that the hot fluid theory is suitable to obtain the dispersion relation, the ratio of the parallel to perpendicular magnetic fluctuation Bz/B⊥, and the ratio of the electric to magnetic fluctuation E/B. Except the near-parallel low-frequency M/W mode, the hot fluid theory would be used to calculate the ratio between two magnetic fluctuations perpendicular to the wave vector B1/B2, the magnetic helicity σ, and the ratio of the parallel to perpendicular electric fluctuation Ez/E⊥ of the M/W mode waves. The cold fluid theory is good at describing the magnetic responses including Bz/B⊥, B1/B2, and σ, but it underestimates ω, E/B, and Ez/E⊥ for the obliquely propagating M/W mode wave. Furthermore, both hot and cold fluid theories can obtain the ratio of the longitudinal to transverse electric fluctuation relative to the wave vector EL/EP of the obliquely propagating low-frequency M/W mode. These results provide an indicator about how to choose the adequate theory to analyze the observations of the M/W mode waves in the solar wind and interplanetary shocks. Besides, from the dispersion surface in kinetic theory, it shows that the relative weak damping arises for the low-frequency branch at the angle around 0°, 60°, and 90° and for the high-frequency branch with ω ∼ [ωcp, 300ωcp] at the normal angle smaller than 60°, which indicates the possible angle and frequency of the freely propagating M/W mode waves.

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.

Blow-up of solutions for a nonlinear Petrovsky type equation with initial data at arbitrary high energy level

In this paper, we study the initial boundary value problem for a Petrovsky type equation with a memory term, nonlinear weak damping, and a superlinear source: \t\t\tutt+Δ2u−∫0tg(t−τ)Δ2u(τ)dτ+|ut|m−2ut=|u|p−2u,in Ω×(0,T).\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$ u_{tt}+\\Delta ^{2} u- \\int _{0}^{t} g(t-\\tau )\\Delta ^{2} u(\\tau )\\,\\mathrm{d} \\tau + \\vert u_{t} \\vert ^{m-2}u_{t}= \\vert u \\vert ^{p-2}u,\\quad \\text{in }\\varOmega \\times (0,T). $$\\end{document} When the source is stronger than dissipations, we obtain the existence of certain weak solutions which blow up in finite time with initial energy E(0)=R for any given Rgeq 0.

Qualitative analysis of solutions for a class of Kirchhoff equation with linear strong damping term, nonlinear weak damping term and power-type logarithmic source term

In this paper, we study the initial boundary value problem for Kirchhoff equation with linear strong damping term, nonlinear weak damping term and power-type logarithmic source term at three different initial energy levels, i.e. subcritical energy E(0)<d, critical initial energy E(0)=d and the arbitrary high energy E(0)>0. By potential well method, we prove global existence, finite time blow up and asymptotic behavior of solutions in cases of E(0)<d and E(0)=d. We also prove the finite time blow up of solutions to the problem with linear weak and strong damping term in the case of E(0)>0.

Parareal Exponential $\theta$-Scheme for Longtime Simulation of Stochastic Schrödinger Equations with Weak Damping

A parareal algorithm based on an exponential $\theta$-scheme is proposed for the stochastic Schrodinger equation with weak damping and additive noise. It proceeds as a two-level temporal paralleliz...

Nonexistence of global solutions of nonlinear wave equations with weak time-dependent damping related to Glassey's conjecture

This work is devoted to the nonexistence of global-in-time energy solutions of nonlinear wave equation of derivative type with weak time-dependent damping in the scattering and scale invariant range. By introducing some multipliers to absorb the damping term, we succeed in establishing the same upper bound of the lifespan for the scattering damping as the non-damped case, which is a part of so-called Glassey's conjecture on nonlinear wave equations. We also study an upper bound of the lifespan for the scale invariant damping with the same method.

Absolute instability modes due to rescattering of stimulated Raman scattering in a large nonuniform plasma

Absolute instability modes due to secondary scattering of stimulated Raman scattering (SRS) in a large nonuniform plasma are studied theoretically and numerically. The backscattered light of convective SRS can be considered as a pump light with a finite bandwidth. The different frequency components of the backscattered light can be coupled to develop absolute SRS instability near their quarter-critical densities via rescattering process. The absolute SRS mode develops a Langmuir wave with a high phase velocity of about $c/\sqrt{3}$ with $c$ the light speed in vacuum. Given that most electrons are at low velocities in the linear stage, the absolute SRS mode grows with very weak Landau damping. When the interaction evolves into the nonlinear regime, the Langmuir wave can heat abundant electrons up to a few hundred keV via the SRS rescattering. Our theoretical model is validated by particle-in-cell simulations. The absolute instabilities may play a considerable role in the experiments of inertial confinement fusion.

Parametric Decay of Beam‐Generated Langmuir Waves and Three‐Wave Interaction in Plateau Plasmas: Implications for Type III Radiation

AbstractInspired by the results of particle‐in‐cell simulations on beam‐plasma interaction, we present a mechanism for the generation of radio waves in solar type III bursts which provides a closed chain of the conversion processes from beam‐generated Langmuir waves into electromagnetic emission. The mechanism is characterized by two key steps. The first is a hitherto unknown parametric decay process in which the primary wave directly decays to low‐k Langmuir waves (plasma oscillations) and ion acoustic waves. This decay becomes possible due to changes in the dispersion properties of longitudinal waves initiated by the presence of a beam or a plateau in the electron velocity distribution. A resonant three‐wave interaction is established between the beam‐induced Langmuir wave, the plasma oscillations, and the ion acoustic wave. Due to weak damping of the waves involved, this interaction persists after the beam has relaxed to a plateau and lasts as long as the latter exists. In the second step, low‐k Langmuir waves in the range of “optical wavelengths” can linearly couple to obliquely propagating radio waves at the plasma frequency in a wave number region around the cross points where quasi‐longitudinal and quasi‐transverse modes approach each other. Our model does not need the persistence of the beam and the associated instability for radiation to be produced. Although the theory is local with respect to the plasma frequency, it may open a way to overcome Sturrock's () dilemma of rapid beam relaxation on the one side and long‐lived radiation on the other. The observed frequency variation is suggested to arise by “adiabatic” motion of the beam‐created interaction region through the heliospheric plasma of decreasing electron density. Implications for the interpretation of in situ Langmuir waveforms and the diversity of their frequency spectra are discussed.

Generation of Vertical Fine Structure by Internal Waves in a Shear Flow

The generation of vertical fine structure by inertia-gravity internal waves in a two-dimensional stratified shear flow is investigated. In the linear approximation, the boundary value problem for the amplitude of the vertical velocity of internal waves has complex coefficients, the imaginary part of which is small. The wave frequency and the eigenfunction of the boundary problem for the internal waves are complex (and we show that a weak damping of the wave occurs). The phase shift between the fluctuations of density and vertical velocity differs from π/2; therefore, the wave-induced vertical mass flux is non-zero. It is shown that dispersion curves are cut off in the low-frequency domain due to the influence of critical layers, where the frequency of the wave with the Doppler shift is equal to the inertial one. The Stokes drift velocity is determined in the weakly nonlinear approximation, on the second order in the amplitude of the wave. The vertical component of the Stokes drift velocity is also non-zero and contributes to wave transfer. The summary wave mass flux exceeds the turbulent one and leads to irreversible deformation of the average density profile which can be interpreted like a fine structure generated by the wave. On the shelf, this deformation is more than in deep-water part of the Black Sea at the same amplitude of а wave. The vertical scale of the fine structure of Brunt-V?is?l? frequency, generated by a wave, corresponds to really observed value.

A Theory for the Seasonal Predictability Barrier: Threshold, Timing, and Intensity

AbstractA theory is developed in a stochastic climate model for understanding the general features of the seasonal predictability barrier (PB), which is characterized by a band of maximum decline in autocorrelation function phase-locked to a particular season. Our theory determines the forcing threshold, timing, and intensity of the seasonal PB as a function of the damping rate and seasonal forcing. A seasonal PB is found to be an intrinsic feature of a stochastic climate system forced by either seasonal growth rate or seasonal noise forcing. A PB is generated when the seasonal forcing, relative to the damping rate, exceeds a modest threshold. Once generated, all the PBs occur in the same calendar month, forming a seasonal PB. The PB season is determined by the decline of the seasonal forcing as well as the delayed response associated with damping. As such, for a realistic weak damping, the PB season is locked close to the minimum SST variance under the seasonal growth-rate forcing, but after the minimum SST variance under the seasonal noise forcing. The intensity of the PB is determined mainly by the amplitude of the seasonal forcing. The theory is able to explain the general features of the seasonal PB of the observed SST variability over the world. In the tropics, a seasonal PB is generated mainly by a strong seasonal growth rate, whereas in the extratropics a seasonal PB is generated mainly by a strong seasonal noise forcing. Our theory provides a general framework for the understanding of the seasonal PB of climate variability.

Exponential Stability for the Generalized Korteweg-de Vries Equation in a Finite Interval with Weak Damping

The aim of this paper is to consider the generalized Korteweg-de Vries equation in a finite interval with a very weak localized dissipation. We obtain the globally uniformly exponentially stability of this equation. The main difficulty in this context comes from the structure of nonlinear term and the lack of regularity.

Time periodic solutions to the beam equation with weak damping

In this paper, we study the beam equation with weak damping in n-dimensional space. In the case of time-dependent periodic external force imposed, we prove the existence and uniqueness of time periodic solutions that have the same period as the time-dependent periodic external force in some suitable function space for all space dimensions n ≥ 1. The proof is based on the spectral analysis for the solution operators and the contraction mapping theorem. Moreover, we show the time asymptotic stability of time periodic solutions by continuous argument.

Damping of linear spin-wave modes in magnetic nanostructures: Local, nonlocal, and coordinate-dependent damping

A general perturbation theory for the description of weak damping of linear spin-wave modes in magnetic nanostructures is developed. This perturbative approach allows one to account for the usual uniform Gilbert damping, as well as for the spatially nonuniform (coordinate-dependent) and nonlocal (magnetization-texture-dependent) Gilbert-like dissipation mechanisms. Using the derived general expression, it is possible to calculate the damping rate of a particular spin-wave mode if the frequency and the spatial profile of this mode, along with the relevant parameters of a magnetic material, are known. The examples demonstrating the applications of the developed general formalism include (i) generalization of the damping rate of a spin-wave mode propagating in a magnetic sample for the case of a nonuniform static magnetization or/and bias magnetic field, (ii) calculation of a damping rate of a gyrotropic mode in a vortex-state magnetic nanodot, (iii) evaluation of the spin diffusion influence on the damping rate of spin-wave modes in a conducting ferromagnet, and (iv) calculation of damping rates of spin-wave modes in a ferromagnetic film in the presence of a spin pumping into an adjacent nonmagnetic metal layer. The developed formalism is especially useful in micromagnetic simulations, as it allows one to calculate damping rates of spin-wave modes based on the numerical solution of a conservative eigenmode problem.

Anti-Langmuir decay instability in Langmuir decay instability cascade

Backward stimulated Raman scattering (BSRS) with Langmuir decay instability (LDI) and anti-Langmuir decay instability (ALDI or anti-LDI) has been researched by Vlasov simulation. The decay productions of anti-LDI in LDI cascade and their evolution with time are demonstrated for the first time. The BSRS reflectivity will be decreased largely through LDI cascade and ALDI in the small wave-number region. Different mechanisms to saturate BSRS in CH (or H) and C plasmas have been demonstrated. The dominant saturation mechanism of BSRS in CH (or H) plasmas is LDI cascade and ALDI. However, in C plasmas, due to very weak Landau damping of ion acoustic waves, LDI cascade will promote stimulated Brillouin scattering (SBS) excitation, then SBS will compete with BSRS and saturate BSRS in the later stage. The proportion of the hot electrons is decreased largely through LDI cascade and ALDI. These results give an effective mechanism to suppress BSRS and hot electron generation in the small wave-number region, which are of important significance in the inertial confinement fusion.