Effect Of Nonlinear Damping Research Articles

Beneficial effects of antisymmetric nonlinear damping with application to energy harvesting and vibration isolation under general inputs

Beneficial effects of nonlinear damping on energy harvesting and vibration isolation under harmonic inputs have been investigated showing that the introduction of nonlinear damping can increase the harvested energy and reduce the vibration over both the resonant and higher frequency ranges. However, the scenario becomes more complicated when the loading inputs are of more general form such as multi-tone and random inputs, which can produce system responses that are induced by an interaction of system input components of different frequencies. In the present study, by introducing the concept of power transmissibility, the study of the beneficial effects of nonlinear damping is extended to the systems subject to general inputs including both multi-tone and random inputs. A rigorous analysis is conducted based on single degree of freedom systems subject to general inputs. The analysis reveals the conditions under which the antisymmetric nonlinear damping is beneficial for improving energy harvester performance and reducing of the power of system output in vibration isolation. Moreover, the beneficial effects are demonstrated by two case studies.

Effects of Nonlinear Damping on Vibrations of Microbeam

The present paper develops a new Bernoulli–Euler theory of microbeams for the consideration of small-scale effects and nonlinear terms, which are induced by the axial elongation of the beam and Kelvin–Voigt damping. The non-resonance and primary resonance of microbeams are researched through the application of Galerkin and multiple scale methods to the new model. The results suggest the following: (1) Nonlinear damping slightly affects the vibration amplitudes under the non-resonance condition; (2) nonlinear damping can significantly change the bifurcation points that induce a jump in the vibration amplitudes under the primary resonance condition. The current researches indicate that nonlinear damping is necessary for an accurate description of microbeam vibrations.

Study on vibration energy harvesting of offshore platform by energy harvester based on nonlinear energy sink

Under the impacts of waves and other marine environment, the jacket offshore platform has an obvious vibration and generates lots of energy. Meanwhile, the platform may suffer fatigue damage. The vibration energy harvesting of a jacket offshore platform under random waves with a nonlinear energy sink (NES) was investigated, and a NES-Energy harvester (NES-EH) was then designed by combining an electromagnetic linear generator with the NES. Moreover, the dynamic model of the NES-EH-offshore platform was built, and the electromagnetic damping and stiffness of the energy harvester were optimized by analyzing the energy capture efficiency and root mean square reduction of the platform displacement. The effects of NES nonlinear stiffness and damping, peak period and effective wave height of irregular waves on the capture power and width of the NES-EH were also analyzed. The results show that nonlinear stiffness and damping of the NES impact the energy capturing efficiency of the NES-EH; the smaller the damping and nonlinear stiffness, the higher the power captured by electromagnetic damping in the NES-EH. Compared with NES, the NES-EH system has a better effect on the vibration control of the platform and can better capture considerable vibration energy.

Cockroach-inspired structure for low-frequency vibration isolation

Insects bear huge external loads without injury, for example, cockroaches can withstand forces up to 900 times body weight owing to the shape-changing ability of their jointed exoskeletons and striated muscles, which can absorb huge energy and dissipate by the damping of body-friction. This paper presents a cockroach-inspired structure (CIS) by mimicking the body topology of cockroaches for low-frequency vibration isolation. The exoskeletons, which provide the low-frequency characteristic, are mimicked by a diamond-shape chamber. The striated muscles providing the restoring force are mimicked by springs, and the front legs are mimicked by rods and sliders. The diamond-shape chamber contributes to nonlinear stiffness and the sliders lead to nonlinear damping and inertia effects. The theoretical model was established and the comprehensive parameter studies and optimization efforts were carried out to verify the vibration isolation performance of CIS. The results demonstrate that the nonlinear properties of CIS can dramatically reduce the resonant frequency and peak transmissibility. The spring assembly direction influences the vibration isolation performance. CIS exhibits an anti-resonance phenomenon under a larger inertia. This study creatively provides a type of insect-inspired structures for high-stability and cost-effectiveness low-frequency vibration isolation.

Combined effects of nonlinear proliferation and logistic damping in a three-component chemotaxis system for alopecia areata

This work considers the zero Neumann initial–boundary problem to the chemotaxis system ut=Δu−χ1∇⋅(u∇w)+w−μ1u2,vt=Δv−χ2∇⋅(v∇w)+w+ruv−μ2v2,0=Δw+u+v−w,in a bounded domain Ω⊂Rn,n≥1, with smooth boundary, which was initially proposed by Dobreva et al. (2020) to describe the process of alopecia areata lesions that involves the complicated interplay between CD4+ T cells, CD8+ T cells and interferon-gamma. Compared with the well-known Keller–Segel-type systems, the appearance of the nonlinear proliferation term ruv constituted by the product of two immune cell densities along with a new production term w activated by the chemical in the first two equations forms a novel feature of this model.For any given suitably regular initial data, it is firstly shown that if the positive parameters χ1,χ2, μ1,μ2 and r satisfy the assumptions μ1−r2>(n−2)+n(2χ1+χ22)andμ2−r>(n−2)+n(2χ2+χ12),then the problem admits a global and bounded classical solution. Moreover, we identify a set of parameter conditions: μ1<μ2<3μ1,r=μ2−μ1andχ12+χ22<2μ1(3μ1−μ2),under which any global smooth solution will stabilize to the constant coexistence equilibrium as the time goes to infinity. In addition, in the case of μ1>μ2, the nonlinear stability of the unique positive stationary solution to the corresponding ODE system is also discussed.

Modeling the Dynamics of a Gyroscopic Rigid Rotor with Linear and Nonlinear Damping and Nonlinear Stiffness of the Elastic Support

This study analytically and numerically modeled the dynamics of a gyroscopic rigid rotor with linear and nonlinear cubic damping and nonlinear cubic stiffness of an elastic support. It has been shown that (i) joint linear and nonlinear cubic damping significantly suppresses the vibration amplitude (including the maximum) in the resonant velocity region and beyond it, and (ii) joint linear and nonlinear cubic damping more effectively affects the boundaries of the bistability region by its narrowing than linear damping. A methodology is proposed for determining and identifying the coefficients of nonlinear stiffness, linear damping, and nonlinear cubic damping of the support material, where jump-like effects are eliminated. Damping also affects the stability of motion; if linear damping shifts the left boundary of the instability region towards large amplitudes and speeds of rotation of the shaft, then nonlinear cubic damping can completely eliminate it. The varying amplitude (VAM) method is used to determine the nature of the system response, supplemented with the concept of “slow” time, which allows us to investigate and analyze the effect of nonlinear cubic damping and nonlinear rigidity of cubic order on the frequency response at a nonstationary resonant transition.

An equivalent mechanical model with nonlinear damping for sloshing rectangular tank with porous media

In this paper, the impulsive and harmonic experiments are carried out to investigate the sloshing frequencies and the linear and nonlinear damping of sloshing liquid in a rectangular tank occupied by porous media. As the oscillatory responses remain linear in the impulsive-excitation tests, the damping ratios are obtained by the free-vibration decay method. The analytical method, which is an equivalent mechanical model based on Darcy's law, is developed for comparison. As the dynamic responses become nonlinear in the harmonic excitations, the relationships between the sloshing force and the ground displacement are constructed and the damping ratio is determined by the resonance energy loss method. The relationships between the equivalent damping ratio, wave amplitude, and ground displacement amplitude for the large-excitation cases are established to justify the nonlinear damping effect. A modified mechanical model with a nonlinear damping mechanism is provided.

New general decay result for a class of neutral viscoelastic equations

We are concerned with the decay estimate of a neutral viscoelastic equation with nonlinear boundary damping and boundary memory effect. We obtain a general decay theorem for the neutral viscoelastic equation by showing that its system energy is controlled by a solution of the associated ODE. Moreover, distinguished from the previous compactness-uniqueness method, we propose an analytical approach to estimate the low-order terms by using the Sobolev imbedding theory.

Nonlinear damping effects in a simplified power grid model based on coupled Kuramoto-like oscillators with inertia

In our work, we simulate an uneven balance of produced and consumed energy in an artificially created network that can be considered as a simplified model of the operation of some energy network. The system under consideration has a ring topology consisting of locally connected power generators alternating with power consumers. Each node of the network is represented as a Kuramoto-type phase oscillator with inertia. Oscillatory network equations are transformed in accordance with the efficient network model proposed in [24], and studied numerically. The purpose of the work is to find conditions that prevent the loss of network synchronization. Nonlinear damping of oscillators has been proposed as a possible solution to the problem of stabilizing synchronicity. The maps of regimes constant with constant damping and with time-varying nonlinear damping are compared. In addition, the case of external action on a separate network node in the form of a rectangular pulse is considered. The research results show that nonlinear damping can prevent asynchronous behavior of oscillators and increase the stability of the ensemble to sudden fluctuations in systems. The results obtained can be applied in the field of power systems as a possible tool for increasing the sustainability of power grids. The opposite side of the results is the limitation of the use of nonlinear damping. The adaptive damping has a strong negative effect on the connected power generators, which leads to overheating and failure.

Experimental comparison of nonlinear damping performance of toroidal and conventional tuned liquid column dampers

Conventional tuned liquid column dampers (TLCDs) are deficient in multidirectionality. In contrast, toroidal TLCDs are designed to extend the application to multidirectional vibration control. This article employs real-time hybrid simulation (RTHS) to experimentally investigate the nonlinear damping effects of toroidal and conventional TLCDs in different directions. The RTHS framework consists of toroidal and conventional TLCD models as the physical substructure and a single-degree-of-freedom (SDOF) structure as the numerical substructure. The excitations cover seismic ground motions and harmonic signals. Different structural parameters and peak ground acceleration (PGA) of the ground motions are assigned to the numerical substructure. It is reported that the conventional TLCD has the most remarkable vibration control effect in its main control direction, while it has efficiency loss in other directions. The efficiencies of toroidal TLCD in arbitrary directions are found to be slightly lower to that of convention TLCD in its main control direction. The toroidal TLCD has advantages on omnidirectional damping effects than the conventional TLCD. Lastly, the satisfactory performance of toroidal TLCD under different structural parameters and PGA values confirms the certain robustness of toroidal TLCD.

Nonlinear Decay of Quantum Confined Magnons in Itinerant Ferromagnets.

Quantum confinement leads to the emergence of several magnon modes in ultrathin layered magnetic structures. We probe the lifetime of these quantum confined modes in a model system composed of three atomic layers of Co grown on different surfaces. We demonstrate that the quantum confined magnons exhibit nonlinear decay rates, which strongly depend on the mode number, in sharp contrast to what is assumed in the classical dynamics. Combining the experimental results with those of linear-response density-functional calculations we provide a quantitative explanation for this nonlinear damping effect. The results provide new insights into the decay mechanism of spin excitations in ultrathin films and multilayers and pave the way for tuning the dynamical properties of such structures.

Modified Adaptive Negative Stiffness Device with Variable Negative Stiffness and Geometrically Nonlinear Damping for Seismic Protection of Structures

Adaptive negative stiffness device is one of the promising seismic protection devices since it can generate seismic isolation effect through negative stiffness when it is mostly needed and achieve similar vibration mitigation as a semi-active control device. However, the adaptive negative stiffness device generally combined with linear viscous damping underpins the drawback of degrading the vibration isolation effect during the high-frequency region. In this paper, a modified adaptive negative stiffness device (MANSD) with the ability to provide both lateral negative stiffness and nonlinear damping by configuring linear springs and linear viscous dampers is proposed to address the above issue. The negative stiffness and nonlinear damping are realised through a linkage mechanism. The fundamentals and dynamic characteristics of a SDOF system with such a device are analyzed and formulated using the Harmonic Balance Method, with a special focus on the amplitude–frequency response and transmissibility of the system. The system with damping nonlinearity as a function of displacement and velocity has been proven to have attractive advantages over linear damping in reducing the transmissibility in the resonance region without increasing that in the high-frequency region. The effect of nonlinear damping on suppressing displacement and acceleration responses is numerically verified under different sinusoidal excitations and earthquakes with different intensities. Compared with linear damping, the MANSD with nonlinear damping could achieve additional reductions on displacement and acceleration under scaled earthquakes, especially intensive earthquakes.

Analysis of total harmonic distortion of miniature loudspeakers used in mobile phones considering nonlinear acoustic damping.

Total harmonic distortion (THD) plays an important role in the performance of miniature loudspeakers used in mobile phones. Traditional nonlinear models fail to predict THD in the higher frequency domain. Significant discrepancies can be found between the prediction and measurement. In this study, an extended model considering nonlinear acoustic damping is proposed to address this issue. Flow separation occurring near the orifices of the sound port is of particular interest. Two velocity-dependent parameters were derived to model the nonlinear damping effect. Based on the extended model, the dynamics of miniature loudspeakers are described using the state-space method. Experiments and calculations confirm the validity of the extended model. The influence of nonlinear acoustic damping on THD is also discussed.

Experimental characterization of a one-dimensional nonreciprocal acoustic metamaterial with anti-parallel diodes

Characterization of a newly developed class of passive nonreciprocal acoustic metamaterials is presented in an attempt to quantify their ability of controlling the flow and distribution of acoustic energy in acoustic cavities and systems. The proposed nonreciprocal acoustic metamaterial (NAMM) cell consists of a one-dimensional acoustic cavity provided with piezoelectric flexible boundaries connected to an array of anti-parallel diodes to introduce the nonlinear damping effect that tends to break the reciprocity of the energy flow through the NAMM cell. A comprehensive experimental characterization of prototypes of the NAMM cells is presented here in order to investigate the effect of various anti-parallel diode arrangements on the nonreciprocal behavior of the cell. Furthermore, the experimental characterization aims also at demonstrating the effectiveness of the proposed NAMM in tuning the directivity, flow, and distribution of acoustic energy propagating through the metamaterial.

A nonlinear interaction between SU(1,1) quantum system and a three-level atom in different configurations with damping term

The effect of nonlinear medium and phase damping is investigated on an atom of three levels in different forms interacting with the SU(1,1) Lie algebra. The SU(1,1) system starts the interaction from the Perelomov coherent state, while the atom starts the interaction from excited-most state. The time dependent wave function is calculated by using the Schrödinger equation. The density matrix is obtained. The influences of damping, nonlinearity (Kerr-like medium), Perelomov coherent parameter and the Bargmann index on some non-classical properties, such as: revivals-collapses phenomenon, entanglement and atomic variables squeezing, are investigated.

Applicability of random decrement technique in extracting aerodynamic damping of crosswind-excited tall buildings

At the vicinity of vortex lock-in wind speed, the nonlinear aerodynamic damping effect is significant. It can greatly promote the surge of crosswind response, even threaten structural safety and serviceability of tall buildings. Techniques dependent on experimental measurement to identify aerodynamic damping have been developed for estimating crosswind response from wind loading spectrum. Random decrement technique (RDT) as one frequently mentioned technique of system identification has been used in literature to extract aerodynamic damping from stochastic crosswind response, although it was originally suitable for linear single degree of freedom system with a constant damping ratio. This study investigates the applicability of RDT in extracting aerodynamic damping of tall buildings. The models of linear and nonlinear aerodynamic damping are applied to simulate crosswind response of a square section tall building. Accordingly, the wind loading spectra based on high-frequency-force-balance (HFFB) testing and the model recommended by AIJ are utilized respectively to consider the effect of random wind load on the characteristics of crosswind response. To examine the accuracy and efficiency of RDT, aerodynamic damping is extracted through two approaches and compared with target value. Moreover, the influence of varying wind loading spectra on amplitude-dependent aerodynamic damping is demonstrated.

A Diversity of Wave-driven Presupernova Outbursts

Abstract Many core-collapse supernova (SN) progenitors show indications of enhanced pre-SN mass loss and outbursts, some of which could be powered by wave energy transport within the progenitor star. Depending on the star’s structure, convectively excited waves driven by late-stage nuclear burning can carry substantial energy from the core to the envelope, where the wave energy is dissipated as heat. We examine the process of wave energy transport in single-star SNe progenitors with masses between 11 and 50 M ⊙. Using MESA stellar evolution simulations, we evolve stars until core collapse and calculate the wave power produced and transmitted to the stars’ envelopes. These models improve upon prior efforts by incorporating a more realistic wave spectrum and nonlinear damping effects, reducing our wave-heating estimates by ∼1 order of magnitude compared to prior work. We find that waves excited during oxygen/neon burning typically transmit ∼1046–1047 erg of energy at 0.1–10 yr before core collapse in typical (M &lt; 30 M ⊙) SN progenitors. High-mass progenitors can often transmit ∼1047–1048 erg of energy during oxygen/neon burning, but this tends to occur later, at about 0.01–0.1 yr before core collapse. Pre-SN outbursts may be most pronounced in low-mass SN progenitors (M ≲ 12 M ⊙) undergoing semidegenerate neon ignition and in high-mass progenitors (M ≳ 30 M ⊙) exhibiting convective shell mergers.

The effects of nonlinear damping on degenerate parametric amplification

This paper considers the dynamic response of a single degree of freedom system with nonlinear stiffness and nonlinear damping that is subjected to both resonant direct excitation and resonant parametric excitation, with a general phase between the two. This generalizes and expands on previous studies of nonlinear effects on parametric amplification, notably by including the effects of nonlinear damping, which is commonly observed in a large variety of systems, including micro- and nano-scale resonators. Using the method of averaging, a thorough parameter study is carried out that describes the effects of the amplitudes and relative phase of the two forms of excitation. The effects of nonlinear damping on the parametric gain are first derived. The transitions among various topological forms of the frequency response curves, which can include isolae, dual peaks, and loops, are determined, and bifurcation analyses in parameter spaces of interest are carried out. In general, these results provide a complete picture of the system response and allow one to select drive conditions of interest that avoid bistability while providing maximum amplitude gain, maximum phase sensitivity, or a flat resonant peak, in systems with nonlinear damping.

A novel lever-type vibration isolator with eddy current damping

This study proposes a lever-type vibration isolator with eddy current damping (LVI-ECD), which can broaden the isolation band by adjusting the lever ratio and improve the vibration suppression performance with eddy current damping (ECD). The LVI-ECD composes of a lever with a permanent magnet (PM) at the tip of the lever, a load plate, a base plate and springs, etc. The relative motion between the PM and the conductive base and load plates induces ECD, which can be amplified by the lever structure and thus to generate nonlinear damping effect. The theoretical models of the lever-type vibration isolator (LVI) and LVI-ECD are established and the amplitude frequency relationship considering nonlinear damping is deduced. The effects of the lever ratio, tip mass, material property and cross-section of the lever, geometric parameters of the PM and excitation amplitude on the vibration isolation performance of the LVI-ECD are analyzed. The analytical predictions are consistent with the experimental results, which demonstrates that the peak transmissibility and natural frequency decrease with the increase of the lever ratio. ECD can further improve the vibration suppression performance in the resonance region. The transmissibility tends to be flat with the increase of the lever ratio in the isolation region. The vibration isolation performance can be also improved by increasing the tip mass of the lever. The material property and cross-section of the lever have little effect on vibration isolation. This study provides a guideline to design, model and optimize a passive damped lever-type vibration isolator.

Application of a new empirical model of nonlinear self-excited force to torsional vortex-induced vibration and nonlinear flutter of bluff bridge sections

Long-span bridges are susceptible to vortex-induced vibration (VIV) and flutter in different reduced wind range. Currently, VIV and flutter are considered as two different types of wind-induced vibration and different empirical models were proposed. The possibility of building a universal empirical model for both torsional VIV and nonlinear flutter was explored. In the previous study, a new empirical model was proposed for describing aerodynamic nonlinearities during soft flutter of a bluff bridge section with a medium side ratio. In this study, the empirical model was refined and extended to both torsional VIV and nonlinear flutter for a general bluff body, especially for a flat bridge deck, which is more common in long-span bridges. In the empirical model, aerodynamic nonlinear damping effect was modeled by a cubic velocity term and its applicability was validated by a series of elastically-mounted sectional model tests of a flat twin-side-girder bridge deck. The results indicated that the proposed empirical model was suitable for predicting the stable amplitude of torsional VIV and nonlinear flutter, although the motion-induced “pure force” varies with side ratios. It was found that torsional VIV and soft flutter share the same nonlinear damping mechanism during the development of LCO.