Effect Of Nonlinear Damping Research Articles

A tunable nonlinear vibrational energy harvesting system with scissor-like structure

Vibrational energy harvesting systems with linear electromechanical generators have been largely studied, due to their simple structures and convenience in application. However, the ambient vibration characteristics such as random, time-varying or low-frequency properties make the linear electromagnetic devices cannot be excited at their resonances, which will greatly affect the energy harvesting efficiency. Some attempts to improve the efficiency of a vibration energy harvesting system involve both expand the operating bandwidth and enlarging the magnitude of power output. To this end, a scissor-like energy harvesting system with equivalent nonlinear damping and linear stiffness has been developed in this study. It has been shown that, due to the beneficial nonlinear damping effects provided by the scissor-like structure, the proposed system can greatly improve the vibration energy harvesting performance in terms of the magnitude of power output and energy harvesting bandwidth. On the other hand, the structure parameters of the proposed system can be modified to achieve more significant energy harvesting performance. Moreover, to achieve tunable resonant frequency of the energy harvesting system, the scissor-like structure has been updated by attaching a new lever-type system. In this way, the energy harvesting performance can be improved by tuning the proposed system according to the properties of the surrounding vibration sources. In this paper, both harmonic and random excitations have been adopted to verify the performance of the proposed energy harvesting system.

A method for non-parametric identification of non-linear vibration systems with asymmetric restoring forces from a resonant decay response

Abstract A method for non-parametric identification of systems with asymmetric non-linear restoring forces is proposed in this paper. The method, named the zero-crossing method for systems with asymmetric restoring forces (ZCA), is an extension of zero-crossing methods and allows identification of backbones, damping curves and restoring elastic and dissipative forces from a resonant decay response. The validity of the proposed method is firstly demonstrated on three simulated resonant decay responses of the systems with off-centre clearance, bilinear and quadratic stiffness. Then, the method is applied to experimental data from a micro-electro-mechanical resonator in order to quantify its non-linear damping and stiffness effects. Throughout the paper the proposed method is also compared with the Hilbert vibration decomposition to demonstrate that the ZCA yields more accurate results with much less effort.

Nonlinear behaviour and mass detection sensitivity of geometrically imperfect cantilevered carbon nanotube resonators

This study analyzes numerically the nonlinear static and dynamic behaviours as well as the mass detection sensitivity of a geometrically imperfect cantilevered carbon nanotube (CNT) resonator. More specifically, a new nonlinear model is developed for the cantilevered CNT nanoresonator, taking into account the effects of the initial curvature and cross-sectional area imperfection; furthermore, the new nonlinear model accounts for nonlinear damping and small-scale effects, employing the Kelvin–Voigt damping model and the modified couple stress-based elasticity theory, respectively. The electrostatic interactions in the CNT nanoresonator are modelled through use of a new electrostatic load model, previously developed by the authors. The nonlinear equation of motion of the geometrically imperfect cantilevered CNT nanoresonator is obtained making use of Hamilton’s principle as well as the inextensibility condition. The electromechanical continuous model of the nanoresonator is reduced into a high-dimensional discretized model employing the Galerkin method. The discretized model, consisting of a set of coupled nonlinear ordinary differential equations, is solved numerically employing a continuation technique. The nonlinear behaviour of the nanoresonator is studied and the effect of different parameters on the static deflection and dynamic response is examined. Furthermore, the mass detection sensitivity of the nanoresonator is examined in detail and methods are proposed for enhancing the detection sensitivity.

Dynamics of cochlear nonlinearity: Automatic gain control or instantaneous damping?

Measurements of basilar-membrane (BM) motion show that the compressive nonlinearity of cochlear mechanical responses is not an instantaneous phenomenon. For this reason, the cochlear amplifier has been thought to incorporate an automatic gain control (AGC) mechanism characterized by a finite reaction time. This paper studies the effect of instantaneous nonlinear damping on the responses of oscillatory systems. The principal results are that (i) instantaneous nonlinear damping produces a noninstantaneous gain control that differs markedly from typical AGC strategies; (ii) the kinetics of compressive nonlinearity implied by the finite reaction time of an AGC system appear inconsistent with the nonlinear dynamics measured on the gerbil basilar membrane; and (iii) conversely, those nonlinear dynamics can be reproduced using an harmonic oscillator with instantaneous nonlinear damping. Furthermore, existing cochlear models that include instantaneous gain-control mechanisms capture the principal kinetics of BM nonlinearity. Thus, an AGC system with finite reaction time appears neither necessary nor sufficient to explain nonlinear gain control in the cochlea.

Automatic correction of nonlinear damping effects in HAADF–STEM tomography for nanomaterials of discrete compositions

HAADF-STEM tomography is a common technique for characterizing the three-dimensional morphology of nanomaterials. In conventional tomographic reconstruction algorithms, the image intensity is assumed to be a linear projection of a physical property of the specimen. However, this assumption of linearity is not completely valid due to the nonlinear damping of signal intensities. The nonlinear damping effects increase w.r.t the specimen thickness and lead to so-called “cupping artifacts”, due to a mismatch with the linear model used in the reconstruction algorithm. Moreover, nonlinear damping effects can strongly limit the applicability of advanced reconstruction approaches such as Total Variation Minimization and discrete tomography.In this paper, we propose an algorithm for automatically correcting the nonlinear effects and the subsequent cupping artifacts. It is applicable to samples in which chemical compositions can be segmented based on image gray levels. The correction is realized by iteratively estimating the nonlinear relationship between projection intensity and sample thickness, based on which the projections are linearized. The correction and reconstruction algorithms are tested on simulated and experimental data.

Displacement transmissibility evaluation of vibration isolation system employing nonlinear-damping and nonlinear-stiffness elements

Undesired oscillations commonly encountered in engineering practice can be harmful to structures and machinery. Vibration isolation systems are used to attenuate undesired oscillations. Recently, there has been growing interest in nonlinear approaches towards vibration isolation systems design. This work is focused on investigating the effect of nonlinear cubic viscous damping in a vibration isolation system consisting of a magnetic spring with a positive nonlinear stiffness, and a mechanical oblique spring with geometric nonlinear negative stiffness. Dynamic model of the vibration isolation system is obtained and the harmonic balance method (HBM) is used to solve the governing dynamic equation. Additionally, fourth order Runge–Kutta numerical simulation is used to obtain displacement transmissibility of the system under investigation. Results obtained from numerical simulation are in good agreement with those obtained using HBM. Results show that introducing nonlinear damping improves the performance of the vibration isolation system. Nonlinear damping purposefully introduced into the described vibration isolation system appears to eliminate undesired frequency jump phenomena traditionally encountered in quasi-zero-stiffness vibration isolation systems. Compared to its rival linear vibration isolation system, the described nonlinear system transmits less vibrations around resonant peak. At lower frequencies, both nonlinear and linear isolation systems show comparable transmissibility characteristics.

Complex dynamics of a particle in an oscillating potential field

In this paper, the classical problem of the motion of a particle in one dimension with an external time-dependent field is studied from the point of view of the dynamical system. The dynamical equations of motion of the particle are formulated. Equilibrium points of the non-oscillating systems are found and their local stability natures are analysed. Effect of oscillating potential barrier is analysed through numerical simulations. Phase diagrams, bifurcation diagrams and variations of largest Lyapunov exponents are presented to show the existence of a wide range of nonlinear phenomena such as limit cycle, quasiperiodic and chaotic oscillations in the system. Effects of nonlinear damping in the model are also reported. Analysis of the physically interesting cases where damping is proportional to higher powers of velocity are presented for the sake of generalizing our findings and establishing firm conclusion.

The vibration transmissibility of a single degree of freedom oscillator with nonlinear fractional order damping

ABSTRACTMotivated by the theoretical analysis of the effects of nonlinear viscous damping on vibration isolation using the output frequency response function approach, the output frequency response function approach is employed to investigate the effects of the nonlinear fractional order damping on vibration isolation based on Volterra series in the frequency domain. First, the recursive algorithm which is proposed by Billings et al. is extended to deal with the system with fractional order terms. Then, the analytical relationships are established among the force transmissibility, nonlinear characteristic coefficients and fractional order parameters for the single degree of freedom oscillator. Consequently, the effects of the nonlinear system parameters on the force transmissibility are discussed in detail. The theoretical analysis reveals that the force transmissibility of the oscillator is suppressed due to the existence of the fractional order damping, but presents different effects on suppressing the force transmissibility of the oscillator over the frequency region by varying the fractional order parameters. Moreover, the fractional order parameters, which affect the force transmissibility, the bandwidth of the frequency region and the resonance frequency, can be used as designing parameters for vibration isolation systems. At last, numerical studies are presented to illustrate the theoretical results.

Research progress on energy dissipation mechanisms in micro- and nano-mechanical resonators

Advances in micro- and nanofabrication technologies have enabled the development of micro- and nano-mechanical resonators which have attracted significant attention due to their advantages of ultra-high resonance frequency, quality factor and sensitivity, and growing potential for physical sensing, biological and chemical detection, radio frequency communications and energy harvesting applications. It has become one of the emphases and hotspots in micro- and nano-electromechanical systems (MEMS/NEMS). Energy dissipation is always the key problem and significant bottlenecks, which restricts its performance improvement and application development. Energy dissipation in a mechanical resonator represents the relaxation or loss of energy contained in a resonant mode to the external environment coupled to the resonator structure as well as to the other resonant modes. In micro- and nano-mechanical resonators, a key performance metric is the quality factor ( Q ), which is the ratio of stored mechanical energy to the dissipated energy. Furthermore, energy dissipation has various and complicated mechanisms, which are uncertainty and scaling with system size. It is of great importance to understand the dissipation mechanisms. There exists a host of identifiable mechanisms, both intrinsic and extrinsic, which play an important role in the energy dissipation in micro- and nano-mechanical resonators. This article provides an overview on the progress of energy dissipation mechanisms and nonlinear damping effects in micro- and nano-mechanical resonators. Both intrinsic and extrinsic mechanisms, including thermoelastic damping, phonon interaction, viscous damping, support loss, surface and interface losses, are reviewed and discussed. The energy dissipation caused by viscous damping environments needs to be taken into account in initial design process. Different damping mechanisms are distinguished as the ambient air pressure varies based on the Knudsen number and various models for evaluating air damping mechanisms in different vibration structures from viscous flow regime to molecular flow mechanism have been paid more attention. Furthermore, the quality factor is limited by the thermal physics and specific energy loss mechanisms including thermoelastic, Akhieser, and Landau-Rumer damping in well-optimized designs of mechanical resonators. Support loss occurs because of the strain at the connection to the support structure and must be considered in order to understand the interaction and energy transmission between the resonator-support coupled systems. The support losses become detrimental as the resonator size is reduced but can be suppressed with appropriate device design. As the mechanical resonators become thinner or narrower, the surface- to-volume ratio grows and the surface properties start to play a significant role in the dissipation. Understanding the effect of each mechanism is very important for their application in predicting adequately the quality factor and operation characteristics of micro- and nano-mechanical resonators. In addition, the mergence of nonlinear dissipation mechanisms becomes more and more important in predicting and determining the device performance and discerning the dominant contribution to energy dissipation in resonator devices. Specifically, it reveals the physical mechanisms and the methods of dissipation reduction used in each strategy and provides design guidelines for the development of high-performance resonators. The purpose of this review is to understand, sort, and categorize dominant energy dissipation sources and to determine their significance with respect to physics processes and engineering applications.

Nonlinear passive damping of the X-shaped structure

Nonlinear damping can demonstrate excellent performance in vibration control. It is known that the ideal nonlinear damping could be performed as that the damping effect is as high as possible around resonance frequencies but as low as possible at other frequencies. However, how to realize such a nonlinear damping in real engineering practice with a convenient and passive manner would be an open problem in the literature. To this aim, this study investigates the nonlinear damping effect of an X-shaped structure which is inspired from biological limb skeleton systems. It is shown that, (a) the equivalent damping characteristic of the X-shaped structure is a nonlinear function of the vibration displacement and varies at different frequency; (b) the equivalent damping is adjustable with several structural parameters, and can be very high at around resonance frequencies but very low at other frequencies, showing an ideal passive and nonlinear damping property; (c) the linear horizontally-placed damper and joint friction can both produce the desired equivalent nonlinear damping in the vertical direction. The results of this study demonstrate an innovative and passive solution for designing desired nonlinear damping characteristics in various engineering practices by employing the X-shaped structure.

On Numerical Landau Damping for Splitting Methods Applied to the Vlasov–HMF Model

We consider time discretizations of the Vlasov–HMF (Hamiltonian mean-field) equation based on splitting methods between the linear and nonlinear parts. We consider solutions starting in a small Sobolev neighborhood of a spatially homogeneous state satisfying a linearized stability criterion (Penrose criterion). We prove that the numerical solutions exhibit a scattering behavior to a modified state, which implies a nonlinear Landau damping effect with polynomial rate of damping. Moreover, we prove that the modified state is close to the continuous one and provide error estimates with respect to the time step size.

Nonlinear hysteretic damping effects on the post-critical behaviour of the visco-elastic Beck’s beam

The effects of nonlinear hysteretic damping on the post-critical behaviour of the visco-elastic Beck’s beam are discussed in this paper. The model consists of an inextensible and shear-undeformable cantilever beam, internally and externally damped, loaded at the free end by a follower force. Equations are derived in finite kinematics by taking as the configuration variable the rotation of the cross-section, instead of the usual deflection v of the beam axis, thus making the description of the contact internal actions simpler. The linear stability analysis is carried out and results of the literature are re-obtained. Then, a multiple-scale approach is developed in order to evaluate the nature, super- or subcritical, and the amplitude of the limit-cycle, occurring close to the Hopf critical load. The effects of the nonlinear damping on the amplitude of the limit-cycle are finally discussed for different linear damping coefficients.

ON THE INTERACTIVE-BEATING-MODES MODEL: GENERATION OF ASYMMETRIC MULTIPLET STRUCTURES AND EXPLANATION OF THE BLAZHKO EFFECT

ABSTRACT This paper considers a nonlinear coupling between a radial and a nonradial mode of nearly the same frequency. The results may be of general interest, but in particular have application to the “beating-modes model” of the Blazhko effect which was recently shown to accurately reproduce the light curve of RR Lyr. For weak coupling, the two modes do not phase-lock and they retain separate frequencies, but the coupling nevertheless has important consequences. Upon increasing the coupling strength from zero, an additional side-peak emerges in the spectrum forming an asymmetric triplet centered on the fundamental. As the coupling is further increased, the amplitude of this side-peak increases and the three peaks are also pulled toward each other, decreasing the Blazhko frequency. Beyond a critical coupling strength, phase-locking occurs between the modes. With appropriate choice of coupling strength, this “interactive beating-modes model” can match the side-peak amplitude ratio of any star. The effects of nonlinear damping are also explored and found to generate additional side-peaks of odd order. Consistent with this, the odd side-peaks are found to be favored in V808 Cyg. It is also shown that the Blazhko effect generates a fluctuating “environment” that can have a modulatory effect on other excited modes of the star. An example is found in V808 Cyg where the modulation is at double the Blazhko frequency. An explanation is found for this mysterious doubling, providing additional evidence in favor of the model.

Q factor enhancement of Si resonator by nonlinear damping

The nonlinear damping effect of thin cantilevered Si resonators with thicknesses of 100---1500 nm is investigated from the measurements of the Q factor change versus the vibration amplitude. The Q factor of the 100 nm-thick resonator largely increases as its vibration amplitude become larger due to its large nonlinear damping effect, while the Q factor increment of the thicker resonators (400, 800, 1500 nm of thickness) becomes smaller. The surface condition of the Si resonator also has an interaction to the amplitude dependence on the Q factor. The H2 annealing increases the Q factor change with increasing the amplitude, and the Ar plasma treatment is vice versa. These results show that Si resonators exhibit the nonlinear damping effect, and the large Q factor enhancement by this effect is markedly observed in the thin resonator. The nonlinear damping constant of the 100 nm-thick Si resonator was ź1.12 × 1011 kg/m2s.

Store-Induced Limit-Cycle Oscillations Due to Nonlinear Wing-Store Attachment

Several high-performance fighter aircraft exhibit store-induced limit-cycle oscillations, leading to pilot discomfort, potential structural fatigue, and flight envelope restrictions. The roles of various aerodynamic and structural factors causing the limit-cycle oscillation are not sufficiently understood, and their numerical exploration via time marching is computationally expensive. In this paper, the effects of nonlinear stiffness and damping in the wing-store attachments of the F-16 aircraft are examined, in the presence of steady flow aerodynamic nonlinearity, using the computationally efficient harmonic balance method. Structural mechanisms including cubic restoring force of both softening and hardening types, freeplay, and Coulomb friction are systematically evaluated, and the most likely among these are identified by comparing the computed limit-cycle oscillation results to flight data. An extension of the harmonic balance method to handle nonlinear unsteady aerodynamics along with structural nonlinearity is also proposed to enable rapid and accurate limit-cycle oscillation assessment of candidate store configurations.

Landau Damping in Sobolev Spaces for the Vlasov-HMF Model

We consider the Vlasov-HMF (Hamiltonian Mean-Field) model. We consider solutions starting in a small Sobolev neighborhood of a spatially homogeneous state satisfying a linearized stability criterion (Penrose criterion). We prove that these solutions exhibit a scattering behavior to a modified state, which implies a nonlinear Landau damping effect with polynomial rate of damping.

Bifurcation of Rupture Path-Linear and Nonlinear Damping

Bifurcation of rupture path is studied for the effect of linear and nonlinear cubic damping. Momentum equation with Rayleigh factor was transformed into ordinary differential form. Bernoulli differential equation was obtained and solved by the method separation of variables. Analytical solutions yield the bifurcation of linear and nonlinear cubic damping was visible at imaginary part when the wave was non dispersive. For the dispersive wave, bifurcation of rupture path was invisible due to lower cubic damping. Amplitude attenuated during the seismic moment. Imaginary parts of the solutions illustrate the intersection or collision of soliton, for which, the bifurcation of rupture path is initiated. Intersection is not visible if the energy is well dispersed. Wave profile illustrates the existing of linear exciting and nonlinear damping effect during seismic moment.

On the regularizing effect of nonlinear damping in hyperbolic equations

Global well-posedness in H 2 ( R 3 ) × H 1 ( R 3 ) H^2(\mathbb {R}^3)\times H^1(\mathbb {R}^3) is shown for nonlinear wave equations of the form ◻ u + f ( u ) + g ( u t ) = 0 , \Box u+f(u)+g(u_t)=0, where t ∈ R + . t\in \mathbb {R}_+. The main assumption is that the nonlinear damping g ( u t ) g(u_t) behaves like | u t | m − 1 u t |u_t|^{m-1}u_t with m ≥ 2 m\geq 2 and the defocusing nonlinearity f ( u ) f(u) is like | u | p − 1 u |u|^{p-1}u with p ≥ 2. p\geq 2. The result also applies to certain exponential functions, such as f ( u ) = sinh ⁡ u . f(u)=\sinh u. It is observed that the nonlinear damping gives rise to a new monotone quantity involving the second-order derivatives of u u and leading to a priori estimates for initial data of any size. Global well-posedness in H 1 ( R 3 ) × L 2 ( R 3 ) H^1(\mathbb {R}^3)\times L^2(\mathbb {R}^3) is shown for the same equation in the critical case f ( u ) = u 5 f(u)=u^5 and g ( u t ) = | u t | 2 / 3 u t g(u_t)=|u_t|^{2/3}u_t . The main tool is a new estimate for the solution of the nonlinear equation in L 4 ( R + , L 12 ( R 3 ) ) . L^4(\mathbb {R}_+,L^{12}(\mathbb {R}^{3})).

J2210303 非線形減衰を用いたSi振動子のQ値向上

The Q factor enhancement of Si resonators using nonlinear damping is investigated for highly sensitive resonant sensors. The thermomechanical noise, which limits the physical resolution of resonant sensors, can be improved by increasing the Q factor. In this paper, the nonlinear damping effect of thin Si resonators was investigated and the Q factor enhancement caused by nonlinear damping is measured. The resonator thickness used for the Q factor measurements are 100, 400, 800, 1500 nm. The Q factor of the 100 nm-thick resonator is dramatically increased as its vibration amplitude become larger, while the Q factor change become smaller as the resonator thickness become thicker. These results show that Si resonators have the nonlinear damping effect, and the large Q factor enhancement by this effect is markedly observed in the thin resonator. It is concluded that the Q factors of nanomechanical resonators can be increased by only adjusting its vibration amplitudes.

Analysis of the effects of nonlinear viscous damping on vibration isolator

In this paper, vibration isolator of single degree of freedom systems having a nonlinear viscous damping is studied under force excitation. Stability of the steady state periodic response has been discussed. The influence of damping coefficients on the force transmissibility and displacement transmissibility is investigated. The relationship between amplitude and frequency is derived by using the averaging method. Results reveal that the performance of the nonlinear isolator has some beneficial effects compared with linear isolator in a certain range. Numerical simulations are presented to illustrate the results.