Nonlinear Damping Research Articles

Model predictive control of a wave-to-wire wave energy converter system with non-linear dynamics and non-linear constraints using a tailored pseudo-spectral method

A novel pseudo-spectral method is proposed to tackle the non-linear control problem of a wave energy converter (WEC) integrated with an all-electrical power-take-off (PTO). The WEC hydrodynamic model is constructed using linear wave theory together with a non-linear viscous damping term. The PTO model encompasses a permanent magnet synchronous generator (PMSG) whose local field weakening mechanism imposes non-linear operational constraints on the WEC’s motion and PTO torque. The energy-maximizing control problem of this wave-to-wire model is non-linear and has not been investigated before. In comparison to pseudo-spectral methods previously studied, the proposed pseudo-spectral method is exempt from the assumption of ideal incoming wave prediction. This is made possible by the introduction of a novel mapping function to convert the finite control horizon onto the Gaussian quadrature interval. This mapping function increases more slowly with time at the beginning of the control horizon where wave prediction attains greater precision. As a result, the collocation points are utilized to the advantage of the better approximation of the objective function, thus better overall control performance.

Chaos detection and control of a fractional piecewise-smooth system with nonlinear damping

Chaotic response is a robust effect in natural systems, and it is usually unfavorable for applications owing to uncertainty. In this paper, we propose several control strategies to stabilize the chaotic rhythm of a fractional piecewise-smooth oscillator. First, the Melnikov analysis is applied to the system, and the critical condition for the occurrence of homoclinic chaos is scrupulously established. Then, by applying appropriate control mechanisms, including delayed feedback control and periodic excitations, to the system, we can eliminate the zeros in the original Melnikov function, which serve as sufficient criteria for chaos suppression. Numerical simulations further demonstrate the accuracy of the theoretical results and the validity of the control schemes. Finally, the effects of parameter variations on the efficiency of control strategies are investigated. Note that we use the complex Simpson formula to calculate the complicated Melnikov functions presented in this paper. The current work may open a new innovative path to detect and control the chaotic dynamics of fractional non-smooth models.

Global well-posedness and decay to 3D MHD equations with nonlinear damping

In this paper, we consider the Cauchy problem for the 3D MHD system with nonlinear damping terms κ|u|α−1u and γ|b|β−1b and prove the existence and uniqueness of global strong solution when one of the following two conditions is verified (1)3≤α<4,β≥6α−1+1;(2)α≥4,β≥1. This greatly improves the previous results. Moreover, we also discuss the uniqueness of weak solutions when α and β satisfy certain conditions. Finally, we study the decay of weak solutions when α,β>73 and obtain the upper bound for the derivative of strong solution when 3≤α<4,β≥6α−1+1 or α≥4,β>73.

Nonlinear acoustic damping mechanism in micro and nanobeam resonators due to nonlinear shear stress at clamping

Nonlinear acoustic damping mechanism in micro and nanobeam resonators due to nonlinear shear stress at clamping

Study of aerodynamic damping of a crosswind-excited circular cylinder and its application to full-scale flexible structures

The accurate assessment of aerodynamic damping is essential when estimating the impact of aero-elastic effects on crosswind-excited line-like structures. This study aims to determine the crosswind aerodynamic damping of a circular cylinder by curve-fitting to the response probability density function. The generalized Van der Pol oscillator model is employed to depict the nonlinearity associated with amplitude-dependent aerodynamic damping. The initial section of this study presents the theoretical foundation of the identified approach used in this research. Subsequently, the efficacy of the identification methodology is validated by means of a stochastic simulation of the crosswind response of a circular cylinder. Moreover, identification of nonlinear aerodynamic damping is further accomplished by the utilization of an aero-elastic model wind tunnel test. The identified nonlinear aerodynamic damping is then utilized to determine the response statistical quantities for a total of 16 chimneys. The determined aerodynamic damping provides a satisfactory assessment of the peak response, which is crucial for design considerations.

Girder quasi-static cumulative displacement-based suspension bridge nonlinear damper leakage diagnosis by eliminating stochastic traffic effects

Fluid viscous dampers (FVDs) are the key energy dissipation devices for long-span suspension bridges, and their leakage poses a threat to the stable and reliable operation of bridge restraint systems. Therefore, this paper proposed an FVD fluid leakage diagnosis method based on girder longitudinal displacement monitoring data. First, the longitudinal vibration equation of the main girder under traffic loads was derived to reveal the displacement characteristic of girder-end motion. On this basis, considering that different displacement components under traffic loads are coupled and transient analysis directly utilizing traffic loads as the excitation is complicated and inefficient, an analysis framework focusing on the influence mechanism of FVD leakage on quasi-static displacement was established. Second, an equivalent mechanical model for simulating the hysteresis relationship of leaked FVD was proposed and verified. Then, the influence of variations in the location, number, leakage level and parameters of the leaked FVD on the quasi-static displacement was studied. Third, the equivalent traffic load (ETL) indicator was constructed to characterize the traffic volume. Furthermore, a quasi-static cumulative displacement and ETL correlation model, which can effectively eliminate the interference of traffic flow variations, was proposed for the leakage diagnosis of FVD. Finally, the proposed method was verified by real suspension bridge monitoring data. The results demonstrated that the proposed method can effectively detect a mild increase in the girder-end cumulative displacement due to FVD fluid leakage.

On the role of different nonlinear damping forms in the dynamic behavior of the generalized Beck’s column

The influence of internal and external nonlinear damping forms on the dynamics of a generalized Beck’s column, namely a visco-elastic cantilever beam, subjected to conservative and non-conservative loads at its free end, is investigated. A variational principle provides the equations of motion of the system, which are properly recast into an integro-differential form. The linear stability analysis of the system is then carried out and bifurcation points are detected in the space of parameters associated with the conservative and non-conservative loads. Starting from Hopf’s bifurcation points, a post-critical analysis, based on the Method of Multiple Scales is directly performed on the continuous system, avoiding any a-priori discretization. This method provides the bifurcation equations whose analysis reveals the double nature of nonlinear damping, which can be beneficial or detrimental in terms of stable or unstable bifurcated equilibria. It is found that both the internal and external forms of nonlinear damping can turn a supercritical instability of the system into a subcritical one, thus revealing another destabilizing effect of damping, beyond the very well-known one occurring in the linear field. Numerical simulations, grounded on a Galerkin discretization of the original system, confirm the analytical findings.

A modified perturbation method for global dynamic analysis of generalized mixed Rayleigh–Liénard oscillator with cubic and quintic nonlinearities

Deriving analytical relationship between the system parameters and amplitude of the limit cycle is a meaningful and challenging task. Currently, numerous existing analytical approximate methods struggle to achieve this goal when expressions of restoring force or nonlinear damping is complicated. To overcome this shortcoming, this study proposes a modified generalized harmonic function perturbation method. Using the proposed method, a generalized mixed RayleighLiénard oscillator with cubic and quintic nonlinearities was investigated. The analytical relationships between the system parameters and amplitude of the limit cycle, as well as the expression of its characteristic quantity, were derived. By employing these analytical relationships, the existence, stability, number, position, and amplitude of each limit cycle are quantitatively analysed. The homoclinic and heteroclinic bifurcations were also predicted using the above analytical relationships. Additionally, analytical approximate solutions for this oscillator were calculated using the proposed method. All results obtained in this study were subsequently confirmed numerically to demonstrate their feasibility and validity. Consequently, the proposed method can be considered an effective supplement to perturbation-based methods. This also implies that the work presented in this paper has a certain theoretical significance and application value in the research area of quantitative analysis methods for strongly nonlinear oscillators.

Experimental analysis of structural nonlinear damping ratio induced by bolt joint friction

Friction is an important source of energy dissipation in structural damping. The effect of friction on the damping ratio, however, has not been fully investigated. This paper presents an experimental study of the nonlinear damping ratio induced by friction at bolted joints of a bridge model in the laboratory. The decay responses of the bridge were tested under various bolt configurations and pre-torques. The nonlinear characteristics of the damping ratio were analyzed, and the experimental results were interpreted through numerical simulations. The relationship between damping ratio and amplitude of the Iwan model was derived. The results show that friction induces a nonlinear damping ratio. The damping ratio exhibits two opposite nonlinear characteristics under the influence of bolt joints. The damping ratio may either decrease with decreasing amplitude or may increase, and both of these nonlinear patterns can be elucidated by the Iwan model. Numerical simulations successfully replicate these two nonlinear damping ratios. A case study of an actual steel truss bridge is used to discuss the possible effects of bolt joints on the damping ratio. The results of this paper reveal the nonlinear damping patterns induced by bolt joints and provide an optional model for such structures.

Secondary cosmic-ray nuclei in the Galactic halo model with nonlinear Landau damping

We employed our recent model of the cosmic-ray (CR) halo to compute the Galactic spectra of stable and unstable secondary nuclei. In this model, confinement of the Galactic CRs is entirely determined by the self-generated Alfvénic turbulence whose spectrum is controlled by nonlinear Landau damping. We analyzed the physical parameters affecting propagation characteristics of CRs and estimated the best set of free parameters providing accurate description of available observational data. We also show that agreement with observations at lower energies may be further improved by taking into account the effect of ion-neutral damping that operates near the Galactic disk.

Nonlinear vibration of five-layered functionally graded piezoelectric semiconductor nano-plate on Pasternak foundation

The vibration character of piezoelectric semiconductor nano-plate is important for understanding the multi-fields coupling and optimizing the serving behavior. In this article, the nonlinear vibration of five-layered functionally graded piezoelectric semiconductor nano-plate based on Pasternak foundation is studied, and the nonlocal theory is used to analyze the size-dependent dynamic response of nano-plate. Combining the Von karman’s nonlinear deformation theory and the constitutive of piezoelectric semiconductor layers, Hamilton’s principle is introduced to derive the nonlinear governing equations. To solve the nonlinear governing equations, the updated iteration method for this problem is proposed. Through numerical examples, it is found that the initial electron concentration in piezoelectric semiconductor layer, the nonlocal parameter, the functionally graded index in the plate, the elastic modulus of Pasternak foundation and the geometrical parameters can be designed to effectively tune the dynamic nonlinear frequency and damping of layered functionally graded piezoelectric semiconductor nanoplate. The interaction of these parameters is also analyzed in detail. Comparison with existing numerical results is also presented. A new way is provided to tune the nonlinear vibration of multi-layered piezoelectric semiconductor nano-plate.

Nonlinear passive magnetorheological damping characteristics of the scissor-like isolation platform

Nonlinear passive magnetorheological damping characteristics of the scissor-like isolation platform

Stochastic Roll Dynamics of Smooth and Impacting Vessels in Random Waves

Ship instability is frequently associated with extreme roll motion. In this paper smooth and vibro-impact dynamics of vessels rolling under random wave excitations including nonlinearities is investigated. The vessel is represented by a single degree of freedom roll model. The random excitation due to waves and ice is modeled by a sum of random pulses with Poisson arrival rate. Stochastic P-bifurcation analysis is carried out by examining the variation with parameter of the joint probability density functions (jpdf) of the response computed numerically by the solution of the corresponding Fokker–Planck–Kolmogorov (FPK) equation. The finite element (FE), finite difference (FD), path integral (PI) and radial basis neural (RBN) network formulation methods are used in the solution of the FPK equation. The D-bifurcation analysis is analyzed by computing the largest Lyapunov exponent. The mean upcrossing rate is computed using Rice’s formula. The random wave excitation is also modeled as the response of a second order linear filter to white noise and the random response of the ship is investigated by solution of the corresponding FPK equation of the four dimensional Markov system by the FD method. Non-smooth coordinate transformations like the Zhuravlev and Ivanov transformations are used converting the discontinuous systems to equivalent smooth systems in the impact dynamics analysis. The adaptive time stepping method (ATSM) approach is used to accurately locate the discontinuity point and a Brownian tree approach is used to direct the integration along the correct Brownian path. Different models for nonlinear damping and the restoring moment are considered and their effects on ship stochastic response such as chaotic motion, unbounded rotational motion, impact modulation motion and ship capsizing are investigated.

Uniform Stability for a Semilinear Laminated Timoshenko Beams Posed in Inhomogeneous Medium with Localized Nonlinear Damping

Uniform Stability for a Semilinear Laminated Timoshenko Beams Posed in Inhomogeneous Medium with Localized Nonlinear Damping

Research on vibration suppression of nonlinear energy sink with linear damping and geometrically nonlinear damping

Research on vibration suppression of nonlinear energy sink with linear damping and geometrically nonlinear damping

Improving Output Power of a Torsional-Flutter Harvester in Stochastic Thunderstorms by Duffing - Van Der Pol Restoring Torque

Abstract Wind energy harvesters are usually designed to operate in the low wind speed range. They rely on smaller swept areas, as a complement to larger horizontal-axis wind turbines. A torsional-flutter-based apparatus is investigated herein to extract wind energy. A nonlinear hybrid restoring toque mechanism, installed at equally spaced supports, is used to produce energy through limit-cycle vibration. Energy conversion and storage from the wind flow are enabled by eddy currents. The apparatus is used during thunderstorm outflows to explore the efficiency in non-ideal wind conditions. The thunderstorm flow model accounts for both non-stationary turbulence and slowly varying mean speed, replicating thunderstorm's intensification and decay stages. This paper evolves from a recent study to examine stochastic stability. More Specifically, the output power is a random process that is derived numerically. Various thunderstorm features and variable apparatus configurations are evaluated. Numerical investigations confirm the detrimental effect of non-ideal, thunderstorms on harvester performance with, on average, an adverse increment of operational speed (about +30\%). Besides nonlinear damping, the benign flutter-prone effect is controlled by the square of the flapping angle. Since flapping amplitudes are moderate at sustained flutter, activation of the apparatus is delayed and exacerbated by the non-stationary outflow and aeroelastic load features. Finally, efficiency is carefully investigated by quantification of output power and “quality factor”.

Adaptive nonlinear damping control of active secondary suspension for hunting stability of high-speed trains

This study employs an active secondary suspension with adaptive nonlinear damping to enhance the hunting stability of high-speed trains. Adjusting passive suspension parameters to optimize ride comfort and hunting stability simultaneously in varied extreme operational conditions poses a significant challenge for high-speed trains. This research integrates high-order displacement-dependent nonlinear damping into the secondary lateral suspension, drawing on insights from field test data. We analyze three typical hunting motion bifurcations: carbody hunting and both subcritical and supercritical bifurcations of bogie hunting. Theoretical analysis demonstrates that (a) the adaptive nonlinear damping narrows the unstable speed range and reduces the amplitude of the limit cycle in carbody hunting, (b) while it does not increase the critical speed for supercritical bogie hunting bifurcation, it substantially reduces the amplitude of the limit cycle, and (c) it increases the nonlinear critical speed for subcritical bogie hunting bifurcation, with the potential to alter the bifurcation from subcritical to supercritical, which holds considerable practical significance. Implementing such nonlinear damping directly through passive structure is challenging. Therefore, in view of this underactuated control problem, the constraint-following control is applied in the active suspension system to inherit the benefits of adaptive nonlinear damping. The simulation results show that the proposed active suspension system can effectively suppress the abnormal vibration caused by hunting motions.

New decay results for Timoshenko system in the light of the second spectrum of frequency with infinite memory and nonlinear damping of variable exponent type

In this study, we consider a one-dimensional Timoshenko system with two damping terms in the context of the second frequency spectrum. One damping is viscoelastic with infinite memory, while the other is a non-linear frictional damping of variable exponent type. These damping terms are simultaneously and complementary acting on the shear force in the domain. We establish, for the first time to the best of our knowledge, explicit and general energy decay rates for this system with infinite memory. We use Sobolev embedding and the multiplier approach to get our decay results. These results generalize and improve some earlier related results in the literature.

Optimal temporal decay rates for 3D compressible magnetohydrodynamics system with nonlinear damping

Recently, Li–Fu–Wang (Li et al., 2022) established the optimal temporal decay rates of solutions near the equilibrium state to the 3D compressible magnetohydrodynamic system with nonlinear damping αuβ−1u for β⩾3. In this paper, we further extend Li–Fu–Wang’s result to the case β>1 by finer energy estimates.

Amplitude deflection in a nonlinear MEMS resonator under parametric excitation

In this paper, the dynamic characteristics of a parametrically excited MEMS micro-resonator incorporating high-order nonlinearity and nonlinear damping are investigated experimentally and theoretically. An intriguing phenomenon of amplitude deflection is observed when the parametric excitation strength exceeds a certain value. We establish a dynamic model of the micro-resonator under parametric excitation and employ the averaging method to obtain an approximate analytical solution. Then the theoretical study is made to explain the amplitude deflection under large excitation, attributing it to the combined effects of high-order nonlinearity and nonlinear damping. These findings contribute to a more comprehensive understanding of the characteristics of parametrically excited systems.