Effect Of Nonlinear Damping Research Articles

Nonlinear damping effects for the 2D Mindlin–Timoshenko system

AbstractIn this article, we investigate the asymptotic behavior of the Mindlin–Timoshenko system under the influence of nonlinear dissipation affecting the rotation angle equations. Initially, we provide a concise review of the system’s solution existence. Subsequently, we demonstrate that the energy associated with the solution of the Mindlin–Timoshenko setup follows a dissipation. Furthermore, under the condition of equal wave speeds, we establish a comprehensive decay theorem for the energy, offering explicit insights into its general behavior.

Depinning of domain walls in a notched ferromagnetic nanostrip: role of inertial and nonlinear damping effects

Abstract In this work, we investigate theoretically the static and kinetic depinning field of a domain wall in a notched magnetic nanostrip under the generalized framework of the Landau–Lifshitz-Gilbert equation, which combines inertial and nonlinear viscous-dry friction damping effects. We assume a head-to-head transverse domain wall configuration and analyzed its motion subject to a time-varying external magnetic field. To deduce the equation ruling the spatio-temporal evoution of the magnetic domain wall, we adopt the Schryer and Walker trial function approach. The results show that static and kinetic depinning fields increase as the dry friction dissipation increases. Moreover, viscous dissipation exhibits a weak dependence on the kinetic depinning field and saturated domain wall velocity, while inertial damping due to the relaxation time of angular momentum significantly impacts the kinetic depinning field, depinning time, and breakdown velocity. Our numerical results are in good qualitative agreement with the recent observations reported in the literature.

Dynamic responses of ROV system experiencing vessel heave during deployment and recovery processes

Remotely operated vehicle (ROV) system is significantly affected by the excitations coming from the top-end vessel motion and the environmental hydrodynamic forces. Especially, during initial deployment and final recovery stages, the relative motion between suspending ROV and moving top-end vessel gets more complicated and even larger. This may cause a body collision, and consequently the cable tension can also be severely changed by larger ROV motion. Sometimes, cable slack may occur, which seriously affects structural safety.To study the dynamic responses of ROV system induced by vessel heave during initial deployment and final recovery processes, the FEM numerical simulations, combining with the hydrodynamic model are conducted. Then the ROV displacement and cable tension time histories are presented. The influences of vessel motion amplitude and frequency, along with initial condition, on the dynamic responses of ROV system are also discussed. Moreover, to explore the dynamic behaviors of the ROV system further, we discuss the physical mechanisms driving response amplification through theoretical models. The governing equation of ROV system dynamics with a vertical moving boundary is established, and a dimensionless control parameter called amplitude-frequency factor, which characterizes the dynamic excitation effect of vessel heave, is proposed. Then, in order to study the influences of nonlinear hydrodynamic damping effect on ROV response, an empirical formula for hydrodynamic damping ratio is proposed based on ROV displacement time histories. Finally, under consideration of the nonlinear damping effect, the unstable regions of vessel motion amplitude and frequency at different initial conditions are obtained.The results show that the vessel heave may induce a parametric excitation response to the ROV system. Particularly, parametric resonance is most pronounced, when the vessel motion frequency is close to twice the natural frequency of the ROV system. While, under the nonlinear damping effect generated by hydrodynamic force, the parametric resonance occurs when the amplitude-frequency factor reaches its threshold. The unstable regions under hydrodynamic damping are smaller compared with that without damping. Furthermore, as the initial angular displacement of ROV increases, the unstable region becomes smaller further, or, in other words, the parametric conditions of vessel heave for ROV response amplification become more demanding.

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.

Fault-tolerant control of the main drive system of rolling mill based on fault reconfiguration

A mathematical model of the main drive system of rolling mill is developed for the motor armature faults in the main drive system of rolling mill, taking into account the effects of nonlinear damping, friction damping between rolls and external perturbations on the system during operation. The unknown input observer is designed to process perturbations and errors as unknown inputs, and the [Formula: see text] performance index is designed to improve the robustness of the unknown input observer to fault reconfiguration. At the same time, in order to ensure the stability of the main drive system of rolling mill after the occurrence of faults, an active fault-tolerant controller is designed for the main drive system of rolling mill after obtaining the accurate fault reconfiguration value, which realizes the active fault-tolerant control of the main drive system of rolling mill. Through the simulation study on the main drive system of 2030 mm cold rolling mill stand F4, it is shown that the system is restored to the normal state after adding the fault-tolerant controller, and the motor angular speed error and roll angular speed error are 2.12% and 2.43%, respectively. Comparing with the fault-tolerant control method based on fault estimation, the root-mean-square errors of the motor angular speed and roll angular speed estimates of the designed fault-tolerant control method are reduced by 4.24% and 3.28%, respectively. Simulation verifies the effectiveness of the proposed method.

On the nonlinear moonpool responses in a drillship under regular heading waves

In this study, the nonlinear and viscous damping effects on the free-surface elevations of the recess-type moonpool inside a drillship are investigated. Based on a three-dimensional nonlinear potential flow (NPF3D) model, the nonlinear moonpool responses excited by regular heading waves are simulated in the time domain. To consider the vortex-shedding damping effects, induced by nonlinear moonpool responses, the pressure drop model of Chu et al. [Chu et al., “Effects of nonlinearity and viscous damping on the resonant responses in two-dimensional moonpools with a recess,” Appl. Ocean Res. 127, 103295 (2022)] is extended to three-dimensional and combined with NPF3D to form a viscous modified nonlinear potential flow model (referred to as NPF3D_V). The pressure drop model is composed of two parts in order to account for the energy loss from the first harmonic (piston-mode motions) and higher harmonics (sloshing-mode motions), respectively. The investigation focuses on the piston-mode resonance and secondary resonances of the first and second longitudinal sloshing modes. The response amplitude operators of the higher harmonics, by which the nonlinear effects are evaluated, are computed by the NPF3D_V model. It is found that the higher harmonics are noticeable at the excitation frequencies ωn0/m, where secondary resonances of the nth longitudinal sloshing mode are triggered. In addition, it is found that increasing the length of the recess can promote the nonlinear response of the moonpool significantly. For the moonpool with a long recess, the higher harmonics at secondary resonance are comparable to the first harmonics.

Conditions of Existence and Uniqueness of Limit Cycle for Grid-Connected VSC With PLL

This paper investigates the large disturbance stability of single voltage source converter (VSC) connected to the infinite bus system through the transmission line. One conservative stable region is obtained via the direct method of Lyapunov. Based on the Poincaré Theorem, it is interesting to find there might exist limit cycle between the obtained stable boundary and the angle of unstable equilibrium point (UEP). Accordingly, the nonlinear damping effect on the system stability is defined, and one limit cycle exists when the positive and negative damping effect over one period is mutually balanced. A conservative existence condition of limit cycle is further derived by constructing a proper piece-wise curve to approximate one specified unstable system trajectory. The derived analytical existence condition can directly predict the limit cycle without numerical simulations. Finally, the paper also proves that the studied dynamic system has at most one limit cycle, and if it exists, it is unstable.

Investigative Study of the Effect of Damping and Stiffness Nonlinearities on an Electromagnetic Energy Harvester at Low-Frequency Excitations

Ambient vibration energy is widely being harnessed as a source of electrical energy to drive low-power devices. The vibration energy harvester (VEH) of interest employs an electromagnetic transduction mechanism, whereby ambient mechanical vibration is converted to electrical energy. The limitations affecting the performance of VEHs, with an electromagnetic transduction structure, include its operational bandwidth as well as the enclosure-size constraint. In this study, an analysis and design of a nonlinear VEH system is conducted using the Output Frequency Response Function (OFRF) representations of the actual system model. However, the OFRF representations are determined from the Generalised Associated Linear Equation (GALE) decompositions of the system of interest. The effect of both nonlinear damping and stiffness characteristics, to, respectively, extend the average power and operational bandwidth of the VEH device, is demonstrated.

A nonlinear damped metamaterial: Wideband attenuation with nonlinear bandgap and modal dissipation

In this paper, we incorporate the effect of nonlinear damping with the concept of locally resonant metamaterials to enable vibration attenuation beyond the conventional bandgap range. The proposed design combines a linear host cantilever beam and periodically distributed inertia amplifiers as nonlinear local resonators. The geometric nonlinearity induced by the inertia amplifiers causes an amplitude-dependent nonlinear damping effect. Through the implementation of both modal superposition and numerical harmonic methods with Alternating Frequency Time and numerical continuation techniques, the finite nonlinear metamaterial is accurately modeled. The resulting nonlinear frequency response reveals the bandgap is both amplitude-dependent and broadened. Furthermore, the nonlinear interaction between the local resonators and the mode shapes of the host beam is discussed, which leads to efficient modal frequency dissipation ability. The theoretical results are validated experimentally. By embedding the nonlinear damping effect into locally resonant metamaterials, wideband and shock wave attenuation of the proposed metamaterial is achieved, which opens new possibilities for versatile metamaterials beyond the conventional bandgap ranges of their linear counterparts.

Nonlinear nonlocal damping effects under magnetic loads of a ferromagnetic-viscoelastic nanotube exposed to a nonlinear elastic medium with nonlocal viscosity

This study presents innovative results on a nonlinear dynamic model of a ferromagnetic-viscoelastic nanotube (FVN) whose dissipation effects are captured by material behavior with a linear dissipation law operating in a nonlinear geometric regime. It investigates a possible system derived from a Kelvin–Voigt type dissipation model that describes internal viscoelastic damping in the form of a parallel spring and a dashpot. In addition, a class of losses by linear viscous media in local and nonlocal damping is presented in the modeling. Magnetic load effects are studied using axial rod theory regardless of rotational inertia and shear effects. The governing equation is derived by Hamilton's principle for the FVN subjected to a transverse magnetic field resting on a nonlinear elastic foundation with viscose effects. Formulas have been developed to obtain the nonlinear damping characteristics of a single-walled nanotube. Then, multiple scale method (MSM)-based solutions and Eringen elasticity theory are applied to demonstrate the aforementioned effects on a narrow clamped-clamped (CC) nanotube in detail. The approximate analytical solution is verified by numerical integration methods and a good agreement between the approximate analytical and numerical results is observed. The effect of all important parameters such as local and nonlocal viscosity damping, nonlinear damping coefficient, linear and nonlinear stiffness of the elastic medium due to changes in amplitude vibration of the magnetic field (AVMF) and displacement responses (DR) have been investigated. The original research proposed in this paper may enable the systematic study of nonlinear damping in nanomechanical oscillators, which may help to reveal the underlying physical mechanism.

A general decay criterion for a viscoelastic equation with nonlinear distributed delay and damping effects

In this paper, a viscoelastic equation with nonlinear distributed delay and nonlinear damping effects is considered. Under very general conditions that do not involve differential inequalities for the kernel function, a general decay criterion is established through the perturbed energy method and properties of convex functions. We extend the stability result of wave equation with linear delay and linear damping to the nonlinear case.

On nonlinear damping effects with nonlinear temperature-dependent properties for an axial thermo-viscoelastic rod

The present manuscript develops a new axisymmetric model of thermo-viscoelastic rods to account for uniform temperature effects and nonlinear terms, which are induced by Kelvin–Voigt damping. A fundamental relationship between the damping of viscoelastic material and nonlinear geometry are researched through the application of Galerkin and multiple scale (MS) methods to the new model. Then, the MSM-based solutions are confirmed with a numerical integration method, and a good agreement between the approximate analytical and numerical results is observed. Free axial vibrations based on the standard linear solid model in uniform thermal rises with nonlinear material properties as a function of temperature is considered. The temperature of the viscoelastic rod remains constant under conditions of uniform temperature rise. Studying the behavior of the dynamic system in the presence of uniform temperatures increases the effect of nonlinear damping on its vibration behavior. Approximate analytical results are presented for use as a reference point in future analysis of nonlinear thermo-viscoelastic rods with a weak hardening system. Also, the results of this research can be useful and practical for finding the modal damping ratio of the system as well as the dynamic analysis of damping in the presence of thermal environment.

Vibration control in fluid conveying pipes using NES with nonlinear damping

Control of vibrations in fluid transmitting pipes has emerged as a major engineering challenge. For higher fluid flow rate, support vibration, and excitation load, the vibrations in pipes that convey fluid can be complex and, at times, catastrophic. Recent works have demonstrated that Nonlinear Energy Sink (NES) can be effectively employed for passive vibration control of fluid-conveying pipes. The present work explores the possibility of using NES with nonlinear damping to overcome the limitations of conventional NES-based vibration control in fluid-transmitting pipes. Geometric nonlinear damping (velocity-displacement dependent damping), whose physical realization is possible by a suitable geometric configuration of the linear viscous damper, is considered in this study. Euler–Bernoulli beam theory models the fluid conveying pipe under an external harmonic load. The reduced order model obtained through the Galerkin procedure is investigated analytically using the complex averaging method. The occurrence of strongly modulated and weakly modulated responses are demonstrated, and their effect on vibration mitigation is shown. The frequency range exhibiting strongly modulated response in the system is significantly increased with the addition of nonlinear damping to NES. This assists in mitigating pipe vibrations by initiating targeted energy transfer from pipe to NES. The Saddle–Node and Hopf bifurcation boundaries in the model are identified using the slow-flow dynamics obtained by complex averaging. The effect of nonlinear damping, external excitation, the location of NES, and the flow rate on the bifurcation boundaries are investigated in detail. It is shown that the external excitation needed to trigger Saddle–Node bifurcation is largely reduced for NES having nonlinear damping. Furthermore, a study of Hopf bifurcation in the frequency domain shows that using NES with nonlinear damping significantly decreases the frequency range in which high-amplitude isolated solutions occur. The method of multiple scales is used to derive the analytical expression for the slow invariant manifold of the pipe-NES system. The vibration suppression mechanism and the occurrence of strongly modulated responses are explained with the help of flow on slow invariant manifolds. A comparison of the topology of the slow invariant manifolds shows that using nonlinear damping with NES substantially reduces the vibration amplitude of the pipe structure. The percentage of energy transferred to the NES is quantified to show the effectiveness of the proposed absorber over normal NES for different flow speeds.

Estimation of wind-induced response of large membrane structures with nonlinear motion-induced aerodynamic force and nonlinear geometric stiffness

Wind-induced dynamic response for large membrane structures with consideration of the coupling influences of nonlinear motion-induced aerodynamic force and nonlinear geometric stiffness is analytically evaluated in this study. By utilizing the equivalent nonlinear system approach, the Fokker-Planck-Kolmogorov equation of the membrane structures is derived, and the analytical response solutions, including probability density function, root-mean-square value, kurtosis, peak response, and peak factor, are presented. The accuracy of the proposed analytical solutions is checked by the numerical results obtained with the fourth-order Runge-Kutta approach. The findings reveal that vortex-induced vibrations occur at high wind speed regions due to the effect of nonlinear negative aerodynamic damping. Additionally, the geometric stiffness nonlinearity caused by large deformation is found to be significant for reducing the dynamic response amplitude in membrane structures. This study proposed herein presents an effective analytical approach for predicting the aero-elastic response of such flexible structures subjected to wind loads.

Nonlinear damping effects in vertically vibrating systems with violently sloshing liquid

Damping induced by vertically sloshing liquids at large amplitudes is of interest in the understanding of the dynamic response of aircraft wings containing fuel. This work presents the experimental investigation of sloshing-induced damping in two small rectangular tanks (L=100mm, h=37.5mm and 50mm) under vertical excitation at various frequencies (3.3 to 10.3Hz) and amplitudes (up to 1.57 tank heights). The focus is placed on large amplitudes that lead to violent vertical interactions between the liquid and the tank and the nonlinear damping effects they cause. The sloshing-induced dissipative energy in dimensional form shows a deviation from linearity with increasing amplitude of excitation, which is attributed to force–displacement hysteresis sub-cycle formations. When increasing the frequency of excitation, it is shown that the damping increases initially, and then remains constant. These findings are confirmed by a kinematics-based ballistic–harmonic model. Optical flow and a new technique based on pixel intensity standard deviation are employed in correlation with an analysis of the hysteresis cycles in order to offer insight into the sloshing force variation within one liquid cycle of oscillation.

Nonlinear Damping Property and Limit Cycle of VSC

The synchronization stability of the system that one single VSC is connected to an infinite source via the line is studied in this letter. Based on Bendixson criterion, closed orbit (limit cycle) does not exist in the derived stable region, while may exist in the region between the conservative stable boundary and the unstable equilibrium point (UEP). Nonlinear damping effect on the system stability is analytically defined, and an unstable limit cycle appears when the positive and negative damping effect of the system over one period is mutually balanced. Numerical results verify the existence of limit cycle and nonlinear damping property of VSC.

Effects of nonlinearity and viscous damping on the resonant responses in two-dimensional moonpools with a recess

In this study, the nonlinear and viscous damping effects on the resonant responses inside a two-dimensional moonpool with a recess are investigated. Based on a fully nonlinear potential flow (FNPF) model, the nonlinear moonpool responses excited by the forced heave motion of a structure are simulated in the time domain. To consider the vortex-shedding damping effects in the moonpool, induced by both piston-type motion (the first harmonic component) and sloshing-type motions (the higher harmonic components), a pressure drop model based on Faltinsen and Timokha (2015) is developed and applied to the FNPF model (FNPF-V for short). The response amplitude operators (RAOs) of the higher harmonics, by which the nonlinear effects are evaluated, are computed by the FNPF-V model. It is found that the higher harmonics are noticeable for the excitation frequencies ω n / ( n + 1 ) ( n is a positive integer, ω n denotes the natural frequency of the n th sloshing mode), where secondary resonances can be triggered. In addition, it is found that the strong nonlinear interactions between the first and higher harmonics can lead to a significant amplification of the moonpool responses. The nonlinear behaviour (the secondary resonance, as well as the sum- and difference-frequency effects) is substantially enhanced as the excitation amplitude increases. Moreover, it is found that the length of the recess influences the nonlinear response of the moonpool in two respects with opposite effects. On the one hand, for the same first harmonic response, moonpools with a longer recess are more apt to exhibit nonlinearity. On the other hand, for the same external excitation, as the length of the recess increases, the first harmonic responses at the excitation frequencies ω n / ( n + 1 ) decrease, suppressing the nonlinear behaviour. • This paper studies the secondary resonances triggered by the piston-mode response. • A pressure drop model is introduced to consider the vortex-shedding effects. • The nonlinear interactions between different harmonic components are investigated. • The effects of recess length on the nonlinear response are analysed and interpreted.

Dynamic modeling of a non-ideal gyroscopic rotor system with nonlinear damping and nonlinear rigidity of an elastic support

The article considers the effect of joint linear and nonlinear cubic damping on dynamics of a gyroscopic rigid rotor interacting with an electric motor with a rectilinear characteristic, taking into account the nonlinear rigidity of the support material. The method of regulating the control parameter (voltage on the motor), the amplitude of vibration, and the angular velocity of the shaft in the frequency equation, depending on the value of the coefficient of nonlinear cubic damping of the support, offers the most effective options for controlling resonant oscillations of large amplitudes. It is shown that the greater the value of the coefficient of nonlinear cubic damping, the easier it is to control these oscillations. Moreover, it is proved that the Sommerfeld effect (of the first kind) can also be weakened and eliminate with the help of joint linear and nonlinear damping. To do this, in the case of a rigid characteristic of the nonlinear elasticity of the support material, in a rotor system with a nonideal energy source to eliminate the bistability region, that is, jumping effects, more nonlinear damping of support or energy from a nonideal energy source will be required than in the case of an ideal rotor system.

Nonlinear damped spatially periodic breathers and the emergence of soliton-like rogue waves

The spatially periodic breather solutions (SPBs) of the nonlinear Schrödinger equation, prominent in modeling rogue waves, are unstable. In this paper we numerically investigate the routes to stability of the SPBs and related rogue wave activity in the framework of the nonlinear damped higher order nonlinear Schrödinger (NLD-HONLS) equation. The NLD-HONLS solutions are initialized with single-mode and two-mode SPB data at different stages of their development. The Floquet spectral theory of the NLS equation is applied to interpret and provide a characterization of the perturbed dynamics in terms of nearby solutions of the NLS equation. A broad categorization of the routes to stability of the SPBs is determined. Novel behavior related to the effects of nonlinear damping is obtained: tiny bands of complex spectrum develop in the Floquet decomposition of the NLD-HONLS data, indicating the breakup of the SPB into either a one or two “soliton-like” structure. For solutions initialized in the early to middle stage of the development of the modulational instability, we find that all the rogue waves in the NLD-HONLS flow occur when the spectrum is in a one or two soliton-like configuration. When the solutions are initialized as the modulational instability is saturating, rogue waves also occur when the spectrum is not in a soliton-like state. Another distinctive feature of the nonlinear damped dynamics is that the growth of instabilities can be delayed and expressed at higher order due to permanent frequency downshifting.

Wind-Induced Instability Mechanism of Old Tacoma Narrows Bridge from Aerodynamic Work Perspective

Postflutter limit cycle oscillations (LCOs) are typical nonlinear aeroelastic phenomena for bridge girders. An H-shaped section with a roughly 5:1 aspect ratio, treated as a simplified section of the Old Tacoma Narrows Bridge, was chosen for wind-induced instability re-evaluation, considering its vibration amplitude-dependent aerodynamics characteristics and nonlinear structural damping effects from the energy perspective of aerodynamic work. Forced vibrations at large torsional amplitudes in a wind tunnel were realized with the help of an improved forced motion apparatus (FMA), and synchronous measurements of forces and displacements on the FMA were achieved. Self-excited forces (SEFs) were extracted, and an energy map showing quantitative relationships between vibration amplitude, reduced velocity, and aerodynamic work acting on the section were established. Furthermore, the postflutter LCOs phenomena originating from the energy balance between nonlinear aerodynamic work input and energy consumption by structural damping effects were reillustrated, and nonlinear structural damping effects of prototype bridges are therefore discussed. Moreover, the instability paths of the bridge were investigated by the energy map, considering its vibration amplitude-dependent aerodynamics and structural damping effects from an aerodynamic work perspective. The results show that LCO velocity basically increases with vibration amplitude at different structural damping ratios in torsional degree of freedom, characterizing postflutter LCOs phenomena. The structural damping ratio at the bridge’s collapse is also re-estimated as about 0.0115 with better coincidence of on-the-spot observation and theoretical analysis. In addition, both the aerodynamic damping ratio considering nonlinear characteristics of the SEFs and the structural damping ratio basically increasing with vibration amplitude contribute to postflutter LCOs phenomena of the Tacoma Bridge. The instability paths of the bridge essentially rely on the competitive relationships between structural damping ratios, structural stiffness degeneration, and oncoming wind velocities in the process of collapse.