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Suspension bridges are essential in lifeline civil structures that have been constructed in many countries due to their superior effectiveness when it comes to long spans. In this paper, we study a mathematical model for a one-dimensional suspension bridge problem with viscoelastic damping and nonlinear frictional damping. The model takes into consideration the vibration of the bridge deck in the vertical plane and main cable from which the bridge deck is suspended by the suspenders. Using the multiplier method, we establish an explicit formula for the energy decay rate and show that this rate depends on the rates of both the relaxation function and the nonlinear frictional damping. Our result improves and generalizes many existing results in the literature. [ABSTRACT FROM AUTHOR]

We investigate the dynamics of a nonlinear Lamé lattice system with nonlinear damping. Under certain conditions on the nonlinear terms, we prove the global well-posedness of the initial value problem in a suitable space and the existence of a global attractor for the associated semigroup. Moreover, we study the upper semicontinuity of attractors when the sum of the Lamé constants in the discrete elasticity operator tends to zero. [ABSTRACT FROM AUTHOR]

Purpose: Indian Railway uses the American Association of Railroads (AAR) standard automatic coupler system in mainline passenger trains. This coupler system includes an AAR H-type coupler for interconnection with other vehicles and a polymer draft gear to dissipate the vibrations and impacts. Although the H-type coupler has minimal slack among other AAR standard couplers, longitudinal jerks and other coupling-related issues are observed in these trains. Therefore, an accurate model of the coupling system is crucial for the precise estimation of in-train longitudinal forces using longitudinal train dynamic simulations. In the numerical models of trains, the complete coupler system is modeled by the dynamic characteristics of draft gear with the coupler slack combined in it. However, the present mathematical models describing the dynamic hysteresis of polymer draft gears are not very accurate due to the oversimplified modeling and availability of limited experimental data. Therefore, in this study, the shortcomings of oversimplification in the modeling of draft gears and the issues related to the availability of limited experimental data are addressed. Method: A new dynamic model for polymer draft gears is proposed, incorporating the mentioned inadequacies in the purpose statement. The proposed model uses a combined function of exponential and polynomial expressions, fitted on experimental characteristics. The relevant parameter has been identified, and a suitable range of its values has been proposed to control the rates of loading and unloading responses independently. The proposed draft gear model is then implemented in a shunting simulation model of rail vehicles to estimate the safe shunting velocity to avoid structural damage to vehicles. Results: The proposed model requires a smaller number of tuning parameters and gives a consistent trend even with an insufficient amount of measured data points while closely resembling the realistic behavior of polymer draft gears. It delivers lower unloading and higher loading rates, which are the actual characteristics of a polymer draft gear. Conclusions: The proposed model offers an accurate representation of a polymer draft gear. It enables precise assessment of the in-train longitudinal forces. Additionally, the model allows for a more accurate estimation of jerks, which are highly sensitive to these forces' magnitude and rate of change. [ABSTRACT FROM AUTHOR]

Solitons of the purely cubic nonlinear Schrödinger equation in a space dimension of n ≥ 2 suffer critical and supercritical collapses. These solitons can be stabilized in a cubic-quintic nonlinear medium. In this paper, we analyze the Crank-Nicolson finite difference scheme for the (2+1)D cubic-quintic nonlinear Schrödinger equation with cubic damping. We show that both the discrete solution, in the discrete L 2 -norm, and discrete energy are bounded. By using appropriate settings and estimations, the existence and the uniqueness of the numerical solution are proved. In addition, the error estimations are established in terms of second order for both space and time in discrete L 2 -norm and H 1 -norm. Numerical simulations for the (2+1)D cubic-quintic nonlinear Schrödinger equation with cubic damping are conducted to validate the convergence. • The (2+1)D cubic-quintic NLS equation can against 2D-soliton collapses. • A Crank-Nicolson finite difference scheme for the damped (2+1)D cubic-quintic NLS equation is proposed. • The existence and uniqueness of solutions are demonstrated using the boundedness of discrete energy and mass. • The scheme converges second order in time and space. • The numerical experiments are demonstrated to verify the theoretical results. [ABSTRACT FROM AUTHOR]

The ultimate isolation offered by levitation provides new opportunities for studying fundamental science and realizing ultra-sensitive floating sensors. Among different levitation schemes, diamagnetic levitation is attractive because it allows stable levitation at room temperature without a continuous power supply. While the dynamics of diamagnetically levitating objects in the linear regime are well studied, their nonlinear dynamics have received little attention. Here, we experimentally and theoretically study the nonlinear dynamic response of graphite resonators that levitate in permanent magnetic traps. By large amplitude actuation, we drive the resonators into nonlinear regime and measure their motion using laser Doppler interferometry. Unlike other magnetic levitation systems, here we observe a resonance frequency reduction with amplitude in a diamagnetic levitation system that we attribute to the softening effect of the magnetic force. We then analyze the asymmetric magnetic potential and construct a model that captures the experimental nonlinear dynamic behavior over a wide range of excitation forces. We also investigate the linearity of the damping forces on the levitating resonator, and show that although eddy current damping remains linear over a large range, gas damping opens a route for tuning nonlinear damping forces via the squeeze-film effect. [ABSTRACT FROM AUTHOR]

The paper establishes the strong convergence rates of a spatio-temporal full discretization of the stochastic wave equation with nonlinear damping in dimension one and two. We discretize the SPDE by applying a spectral Galerkin method in space and a modified implicit exponential Euler scheme in time. The presence of the super-linearly growing damping in the underlying model brings challenges into the error analysis. To address these difficulties, we first achieve upper mean-square error bounds, and then obtain mean-square convergence rates of the considered numerical solution. This is done without requiring the moment bounds of the full approximations. The main result shows that, in dimension one, the scheme admits a convergence rate of order 1 2 in space and order 1 in time. In dimension two, the error analysis is more subtle and can be done at the expense of an order reduction due to an infinitesimal factor. Numerical experiments are performed and confirm our theoretical findings. [ABSTRACT FROM AUTHOR]

We studied the longtime dynamical behavior of a wave equation with critical nonlinearity and nonlinear damping in an expanding domain. First, we employed the penalty approach to establish the local well-posedness of the weak solution. Subsequently, we illustrated energy dissipation and asymptotic compactness for both the penalized equations and the original equation. Lastly, we established the existence of pullback attractors for penalized equations and the original equation. [ABSTRACT FROM AUTHOR]

In this article, we study a mathematical model for a one-dimensional suspension bridge problem with nonlinear damping. The model takes into consideration the vibration of the bridge deck in the vertical plane and main cable from which the bridge deck is suspended by the suspenders. We use the multiplier method to establish explicit and generalized decay results, without imposing restrictive growth assumption near the origin on the damping terms. Our results substantially improve, extend, and generalize some earlier related results in the literature.

This paper investigates the inherent nonlinear damping characteristics of a rotary eddy-current damper (RECD) and evaluates its vibration control performance on a single-degree-of-freedom (SDOF) system subjected to harmonic and seismic excitations. First, a RECD prototype was manufactured to experimentally identify its intrinsic nonlinear eddy-current damping characteristics. A magic formula model is then proposed to characterize the relationship between the eddy-current damping force and the velocity of the RECD, and its applicability in depicting the nonlinear damping characteristics of the RECD is evaluated by comparing with the electromagnetic finite-element (FE) model and the commonly used Wouterse's model. Moreover, by comparing the experimental and analytical frequency–domain responses of an SDOF structure equipped with a RECD, the applicability of the magic formula model in evaluating the structural vibration control performance of the RECD is further verified. Finally, the control performance of the RECD for an SDOF structure subjected to earthquake ground motions is numerically evaluated and compared. Results show that the eddy-current damping force of the RECD presents obvious nonlinear characteristics with increasing velocity, and the proposed magic formula model can adequately depict the nonlinear eddy-current damping characteristics of the RECD. Moreover, the RECD exhibits superior structural control performance under harmonic and seismic excitations. [ABSTRACT FROM AUTHOR]

In recent years, the increasing demand for vibration control has driven the development of viscous damping isolators, and there have been many attempts to apply the shear thickening fluid (STF) system to vibration control to achieve customized damping property according to different application requirements. Previous studies on the performance of STF-based isolators have observed a peculiar "collapse" phenomenon, but researchers have no clear explanation for the mechanism causing this unfavorable phenomenon. The main focus of this work is to explore the nonlinear characteristics and mechanism of STF-based isolators, especially for introducing a novel carbon fiber powder STF system (CFP-STF). The damping mechanism of the CFP-STF isolator is theoretically derived based on Poiseuille's law, the governing equations of arbitrary rheology are solved and demonstrated in details, and the theoretical model is established for multi-scale analysis under multi-frequency loading. To explore the influence of each parameter on the damping coefficient/force–displacement-velocity relationship, attention is paid to the initial viscosity and peak viscosity of the CFP-STF system, and as a result the concept of damping coefficient decrease rate is proposed in this paper. The results show that the the new CFP-STF isolator avoids the "collapse" phenomenon of the force–displacement hysteresis curve at high frequencies, where the damping force does not decrease and the mechanical dissipation tends to increase linearly after the threshold is exceeded, since the viscosity decreases more slowly than the velocity increases with increasing frequency. [ABSTRACT FROM AUTHOR]

Micro-vibrations during the operation of space remote sensing equipment can significantly affect optical imaging quality. To address this issue, a bellows-type viscous damper serves as an effective passive damping and vibration isolation solution. This paper introduces a bellows-type viscous damper with adjustable damping capabilities, designed for mid- to high-frequency applications. We developed a system damping model based on hydraulic fluid dynamics to examine how different factors—such as viscous coefficients, damping hole lengths, hole diameters, chamber pressures, and volumes—influence the damping characteristics. To validate the theoretical model, we constructed an experimental platform. The experimental results show that the theoretical damping curves closely match the measured data. Moreover, increasing the chamber pressure effectively enhances the damper's damping coefficient, with the deviation from theoretical predictions being approximately 4%. [ABSTRACT FROM AUTHOR]

We consider the wave equation with a nonlinear dissipative term in one space dimension. When the power of the nonlinearity is greater than two, we get a pointwise decay estimate for solutions, from which we also obtain the energy decay result by using the L 1 -estimate of Haraux [1]. [ABSTRACT FROM AUTHOR]

• The adaptive nonlinear damping is integrated into lateral suspension to improve hunting stability of high-speed train. • Three typical hunting bifurcations with different wheel/rail equivalent conicity functions are analyzed. • An adaptive constraint-following control method is employed to implement nonlinear damping via active suspension system. • The proposed method can significantly improve both carbody and bogie hunting stability. 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. [ABSTRACT FROM AUTHOR]

Hunting stability is an important performance criterion in railway vehicles. This study proposes an incorporation of a bio-inspired limb-like structure (LLS)-based nonlinear damping into the motor suspension system for traction units to improve the nonlinear critical speed and hunting stability of high-speed trains (HSTs). Initially, a vibration transmission analysis is conducted on a HST vehicle and a metro vehicle that suffered from hunting motion to explore the effect of different motor suspension systems from on-track tests. Subsequently, a simplified lateral dynamics model of an HST bogie is established to investigate the influence of the motor suspension on the bogie hunting behavior. The bifurcation analysis is applied to optimize the motor suspension parameters for high critical speed. Then, the nonlinear damping of the bio-inspired LLS, which has a positive correlation with the relative displacement, can further improve the modal damping of hunting motion and nonlinear critical speed compared with the linear motor suspension system. Furthermore, a comprehensive numerical model of a high-speed train, considering all nonlinearities, is established to investigate the influence of different types of motor suspension. The simulation results are well consistent with the theoretical analysis. The benefits of employing nonlinear damping of the bio-inspired LLS into the motor suspension of HSTs to enhance bogie hunting stability are thoroughly validated. [ABSTRACT FROM AUTHOR]

The over-track complex structures are driven by transit-oriented urban development, leading to the necessity for advanced seismic performance upgrades. An innovative solution is presented in this study, involving the negative-stiffness amplification system-enabled isolation system (NSAS-IS) with nonlinear viscous damping to establish a flexible isolation layer beneath over-track buildings. The multi-benefit-based design procedure and easy-to-use formula are developed. Its effectiveness and comparative superiority over conventional ones, particularly in mitigating negative effects of over-track buildings on lower podiums, is confirmed by case studies. NSAS-IS with an optimized nonlinear viscous damping exponent exhibits a significant reduction in isolation-layer displacement and robustness against earthquakes. [ABSTRACT FROM AUTHOR]

In this work it is shown how a strong nonlinear increase of the shear stress at the clamping regions of suspended bridge resonators can result in a large nonlinear damping. The multimode Galerkin method is used to demonstrate that the shear stress at the clamping region is enhanced for large amplitudes of vibration as a consequence of the beam deformation induced by the midplane stretching. The extra stress increases the acoustic energy loss through the clampings compared to the one predicted ignoring the effect of the beam stretching on its shape. The total emitted acoustic power is found to be more than two or three times larger for strong nonlinear vibrations. While this new nonlinear damping mechanism is investigated for suspended beam micro and nanoresonators it can have analogs in other physical systems that can suffer nonlinear stretching and generate acoustic waves through the surrounding structures. The damping mechanism evidences the complex interplay between the geometrical nonlinearity and nonlinear damping. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Purpose: In this paper, a high-static-low-dynamic-stiffness (HSLDS) isolator with geometric nonlinear damping is proposed in order to improve the performance of low-frequency vibration isolation. The geometric nonlinear damping characteristic of the HSLDS system is analyzed. Methods: The Lagrange principle is employed to establish the differential equation of motion of a vibration system with the proposed isolator. The harmonic balance method (HBM) is then applied to derive the steady-state responses under base and force excitations, respectively. The vibration isolation performance of the proposed system is thus analyzed and discussed for different parameters. Results: The results show that increasing nonlinear damping can significantly reduce the displacement transmissibility peak in the resonant zone without apparently influencing the performance at higher frequencies. Similarly, when subjected to force excitation, an increase in nonlinear damping notably reduces the force transmissibility peak in the resonant region while the vibration isolation performance at higher frequencies remains unaffected. It is also determined that increasing the stiffness ratio can effectively suppress the displacement and force transmissibility, and extend the isolation region. Conclusion: It is found that the integration of geometric nonlinear damping into the HSLDS isolator effectively enhances system performance and is suitable for low-frequency vibration isolation. [ABSTRACT FROM AUTHOR]

Abstract In this study, nonlinear damping is introduced as the fourth dimension in the operation of a fiber tip optomechanical anemometer. The flow sensing element, featuring a 3D rotor measuring 110 µm in diameter and fabricated through a two‐photon nanomachining process, is monolithically integrated onto the cleaved face of the optical fiber, which serves as an integrated waveguide. As the rotor encounters airflow, it spins, and mirrors on its blades reflect light across the fiber core at each pass. This setup permits precise measurement of gaseous fluid flow with minimal sensor footprint at the point of detection and accommodates a variety of optical sources and measurement apparatuses without the need for specific wavelength or broad‐spectrum capabilities. To stabilize the rotation of the rotor and facilitate consistent frequency‐domain analysis, a polydimethylsiloxane hydrocarbon stabilizing agent is infused into the gap between the rotor and stator of the sensing element via dual‐function microfluidic channels. This enhancement allows for the measurement of gaseous nitrogen flow rates from 10 to 20 liters per minute (LPM), with a consistent periodic response. Comprehensive characterizations of the fiber tip anemometer are presented with and without the stabilizing medium, demonstrating its crucial role in regulating the dynamics between the rotor and the stator.

Abstract Hunting stability is an important performance criterion in railway vehicles. This study proposes an incorporation of a bio-inspired limb-like structure (LLS)-based nonlinear damping into the motor suspension system for traction units to improve the nonlinear critical speed and hunting stability of high-speed trains (HSTs). Initially, a vibration transmission analysis is conducted on a HST vehicle and a metro vehicle that suffered from hunting motion to explore the effect of different motor suspension systems from on-track tests. Subsequently, a simplified lateral dynamics model of an HST bogie is established to investigate the influence of the motor suspension on the bogie hunting behavior. The bifurcation analysis is applied to optimize the motor suspension parameters for high critical speed. Then, the nonlinear damping of the bio-inspired LLS, which has a positive correlation with the relative displacement, can further improve the modal damping of hunting motion and nonlinear critical speed compared with the linear motor suspension system. Furthermore, a comprehensive numerical model of a high-speed train, considering all nonlinearities, is established to investigate the influence of different types of motor suspension. The simulation results are well consistent with the theoretical analysis. The benefits of employing nonlinear damping of the bio-inspired LLS into the motor suspension of HSTs to enhance bogie hunting stability are thoroughly validated.

The issue of nonlinear dampness in the cab of agricultural engineering vehicles is examined by analyzing the vibration reduction system of a specific agricultural loader. Firstly, the specific loader was tested under different conditions. Then, the nonlinear vibration reduction system model of the cab-seat-human body is established by using the measured frame vibration signal as input. Finally, the multi-objective genetic algorithm is used to optimize the root mean square (RMS) value of vertical acceleration of the cab and seat. The test results show that the seat vibration is significantly greater than the acceleration of the cab floor under driving and working conditions, so the seat vibration is amplified and the seat parameter setting is unreasonable; the engine and the working device are also an important part of the cab vibration source, in addition to the uneven road surface. Comparing the RMS values of the vertical acceleration of the cab and seat, which were calculated by the model and obtained from the vehicle test, the error does not exceed 6%, indicating that the model's accuracy meets the requirement. The vehicle experiment proves that the RMS value of the vertical acceleration of the cab and seat is reduced by 16% and 53%, respectively, after optimization. This study provides a theoretical basis for the design of the damping system for the cab of agricultural engineering vehicles. [ABSTRACT FROM AUTHOR]

Scissor-like isolation platform (SIP) with magnetorheological damper (MRD) has been commonly studied and applied successfully in vehicle vibration isolation. This paper concerns passive nonlinear magnetorheological (MR) characteristics of the SIP via geometric nonlinearity induced by MRD's layout ways. A dynamic parametric model of the SIP with six assembly types is derived based on Lagrange equation. Then, the parameter analysis is performed to estimate MR damping function in SIP. The analytical steady-state response of the isolator is derived using harmonic balance method, and its effectiveness is validated with numerical results. Metrics are defined to access the performance of the isolator, followed by comparison on displacement transmissibility for six types. The effect of MR damping coefficient and input amplitude on the performance of the isolator is investigated. Finally, comparative study with existing isolators is conducted. Results indicate that, passive MR damping is dependent on vibration displacement, which is beneficial to suppressing peak transmissibility with a little effect at non-resonant frequencies. The results also reveal that the isolator by type 1 or 3 has broader isolation band over other types. And the SIP in type 1 has wider isolation band and lower peak transmissibility compared with existing isolators in allowable workspace. [ABSTRACT FROM AUTHOR]

This paper presents an experimental insight into the performance of a mechanical oscillator consisting of an X-shaped-spring configuration. This configuration achieves an overall softening characteristic with quasi-zero stiffness behaviour far away from the static equilibrium point. Such a geometrical nonlinear configuration has attracted significant research attention in the last few years, particularly for its application as a vibration isolator with the possibility to extend the quasi-zero-stiffness region beyond that of the classical three-spring nonlinear isolator. However, previous experimental evidence has been limited to small amplitude vibration excitation only. Furthermore, it has been focused mainly on the isolation region, rather than on the large amplitude response, thus circumventing an insight on the damping effects and its modelling. To address this gap, in this paper, both frequency sweeps and random excitations are applied to a prototype device for experimental characterization. A nonlinear stiffness model is developed based on the geometry of the system and a nonlinear damping model is assumed based on experimental observation. The proposed model accurately describes the dynamic behaviour of the system as shown by comparison of theoretical and experimental data. [ABSTRACT FROM AUTHOR]

In this paper, we consider one-dimensional nonlinear piezoelectric beams with thermal and magnetic effects in the presence of a distributed delay term acting on the heat equation. First, we show that the system is well-posed in the sense of a semigroup. Through the construction of an appropriate Lyapunov functional, we establish a general decay result for the solutions of the system, for which the exponential and polynomial decays are only special cases, under a suitable assumption on the weight of the delay that the damping effect through heat conduction is strong enough to stabilize the system even in the presence of a time delay. Furthermore, our result does not depend on any relationship between system parameters. [ABSTRACT FROM AUTHOR]

This paper discussed the decay of a thermoelastic laminated beam subjected to nonlinear delay and nonlinear structural damping. We provided explicit and general energy decay rates of the solution by imposing suitable conditions on both weight delay and wave speeds. To achieve this, we leveraged the properties of convex functions and employed the multiplier technique as a specific approach to demonstrate our stability results.

This paper deals with the free propagation problem of resonant and close-to-resonance waves in one-dimensional lattice metamaterials endowed with nonlinearly viscoelastic resonators. The resonators' constitutive and geometric nonlinearities imply a cubic coupling with the lattice. The analytical treatment of the nonlinear wave propagation equations is carried out via a perturbation approach. In particular, after a suitable reformulation of the problem in the Hamiltonian setting, the approach relies on the well-known resonant normal form techniques from Hamiltonian perturbation theory. It is shown how the constructive features of the Lie Series formalism can be exploited in the explicit computation of the approximations of the invariant manifolds. A discussion of the metamaterial dynamic stability, either in the general or in the weak dissipation case, is presented. [ABSTRACT FROM AUTHOR]

Of concern is a problem of strain gradient porous elastic theory with nonlinear damping terms, whose constitutive equations contain higher-order derivatives of the displacement in the basic postulates. The paper is based on the theory of 'consistency' due to Aouadi et al. [J. Therm. Stress. 43(2)(2020), 191–209] and Ieşan [American Institute of Physics, Conference Proceedings, 1329 (2011), 130–149], and contains four results. We firstly show that the system is global well posed by using maximal monotone operator. The second main result is the existence of global attractors which is proved by the method developed by Chueshov and Lasiecka [Long-time behavior of second order evolution equations with nonlinear damping. Mem. Amer. Math. Soc. vol. 195, no. 912, Providence, 2008; Von Karman evolution equations: well-posedness and long-time dynamics. Springer Monographs in Mathematics, Springer, New York, 2010]. By showing the system is gradient and asymptotically smooth, we establish the existence of global attractors with finite fractal dimension via a stabilizability inequality. Then we study the continuity of global attractors regarding the parameter in a residual dense set. The above results allow the damping terms with polynomial growth. Finally we discuss the exponential decay and global boundedness to the linear case of damping terms of the system. The assumption of equal-speed wave propagations is not needed for all of results obtained. [ABSTRACT FROM AUTHOR]

Background: Eddy current damper (ECD) pledges better control over damping coefficient, provides contactless damping, requires little or no maintenance, has simpler construction, no performance degradation over time, and is cost-effective as compared to mechanical dampers. Its challenge includes the development of a system which provides comparable damping density to other mechanical systems for structural applications. Purpose: ECD has the potential to protect common structures in seismically active areas at low cost and with better vibration control. Further, the application of such dampers may protect industrial assembly structures against undesirable fatigue and increase the lifespan of structures that are constantly prone to vibrations. Methods: This paper produces a review of existing literature in vibration control of structures equipped with ECDs, types of ECDs developed for structural applications, SDOF (single degree of freedom) benchmark structure equipped with ECD, challenges, and opportunities in the development of ECD therein. [ABSTRACT FROM AUTHOR]

Testing wave energy converters in the ocean could be expensive and complex, which necessitates the use of numerical modeling. However, accurately modeling the response of wave energy converters with high-fidelity simulations can be computationally intensive in the design stage where different configurations must be considered. Reduced-order models based on simplified equations of motion can be very useful in the design, optimization, or control of wave energy converters. Given the complex dynamics of wave energy converters, accurate representation, and evaluation of relative contributions by different forces are required. This effort is concerned with a performance characterization of the hydrodynamic response of an oscillating surge wave energy converter that is based on a reduced-order model. A state-space model is used to represent the radiation damping term. Morison's representation of unsteady forces is used to account for the nonlinear damping. Wave tank tests are performed to validate simulations. A free response simulation is used to determine the coefficients of the state-space model. Torque-forced simulations are used to identify the coefficients of the nonlinear damping term for different amplitudes and wave frequencies. The impact of varying these coefficients on the response is investigated. An assessment of the capability of the model in predicting the hydrodynamic response under irregular forcing is performed. The results show that the maximum error is 3% when compared with high-fidelity simulations. It is determined that the nonlinear damping is proportional to the torque amplitude and its effects are more pronounced as the amplitude of the flap oscillations increases. [ABSTRACT FROM AUTHOR]

We study the wellposedness and stabilization for a Cauchy–Ventcel problem in an inhomogeneous medium Ω⊂R2$\Omega \subset \mathbb {R}^2$ with dynamic boundary conditions subject to a exponential growth source term and a nonlinear damping distributed around a neighborhood ω$\omega$ of the boundary according to the geometric control condition. We, in particular, generalize substantially the work due to Almeida et al. (Commun. Contemp. Math. 23 (2021), no. 03, 1950072), in what concerns an exponential growth for source term instead of a polynomial one. We give a proof based on the truncation of a equivalent problem and passage to the limit in order to obtain in one shot, the energy identity as well as the observability inequality, which are the essential ingredients to obtain uniform decay rates of the energy. We show that the energy of the equivalent problem goes uniformly to zero, for all initial data of finite energy taken in bounded sets of finite energy phase space. One advantage of our proof is that the decay rate is independent of the nonlinearity. [ABSTRACT FROM AUTHOR]

This paper discussed the decay of a thermoelastic laminated beam subjected to nonlinear delay and nonlinear structural damping. We provided explicit and general energy decay rates of the solution by imposing suitable conditions on both weight delay and wave speeds. To achieve this, we leveraged the properties of convex functions and employed the multiplier technique as a specific approach to demonstrate our stability results. [ABSTRACT FROM AUTHOR]

Micro-vibrations during the operation of space remote sensing equipment can significantly affect optical imaging quality. To address this issue, a bellows-type viscous damper serves as an effective passive damping and vibration isolation solution. This paper introduces a bellows-type viscous damper with adjustable damping capabilities, designed for mid- to high-frequency applications. We developed a system damping model based on hydraulic fluid dynamics to examine how different factors—such as viscous coefficients, damping hole lengths, hole diameters, chamber pressures, and volumes—influence the damping characteristics. To validate the theoretical model, we constructed an experimental platform. The experimental results show that the theoretical damping curves closely match the measured data. Moreover, increasing the chamber pressure effectively enhances the damper’s damping coefficient, with the deviation from theoretical predictions being approximately 4%.

This article examines the joint impacts of microtemperature, nonlinear structural damping, along with nonlinear time-varying delay term, and time-varying coefficient on a thermoelastic laminated beam, where, the equation representing the dynamics of slip is affected by the last three mentioned terms. A general decay result was established regarding the system concerned given equal wave speeds and particular assumptions related to nonlinear terms.

The problem of Reissner–Mindlin–Timoshenko plate systems with nonlinear damping terms is considered. The main result is the existence of global attractors. By showing the system is gradient and asymptotic smoothness via a stabilizability inequality, we establish the existence of global attractors with finite fractal dimension. The continuity of global attractors regarding the parameter in a residual dense set is also proved. The above results allow the damping terms with polynomial growth. [ABSTRACT FROM AUTHOR]

In this article. we are interested in the study of a Lord-Shulman thermoelastic system with nonlinear damping term. We establish the well-posedness of the problem using the semigroup theory. By using the energy method and some properties of convex functions. we show that the dissipation given by this complementary control guarantees the general stability without imposing any restrictive growth assumption near the origin on the damping term. Furthermore, our result does not depend on any relationship between system parameters. [ABSTRACT FROM AUTHOR]

In this paper. we consider a one-dimensional Timoshenko system with a nonlinear damping term. First. we show the existence and uniqueness of the solution by using the semi-group method. more precisely by the Hille-Yosida theorem. Also. by constructing a suitable Lyapunov functional and using some properties of convex functions. we establish a general decay result for the solution of the system. Moreover. our result does not depend on any relation between the parameters of the system. [ABSTRACT FROM AUTHOR]

We consider a swelling porous-elastic system with single nonlinear damping and nonlinear delay term in the elastic equation. We establish the general decay result using multiplier method. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper is focused on energy decay rates for the viscoelastic wave equation that includes nonlinear time-varying delay, nonlinear damping at the boundary, and acoustic boundary conditions. We derive general decay rate results without requiring the condition a 2 > 0 and without imposing any restrictive growth assumption on the damping term f 1 , using the multiplier method and some properties of the convex functions. Here we investigate the relaxation function ψ , namely ψ ′ (t) ≤ − μ (t) G (ψ (t)) , where G is a convex and increasing function near the origin, and μ is a positive nonincreasing function. Moreover, the energy decay rates depend on the functions μ and G, as well as the function F defined by f 0 , which characterizes the growth behavior of f 1 at the origin. [ABSTRACT FROM AUTHOR]

This article examines the joint impacts of microtemperature, nonlinear structural damping, along with nonlinear time-varying delay term, and time-varying coefficient on a thermoelastic laminated beam, where, the equation representing the dynamics of slip is afiected by the last three mentioned terms. A general decay result was established regarding the system concerned given equal wave speeds and particular assumptions related to nonlinear terms. [ABSTRACT FROM AUTHOR]

In this article, we consider the one-dimensional system of piezoelectric beams with a nonlinear damping term. First, we show the existence and uniqueness of solutions by the semi-group technique more precisely by Hille-Yosida theorem. And by building an appropriate Lyapunov functional, we establish general decay results for the solution of the system whose exponential and polynomial decays are only special cases. Moreover, our results does not depend on any relation between the parameters of the system. [ABSTRACT FROM AUTHOR]