Exponential Damping Research Articles

Study on Dynamic Factors of Damped Beam Members Under Exponential Attenuation Loading

Blast loading is characterized as an impact loading with exponential attenuation, while damping serves as an intrinsic parameter that affects the vibration effect of beam members. The linear attenuation for simplified blast loading and undamped situation for beam members is often adopted by most scholars or codes for the calculation of dynamic factors. These assumptions that do not conform to the actual situation can lead to deviations in the results of the dynamic factor. In this study, the implicit solutions for the dynamic factors of both flexible and rigid beam members were derived by the exponential attenuation loading and damping of beam members. The dynamic response verification of an H-shaped steel beam blast test was completed using LS-DYNA software. The comparison calculation of the theoretical solutions of dynamic factors in this paper with the Chinese blast-resistant design code and finite element simulation was carried out. The results show that the dynamic factor will be higher when the blast loading is simplified to linear attenuation loading for undamped beams. The shape parameter of the exponential attenuation loading and the damping ratio of beam members both reduce the effect of the dynamic factor, with the damping ratio having a more significant effect.

Recursive and batch Bayesian estimation of exponential non-viscous damping systems

Non-viscous damping systems include a convolutional integral and a kernel function in their equation of motion to incorporate time-hysteresis damping effects, which are present in dynamical behavior of most engineering materials yet are absent in commonly used viscous damping models. When an exponential kernel function is adopted by the non-viscous model, the unique damping characteristic is realized by an additional model parameter known as the relaxation parameter. The objective of this paper is to investigate various aspects of estimation problems on exponential non-viscous damping systems through recursive and batch Bayesian time-domain frameworks, with a focus on how the relaxation parameter introduces additional complexity in estimation problems compared to viscous damping systems. Two well-established algorithms are employed: the unscented Kalman filter (UKF) for recursive Bayesian estimation and the transitional Markov Chain Monte Carlo (TMCMC) for batch Bayesian estimation. We first analyze the complexity of estimation problems in SDOF viscous and non-viscous damping systems. The TMCMC algorithm offers a quantitative analysis that reveals greater uncertainty and stronger parameter correlation in non-viscous damping systems compared to viscous damping systems. Subsequently, the same SDOF systems are utilized to study recursive Bayesian estimation via UKF such as the effects of measurement data type, discretization, and initial conditions. Based on the results of the TMCMC algorithm, we study the dependence of UKF performance on the initial condition for various SDOF non-viscous damping systems with different levels of non-viscosity. In the end, a laboratory experiment compares the estimation results between viscous and non-viscous damping systems using both TMCMC and UKF.

Finite element model updating of non-proportional and exponential non-viscous damping systems using complex eigenvalues and eigenvectors

This paper proposes a finite element model updating method for non-proportional viscous and exponential non-viscous damping systems using complex eigenvalues and eigenvectors. The exponential non-viscous damping provides complex eigenvalues/vectors for elastic modes and real-valued eigenvalues/vectors for non-viscous modes. This study first highlights the challenges in accurately identifying real-valued eigenvalues/vectors for non-viscous modes with a commonly used system identification method. In contrast, complex eigenvalues/vectors for elastic modes are reliably identified and, therefore, utilized in the proposed model updating approach. Consequently, an optimization formulation is proposed to minimize the difference between the simulated and experimental complex eigenvalues/vectors. The method applies large structures that can contain multiple substructures with different damping properties. For brevity, damping properties are assumed to be uniform over each substructure. In addition, mass-proportional viscous damping and stiffness-proportional non-viscous damping are adopted for each substructure, which results in overall damping being non-proportional. To improve computational efficiency, the analytical gradient of the proposed optimization formulation is derived and implemented. For validation, the model updating of a full-scale steel pedestrian bridge is performed. The method is first validated in simulation and further validated by experimental data considering the statistical properties of system identification results. The proposed method successfully identifies stiffness and damping parameters using only a limited number of measured DOFs and modes.

Quantum graph wave external triggering: Energy transfer and damping.

The propagation of wave trains resulting from a local external trigger inside a network described by a metric graph is analyzed using quantum graph theory. The external trigger is a finite-time perturbation imposed at one vertex of the graph, leading to a consecutive wave train into the network, supposedly at rest before the applied external perturbation. A complete analytical solution for the induced wave train is found having a specific spectrum as well as mode's amplitudes. Furthermore the precise condition by which the external trigger can transfer a maximal energy to any specific natural mode of the quantum graph is derived. Finally, the wave damping associated with boundary-layer dissipation is computed within a multiple time-scale asymptotic analysis. Exponential damping rates are explicitly found related to their corresponding mode's eigenvalue. Each mode energy is then obtained, as well as their exponential damping rate. The relevance of these results to the physics of waves within networks are discussed.

The ideal wavelength for daylight free-space quantum key distribution

Quantum key distribution (QKD) has matured in recent years from laboratory proof-of-principle demonstrations to commercially available systems. One of the major bottlenecks is the limited communication distance in fiber networks due to the exponential signal damping. To bridge intercontinental distances, low Earth orbit satellites transmitting quantum signals over the atmosphere can be used. These free-space links, however, can only operate during the night, as the sunlight otherwise saturates the detectors used to measure the quantum states. For applying QKD in a global quantum internet with continuous availability and high data rates, operation during daylight is required. In this work, we model a satellite-to-ground quantum channel for different quantum light sources to identify the optimal wavelength for free-space QKD under ambient conditions. Daylight quantum communication is possible within the Fraunhofer lines or in the near-infrared spectrum, where the intrinsic background from the sun is comparably low. The highest annual secret key length considering the finite key effect is achievable at the Hα Fraunhofer line. More importantly, we provide the fundamental model that can be adapted, in general, to any other specific link scenario taking into account the required modifications. We also propose a true single-photon source based on a color center in hexagonal boron nitride coupled to a microresonator that can implement such a scheme. Our results can also be applied in roof-to-roof scenarios and are, therefore, relevant for near-future quantum networks.

Existence of Attractors for the Three-Dimensional Navier-Stokes Equations with Exponential Damping

Existence of Attractors for the Three-Dimensional Navier-Stokes Equations with Exponential Damping

Improved explicit quartic B-spline time integration scheme for dynamic response analysis of viscoelastic systems

A quartic B-spline based explicit scheme is extended for dynamic analysis of viscoelastic systems. In the calculation formulation, different integration approximation schemes for exponential damping models and other damping models are presented. The mathematical derivation of the convolution solving strategy is formulated for viscoelastic systems. For the damping models composed of exponential function, this scheme only requires once convolution calculation in each time step, even though the dynamic equations are used twice. This significantly reduces the calculation time for the damping models composed of exponential function. Numerical examples show that the proposed quartic B-spline based explicit scheme achieves higher accuracy and efficiency compared to other competitive explicit schemes, not only for damping models composed of exponential functions, but also for other viscoelastic damping models.

Numerical Multiscale Methods for Waves in High-Contrast Media

Multiscale high-contrast media can cause astonishing wave propagation phenomena through resonance effects. For instance, waves could be exponentially damped independent of the incident angle or waves could be re-focused as through a lense. In this review article, we discuss the numerical treatment of wave propagation through multiscale high-contrast media at the example of the Helmholtz equation. First, we briefly summarize the findings of analytical homogenization theory, which inspire the design of numerical methods and indicate interesting regimes for simulation. In the main part, we discuss two different classes of numerical multiscale methods and focus on how to treat especially high-contrast media. Some elements of a priori error analysis are discussed as well. Various numerical simulations showcase the applicability of the numerical methods to explore unusual wave phenomena, for instance exponential damping and lensing with flat interfaces.

Comparison of damping models for kink oscillations of coronal loops

ABSTRACT Kink oscillations of solar coronal loops are of intense interest due to their potential for diagnosing plasma parameters in the corona. The accurate measurement of the kink oscillation damping time is crucial for precise seismological diagnostics, such as the transverse density profile, and for the determination of the damping mechanism. Previous studies of large-amplitude rapidly decaying kink oscillations have shown that both an exponential damping model and a generalized model (consisting of Gaussian and exponential damping patterns) fit observed damping profiles sufficiently well. However, it has recently been shown theoretically that the transition from the decaying regime to the decayless regime could be characterized by a superexponential damping model. In this work, we reanalyse a sample of decaying kink oscillation events, and utilize the Markov chain Monte Carlo Bayesian approach to compare the exponential, Gaussian–exponential, and superexponential damping models. It is found that in 7 out of 10 analysed oscillations, the preferential damping model is the superexponential one. In two events, the preferential damping is exponential, and in one it is Gaussian–exponential. This finding indicates the plausibility of the superexponential damping model. The possibility of a non-exponential damping pattern needs to be taken into account in the analysis of a larger number of events, especially in the estimation of the damping time and its associated empirical scalings with the oscillation period and amplitude, and in seismological inversions.

Triple-spherical Bessel function integrals with exponential and Gaussian damping: towards an analytic N-point correlation function covariance model

Spherical Bessel functions (sBFs) appear commonly in many areas of physics wherein there is both translation and rotation invariance, and often integrals over products of several arise. Thus, analytic evaluation of such integrals with different weighting functions (which appear as toy models of a given physical observable, such as the galaxy power spectrum) is useful. Here, we present a generalization of a recursion-based method for evaluating such integrals. It gives relatively simple closed-form results in terms of Legendre functions (for the exponentially damped case) and Gamma, incomplete Gamma, and hypergeometric functions (for the Gaussian-damped case). We also present a new, non-recursive method to evaluate integrals of products of sBFs with Gaussian damping in terms of incomplete Gamma functions and hypergeometric functions.

Synergistic inhibition of azoles compounds on chloride-induced atmospheric corrosion of copper: Experimental and theoretical characterization

Synergistic implementation of corrosion inhibitors is an efficient and economic method for metal protection. The adsorption dynamics and inhibition behavior of 2-phenyl imidazoline (2-PI) and benzotriazole (BTA) are investigated in atmospheric and aqueous environments by electrochemical and quartz crystal microbalance sensors. Moreover, their synergistic mechanisms are illustrated from molecule scales by theoretical calculations. Electrochemical tests show that 2-PI and BTA exhibit promising synergistic effects on the corrosion of copper with inhibition efficiency up to 99.1% in 0.1 mol/L NaCl solution and 94.1% in the atmosphere, respectively. In addition, the adsorption kinetics of inhibitors on copper obey a pseudo-first-order kinetic model characteristic of exponential damping. Quantum chemical and molecule dynamic calculations also suggest that there exists an intermolecular interaction between 2-PI and BTA molecules in a parallel adsorption manner when they are co-adsorbed on the surface of copper.

Quantitative thermal-wave depth profiles of solids with spatially variant cooling coefficients imaged using lock-in thermography

A generalized treatment of the thermal-wave boundary-value problem in a solid slab strip with large sidewalls exposed to the ambient and third-kind boundary conditions over the extended sidewall surfaces was presented. Unlike conventional heat conduction theoretical practice, it was found that the cooling coefficient h is not constant and depends on the thermal gradient variation with depth/length. The exponential damping of the TW amplitude with depth presented an ideal condition to reveal the depth dependence of h which under normal steady heat transfer conditions might appear approximately constant in a non-steeply changing thermal field. The observed depth dependence of the heat loss coefficient can be used to establish the physically expected constancy of thermal diffusivity at different modulation frequencies in juxtaposition to some published reports. It is expected that this work can be used to optimize other thermophysical parameters for materials subject to periodic heating.

FRF-based finite element model updating for non-viscous and non-proportionally damped systems

All structures exhibit some form of damping, but the characterization of damping is not well-understood, and there is no universal damping model for the dynamic systems. Recently, model updating methods have been used to update or identify the damping matrix in dynamic systems. Most of the finite element updating methods assume viscous and proportional damping models for updating or identifying of damping matrix. In this paper, a new finite element model updating method is proposed in which the damping model is assumed as non-viscous and non-proportional. A parametric exponential non-viscous damping model has been used to model the damping in the dynamic system. The proposed method is the frequency response function (FRF)-based updating model, which updates the non-viscous and non-proportional damping matrix in the dynamic system. The effectiveness of the proposed damped finite element updating method is demonstrated by a numerical example and actual laboratory experiments. First, a numerical study is performed on a cantilever beam structure with non-viscous and non-proportional damping. The numerical study is followed by cases involving actual measured data. Joints and boundary conditions are assumed as a major source of damping, therefore joints and boundary conditions are modelled using relaxation functions and damping coefficients. The updated results have shown that the proposed damped element model updating method can be used to derive accurate models for the non-viscous and non-proportional damped systems. This is illustrated by matching complex FRFs obtained from the updated model with from the experimental data.

Analytical Study of a 3D-MHD System with Exponential Damping

In this paper, we investigate the magnetohydrodynamic system with exponential type damping \(\alpha (e^{\beta |u|^2}-1)u\). We prove existence of a global in time weak solution and a global in time unique strong solutions, for any \(\alpha,\beta\in(0,\infty)\). The proofs are based on energy methods and use compactness argument for the existence results, and Gronwall lemma for the uniqueness. Friedrich approximation and standard techniques are also used.

LONG-TIME DECAY OF LERAY SOLUTION OF 3D-NSE WITH EXPONENTIAL DAMPING

We study the uniqueness, the continuity in [Formula: see text] and the large time decay for the Leray solutions of the 3D incompressible Navier–Stokes equations with nonlinear exponential damping term [Formula: see text], ([Formula: see text]).

Multiterminal epitaxial tungsten nanostructures on MgO/GaAs(001) substrates: Temperature effects in ballistic electron transport

High-quality single-crystalline multiterminal tungsten nanostructures were fabricated on MgO/GaAs (001) substrates using subtractive lithography. Single-crystalline tungsten films with a thickness of d = 80 nm and low roughness were grown using sequential epitaxy of MgO (001) and W (001) layers on GaAs (001) via pulsed laser deposition. The temperature dependence of bridge-type nanostructure electron conductivity indicates that they are high-quality metal conductors. The electron mean free path reached 760 nm at low temperatures and was approximately an order of magnitude greater than the tungsten film thickness. Strong non-local effects resulting from ballistic electron transport were observed in the multiterminal cross-type W (001) nanostructures with an arm width Wc = 400 nm below T = 80 K. Such effects can be explained by the exponential damping of ballistic properties of nanostructures as a function of the electron mean free path in the wide temperature range 4.2–100 K. Simulations predict that the ballistic effects in such nanostructures can be significant even at room temperature with an arm width approaching 10 nm and a size ratio of Wc/d ∼ 1.

HBN-based enhancement and regulation of radiative heat transfer between two monolayer graphene sheets

Near-field radiative heat transfer (NFRHT) in many-body systems has opened pathways for enabling novel thermal-radiation applications. In this Letter, we investigate hBN-based enhancement and regulation of NFRHT between two monolayer graphene sheets. On the one hand, we predict that adding an intermediate hBN plate can greatly compensate the exponential damping of evanescent waves due to its hyperbolic modes, thus leading to 1.5 times enhancement of the NFRHT without introducing additional thermal source compared to the graphene-graphene system. On the other hand, we find that adjusting the shift frequency of hBN can greatly change the coupling of its hyperbolic modes and graphene surface plasmon polaritons, thus enabling the remarkable thermal regulation with a ratio of 3.5. We hope that our work may facilitate nanoscale thermal management in many-body systems and benefit the comprehension of hBN-based photon tunneling.

Characteristics of passive vibration control for exponential non-viscous damping system: Vibration isolator and absorber

Materials or structures made of polymers or composites often exhibit non-viscous damping behavior. The non-viscous damping forces that depend on the history velocity can be expressed by the exponential non-viscous damping model. Some polymer or composite materials can be used as damping materials for kinetic energy absorption in the dynamic systems. Vibration isolator and absorber are usually considered for shock absorption. In this study, transfer ratios of vibration isolator and absorber with exponential non-viscous damping system are derived by using the Laplace transform. The dimensionless amplitude of vibration absorber with exponential non-viscous damping is derived too. Compared to viscous damping system, transfer ratio and dimensionless amplitude of exponential non-viscous damping system are influenced by the ratio of the relaxation parameter and natural frequency or the frequency of the external load. With the non-viscous damping material used in vibration control, the ratio is therefore a non-negligible factor which should be considered in analysis.

Nonlinear Compton scattering and nonlinear Breit-Wheeler pair production including the damping of particle states

In the presence of an electromagnetic background plane wave field, electron, positron, and photon states are not stable because electrons and positrons emit photons and photons decay into electron-positron pairs. This decay of the particle states leads to an exponential damping term in the probabilities of single nonlinear Compton scattering and nonlinear Breit-Wheeler pair production. In this paper, we investigate analytically and numerically the probabilities of nonlinear Compton scattering and nonlinear Breit-Wheeler pair production including the particle states' decay. For this, we first compute spin- and polarization-resolved expressions of the probabilities, provide some of their asymptotic behaviors, and show that the results of the total probabilities are independent of the spin and polarization bases. Then, we present several plots of the total and differential probabilities for different pulse lengths and for different spin and polarization quantum numbers. We observe that it is crucial to take into account the damping of the states in order for the probabilities to stay always below unity, and we show that the damping factors also scale with the intensity and pulse duration of the background field. In the case of nonlinear Compton scattering, we show numerically that the total probability behaves like a Poissonian distribution in the regime where the photon recoil is negligible. In all considered cases, the kinematic conditions are such that the final particles momenta transverse to the propagation direction of the plane wave are always much smaller than the particles longitudinal momenta and the main spread of the momentum distribution on the transverse plane is along the direction of the plane wave electric field.

Observability of spontaneous collapse in flavor oscillations and its relation to the [formula omitted] and [formula omitted] symmetries

Spontaneous collapse models aim at solving the measurement problem of quantum mechanics by introducing collapse of wave function as an ontologically objective mechanism that suppresses macroscopic superpositions. In particular, the strength of collapse depends on the mass of the system. Flavor oscillating systems such as neutral mesons feature superpositions of states of different masses and, hence, could be used to test the validity of spontaneous collapse models. Recently, it has been shown that the mass-proportional CSL model causes exponential damping of the neutral meson oscillations which, however, is not strong enough to be observed in the present accelerator facilities. In this Letter, we study how the violation of the CP symmetry in mixing changes the spontaneous collapse effect on flavor oscillations and its observability.