Local Damping Research Articles

Energy uniform decay rates for the semilinear wave equation with nonlinear localized damping and source terms of critical variable exponent

Energy uniform decay rates for the semilinear wave equation with nonlinear localized damping and source terms of critical variable exponent

STABILIZATION OF TWO STRONGLY COUPLED HYPERBOLIC EQUATIONS IN EXTERIOR DOMAINS

In this paper we study the behavior of the total energy and the $L^2$-norm of solutions of two coupled hyperbolic equations by velocities in exterior domains. Only one of the two equations is directly damped by a localized damping term. We show that, when the damping set contains the coupling one and the coupling term is effective at infinity and on captive region, then the total energy decays uniformly and the $L^2$-norm of smooth solutions is bounded. In the case of two Klein-Gordon equations with equal speeds we deduce an exponential decay of the energy.

Well-posedness and asymptotic behavior of a generalized higher order nonlinear Schrödinger equation with localized dissipation

In this work, we study at the L2 – level global well-posedness as well as long-time stability of an initial-boundary value problem, posed on a bounded interval, for a generalized higher order nonlinear Schrödinger equation, modeling the propagation of pulses in optical fiber, with a localized damping term. In addition, we implement a precise and efficient code to study the energy decay of the higher order nonlinear Schrödinger equation and we prove its convergence and exponential stability of the discrete energy.

An improved higher-order explicit time integration method with momentum corrector for linear and nonlinear dynamics

An improved explicit time integration method is proposed for linear and nonlinear dynamics. Its calculation procedure is obtained with cubic B-spline interpolation approximation and weighted residual method. In the formulation, a momentum corrector is used to improve actual computation accuracy, especially for some special discontinuous loads. Analytical solutions of the local truncation errors, algorithmic damping and period elongation have been deduced to obtain the influence of algorithmic parameters on these basis algorithmic properties. The proposed method possesses at least second-order accuracy and can achieve at most third-order accuracy for no physical damping case. With free algorithmic parameters, the proposed method has controllable stability and numerical dissipation. Some demonstrative numerical examples are tested to confirm high efficiency of the proposed method for a variety of dynamic problems such as, dynamic response analysis of linear systems under various representative applied loads, finite element analysis (FEA) for dynamic response of engineering structures, and nonlinear dynamic analysis for strong nonlinear system.

On the stability of Bresse system with one discontinuous local internal Kelvin–Voigt damping on the axial force

In this paper, we investigate the stabilization of a linear Bresse system with one discontinuous local internal viscoelastic damping of Kelvin–Voigt type acting on the axial force, under fully Dirichlet boundary conditions. First, using a general criteria of Arendt–Batty, we prove the strong stability of our system. Finally, using a frequency domain approach combined with the multiplier method, we prove that the energy of our system decays polynomially with different rates.

Modelling and Validation of Joint Properties for NVH Simulation Model of an Electrified Passenger Vehicle Drivetrain


 
 
 The constantly changing automotive market, which is characterized by the progressing electrification of vehicles, presents challenges with respect to the acoustic behaviour of powertrains. As indicated frequently, the characteristic noise of electric cars differs from that of conventional drives. In particular, energy dissipation of the assembled housing parts from material and joint damping; is an important aspect. In modelling the NVH behavior of electric vehicles or drivetrains in general, the breakdown of global material and local joint damping is not yet state of the art. Instead, measured global modal damping values from similar constructions are frequently used. Often, a constant degree of damping is defined for all modes. However, moderate changes in the geometry of components or in the load level can lead to severe fluctuations in the damping. In order to improve predictability and to be able to estimate the effects of constructive changes in natural frequency, mode shape, and damping, the goal will be to take into account the global material and local joint damping separately. For that, a local model which is able to take the joint properties into account has to be developed. The analytical based Iwan model for the contact interface was expanded upon to facilitate model updating against forced response measurements on a simple mass spring structure in one dimension and to extend the model from one-dimensional to three-dimensional.
 
 

On the stabilization for the high-order Kadomtsev-Petviashvili and the Zakharov-Kuznetsov equations with localized damping

<p style='text-indent:20px;'>In this paper we prove the exponential decay of the energy for the high-order Kadomtsev-Petviashvili II equation with localized damping. To do that, we use the classical dissipation-observability method and a unique continuation principle introduced by Bourgain in [<xref ref-type="bibr" rid="b3">3</xref>] here extended for the high-order Kadomtsev-Petviashvili. A similar result is also obtained for the two-dimensional Zakharov-Kuznetsov (ZK)equation. The method of proof works better for the ZK equation, so we were led to make some subtle modifications on it to include KP type equations. In fact, to reach a key estimate we use an anisotropic Gagliardo-Nirenberg inequality to drop the <inline-formula><tex-math id="M1">\begin{document}$ y $\end{document}</tex-math></inline-formula>-derivative of the norm.</p>

Exponential decay for the linear KdV with a rough localized damping

We show the exponential decay of the linear damped KdV equation on the real line, whenever the damping coefficient satisfies some locally integrable assumptions and has a positive lower bound on translates of a set with positive measure.

A novel damping based feature for rich resin defect detection in a four layer composite plate using S0 Lamb mode

ABSTRACT In this paper, local damping behaviour of S0 ultrasonic Lamb mode is investigated to determine the reason of amplitude reduction of signals come from a rich resin defect in a composite plate. A four-layer woven glass fibre-epoxy (WGF/epoxy) composite plate, containing a predefined rich resin area as the damage, has been manufactured and inspected with S0 Lamb mode via through transmission and pulse-echo method. Results have shown that there is a considerable amplitude reduction in the transmitted wave while a negligible damage reflected wave has been captured in the related receiver. An experimental based method has been employed in order to extract Rayleigh damping coefficients for the healthy composite plate, followed by a novel methodology to evaluate the damping coefficients at the defected area. Having calculated Rayleigh damping coefficients for both damaged and undamaged areas of the composite plate, several finite element simulations have been carried out, in order to quantify the wave amplitude reduction due to attenuation at the damage. The Amplitude Reduction Ratio (%ARR), obtained from numerical simulation matches closely with experimental ARR, represents that the proposed method for Rayleigh damping coefficients evaluation at the rich resin area can be used for further rich resin defect investigations.

Stability results of coupled wave models with locally memory in a past history framework via nonsmooth coefficients on the interface

In this paper, we investigate the stabilization of a locally coupled wave equations with local viscoelastic damping of past history type acting only in one equation via non smooth coefficients. First, using a general criteria of Arendt–Batty, we prove the strong stability of our system. Second, using a frequency domain approach combined with the multiplier method, we establish the exponential stability of the solution if and only if the two waves have the same speed of propagation. In case of different speed propagation, we prove that the energy of our system decays polynomially with rate t−1. Finally, we show the lack of exponential stability if the speeds of wave propagation are different.

Quantifying the hydrodynamic limit of Vlasov-type equations with alignment and nonlocal forces

In this paper, we quantify the asymptotic limit of collective behavior kinetic equations arising in mathematical biology modeled by Vlasov-type equations with nonlocal interaction forces and alignment. More precisely, we investigate the hydrodynamic limit of a kinetic Cucker–Smale flocking model with confinement, nonlocal interaction, and local alignment forces, linear damping and diffusion in velocity. We first discuss the hydrodynamic limit of our main equation under strong local alignment and diffusion regime, and we rigorously derive the isothermal Euler equations with nonlocal forces. We also analyze the hydrodynamic limit corresponding to strong local alignment without diffusion. In this case, the limiting system is pressureless Euler-type equations. Our analysis includes the Coulomb interaction potential for both cases and explicit estimates on the distance towards the limiting hydrodynamic equations. The relative entropy method is the crucial technology in our main results, however, for the case without diffusion, we combine a modulated macroscopic kinetic energy with the bounded Lipschitz distance to deal with the nonlocality in the interaction forces. The existence of weak and strong solutions to the kinetic and fluid equations is also obtained. We emphasize that the existence of global weak solution with the needed free energy dissipation for the kinetic model is established.

Asymptotic stability for a generalized nonlinear Klein-Gordon system

We consider a nonlinear Klein-Gordon system posed in an inhomogeneous medium Ω with smooth boundary ∂Ω subject to a local damping distributed around a neighborhood ω of the boundary according to the Geometric Control Condition, where the nonlinearities have not growth restrictions. We show that the energy of the system goes uniformly and exponentially to zero for all initial data of finite energy taken in bounded sets of finite energy phase-space.

Ergodicity effects on transport-diffusion equations with localized damping

The main objective of this paper is to study the time decay of transport-diffusion equation with inhomogeneous localized damping in the multi-dimensional torus. The drift is governed by an autonomous Lipschitz vector field and the diffusion by the standard heat equation with small viscosity parameter $\nu$. In the first part we deal with the inviscid case and show some results on the time decay of the energy using in a crucial way the ergodicity and the unique ergodicity of the flow generated by the drift. In the second part we analyze the same problem with small viscosity and provide quite similar results on the exponential decay uniformly with respect to the viscosity in some logarithmic time scaling of the \mbox{type $t\in [0,C_0\ln(1/\nu)]$}.

An adaptive fixture for suppress vibrations and measuring workpiece deformation of thin-walled casings

Thin-walled casings are key components in aerospace engines. Due to the poor rigidity, workpiece vibration and deformation become the main factors to limit cutting efficiency. Auxiliary support is usually used to increase the rigidity of the workpiece. This paper proposes a novel adaptive auxiliary fixture, which integrates vibration suppression and deformation measurement functions. The fixture provides an adaptive support force to increase the local stiffness and damping by using air cylinders. The integrated displacement sensors measure the deformation of the workpiece during and after machining. Cutting experiment verifies the effectiveness of the fixture in vibration suppressing and deformation measurements.

Electric steering of spin excitation in nanostructured synthetic antiferromagnet

Two or more ferromagnetic layers separated by metallic nanoscale spacers may couple antiferromagnetically forming a synthetic antiferromagnet (SAF) with versatile functionalities that are derived from their ferro- and antiferromagnetic nature. Here, we present a nanostructure consisting of a SAF deposited on a conductive substrate with strong spin–orbit coupling. As demonstrated analytically and fully numerically, the system exhibits exceptional points at which a charge current flowing in the substrate results in extraordinary characteristics of magnetic excitation and signal propagation in the SAF. We predict local electric steering, amplification, and damping of magnonic excitations by tuning the voltage on the substrate. Electrical amplification and local control of spin-pumping currents are also demonstrated. The results point to an alternative way for electrical spatiotemporal control of the nanoscale SAF with promising applications in spintronics and spin-based logic computing.

Stability of N-D transmission problem in viscoelasticity with localized Kelvin-Voigt damping under different types of geometric conditions

<p style='text-indent:20px;'>We investigate a multidimensional transmission problem between viscoelastic system with localized Kelvin-Voigt damping and purely elastic system under different types of geometric conditions. The Kelvin-Voigt damping is localized via non smooth coefficient in a suitable subdomain. It was shown that the discontinuity of the material coefficient along the interface elastic/viscoelastic can't assure an exponential stability of the total system. So, it is natural to hope for a polynomial stability result under certain geometric conditions on the damping region. For this aim, using frequency domain approach combined with a new multiplier technic, we will establish a polynomial energy decay estimate of type <inline-formula><tex-math id="M1">\begin{document}$ t^{-1} $\end{document}</tex-math></inline-formula> for smooth initial data. This result is obtained if either one of the geometric assumptions (A1) or (A2) holds (see below). Also, we establish a general polynomial energy decay estimate on a bounded domain where the geometric conditions on the localized viscoelastic damping are violated and we apply it on a square domain where the damping is localized in a vertical strip. However, the energy of our system decays polynomially of type <inline-formula><tex-math id="M2">\begin{document}$ t^{-2/5} $\end{document}</tex-math></inline-formula> if the strip is localized near the boundary. Else, it's of type <inline-formula><tex-math id="M3">\begin{document}$ t^{-1/3} $\end{document}</tex-math></inline-formula>. The main novelty in this paper is that the geometric situations covered here are richer and less restrictive than those considered in [<xref ref-type="bibr" rid="b31">31</xref>], [<xref ref-type="bibr" rid="b28">28</xref>], [<xref ref-type="bibr" rid="b19">19</xref>] and include in particular an example where the damping region is localized faraway from the boundary. Note that part of the results of this paper was announced in [<xref ref-type="bibr" rid="b22">22</xref>].</p>

Aeroelastic vibration analysis of wind turbine blade with Gurney flap

In this paper, based on the parametric design of 3 D blades including typical cross-section and natural frequency calculation of the equivalent model, an integral method for aerodynamic performance and aeroelastic vibration analysis of blade with Gurney flap is proposed. Parametric design and unstructured grid are used to pre-process the blades with/without the Gurney flap. The discrete aerodynamic performance parameters distribution including the lift, drag, and torsion coefficients calculated by Fluent is fitted by the nonlinear least square method based on the trust-region algorithm, and the natural frequencies of the rotating blade are accurately solved by the equivalent thin-walled beam model and Green’s functions. Based on the aerodynamic performance coefficients and natural frequencies obtained by the accurate calculation above, the aeroelastic response equation of typical cross-section considering local aerodynamic damping matrix is established, and the vibration response of blade in flap and torsion direction is further described. From the analysis results, it can be seen that the Gurney flap structure can not only bring higher lift performance to the blade, but also can reduce the amplitude and vibration range of aeroelastic vibration, improve the aeroelastic stability of the blade, and prove the effectiveness of Gurney flap.

Stochastic dynamic for an extensible beam equation with localized nonlinear damping and linear memory

In this paper, we concerned to prove the existence of a random attractor for the stochastic dynamical system generated by the extensible beam equation with localized non-linear damping and linear memory defined on bounded domain. First we investigate the existence and uniqueness of solutions, bounded absorbing set, then the asymptotic compactness. Longtime behavior of solutions is analyzed. In particular, in the non-autonomous case, the existence of a random attractor attractors for solutions is achieved.

Protecting Qutrit-Qutrit Entanglement Under Decoherence via Weak Measurement and Measurement Reversal

We investigate the entanglement protection of a qutrit-qutrit system under local amplitude damping channels by weak measurement and measurement reversal. We examine the Δ-type of initially entangled qutrit-qutrit states. We find that the entanglement decays with the decoherence strength increasing for the qutrit-qutrit state. Therefore, we focus on how to protect the quantum entanglement from decoherence by weak measurement and measurement reversal. Our results show that we can prevent amplitude damping decoherence by the combination of prior weak measurement and post optimal measurement reversal comparing with the dynamics without protection. Regardless of the value of decoherence, the protection scheme has better effect on the kind of V-configuration. And with the increase of decoherent strength, the difference is more obvious. Another interesting result is that the enhancement of the entanglement is very weak when decoherent strength is zero.

Formulation of Localized Damping Models for Large Displacement Analysis of Single-Degree-of-Freedom Inelastic Systems

ABSTRACT Issues with traditional implementations of tangent-stiffness-proportional damping model are associated with negative damping forces that develop in the post-yield range when the system stiffness becomes negative and with unrealistic damping forces arising at degrees of freedom undergoing second-order movements only. To overcome these issues, this paper proposes a localized formulation of the tangent-stiffness-proportional damping model which can be used in nonlinear dynamic analysis of simple inelastic systems. Results show the consistency of the local and global damping formulations in small displacements and the effectiveness of the localized tangent-stiffness-proportional damping model in the presence of material and geometrical nonlinearities.