Optimal decay of an abstract nonlinear viscoelastic equation in Hilbert spaces with delay term in the nonlinear internal damping

2020 ◽  
pp. 1-30
Author(s):  
Houria Chellaoua ◽  
Yamna Boukhatem ◽  
Baowei Feng
Keyword(s):  
Hilbert Spaces ◽  
Nonlinear Damping ◽  
Delayed Feedback ◽  
Internal Damping ◽  
General Decay Rate ◽  
Delay Term ◽  
Nonlinear Viscoelastic ◽  
Optimal Decay ◽  
Viscoelastic Equation ◽  
Nonlinear Internal Damping

In this paper, we consider a second-order abstract viscoelastic equation in Hilbert spaces with delay term in the nonlinear internal damping and a nonlinear source term. Under some suitable assumptions on the weight of the delayed feedback, the weight of the non-delayed feedback and the behavior of the relaxation function, we establish two explicit and general decay rate results of the energy by introducing a suitable Lyaponov functional and some properties of the convex functions. Moreover, we give some applications and examples. This work generalizes the previous results without time delay term to those with delay in the nonlinear damping.

scholarly journals General decay rate of a weakly dissipative viscoelastic equation with a general damping

2020 ◽  
Vol 40 (6) ◽  
pp. 647-666
Author(s):  
Khaleel Anaya ◽  
Salim A. Messaoudi
Keyword(s):  
Decay Rate ◽  
Wide Class ◽  
Nonlinear Damping ◽  
Numerical Results ◽  
General Decay ◽  
General Decay Rate ◽  
Relaxation Functions ◽  
Viscoelastic Equation

In this paper, we consider a weakly dissipative viscoelastic equation with a nonlinear damping. A general decay rate is proved for a wide class of relaxation functions. To support our theoretical findings, some numerical results are provided.

scholarly journals Global Nonexistence for a Nonlinear Viscoelastic Equation with Nonlinear Damping and Velocity-Dependent Material Density

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Jian Dang ◽  
Qingying Hu ◽  
Hongwei Zhang
Keyword(s):  
Global Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlinear Damping ◽  
Initial Energy ◽  
Material Density ◽  
Nonexistence Result ◽  
Nonlinear Viscoelastic ◽  
Global Nonexistence ◽  
Viscoelastic Equation

We consider the initial boundary value problem of a nonlinear viscoelastic equation of Kirchhoff-type with nonlinear damping and velocity-dependent material density. We establish a nonexistence result of global solutions with positive initial energy and negative initial energy, respectively.

Research on the Identification of Nonlinear Internal Damping and Kinematical Joint Damping of Mechanical Systems

Tribology ◽  
2005 ◽  
Author(s):  
Ziying Wu ◽  
Hongzhao Liu ◽  
Lilan Liu ◽  
Daning Yuan
Keyword(s):  
Free Vibration ◽  
Coulomb Friction ◽  
Characteristic Curve ◽  
Nonlinear Damping ◽  
Internal Damping ◽  
Window Method ◽  
Joint Damping ◽  
Alloy Material ◽  
Nonlinear Internal Damping ◽  
Simultaneous Identification

A simultaneous identification method of the nonlinear internal damping of alloy material and the Coulomb friction in the kinematical joints in a mechanical system is put forward in this paper. The free vibration differential equation of a vibration system with these two kinds of damping is established. According to the free vibration response signal, the nonlinear internal damping characteristic curve and the Coulomb friction are got by using the moving rectangle window method. Several types of the nonlinear damping models are investigated in simulations. The validity and accuracy of the proposed method are illustrated by the good simulation results, in which the computing accuracy of the nonlinear internal damping is higher than that of the Coulomb damping in kinematical joints.

Stability of a Simple Rotor With Nonlinear Internal Damping

1991 ◽  
Author(s):  
Erik Medgyesi
Keyword(s):  
Stability Analysis ◽  
Numerical Methods ◽  
Hysteresis Loop ◽  
Nonlinear Damping ◽  
Internal Damping ◽  
Nonlinear Internal Damping

Abstract The paper contains a stability analysis of the assumed inplane motion of a simple rotor with nonlinear damping, the form of which can approximate different hysteresis loop shapes. The analysis is carried so far as possible without resorting to numerical methods.

New Methods for Nonlinear Damping Identification of Damping Alloy

2007 ◽  
Vol 129 (5) ◽  
pp. 678-684 ◽  
Author(s):  
Ziying Wu ◽  
Hongzhao Liu ◽  
Lilan Liu ◽  
Daning Yuan
Keyword(s):  
Stress Field ◽  
Autoregressive Model ◽  
Nonlinear Behavior ◽  
Nonlinear Damping ◽  
Internal Damping ◽  
New Methods ◽  
Uniform Stress Field ◽  
Nonuniform Stress Field ◽  
Nonlinear Internal Damping ◽  
Versus Strain

This paper presents two methods for the identification of nonlinear internal damping of alloy. One is the moving autoregressive model (MARM) method, and the other is the time-varying autoregressive model (TVARM) method. These procedures have been successfully implemented on two numerical examples. Comparison between simulation results demonstrates that the computation accuracy of the TVARM method is higher than that of the MARM method. In the experiments, the internal damping properties of the alloy Al-33Zn-6Si are researched, employing the rectangle beam with a nonuniform stress field and the trapezoid beam with a quasi-uniform stress field, respectively. Experimental results show that the internal damping of the alloy increases with the increasing strain and appears a nonlinear behavior. Moreover, the damping values of the trapezoid beam are relatively higher than those of the rectangle beam. Compared to the MARM method, the TVARM method can give a better description of nonlinear damping because the relation curve of loss factor versus strain obtained by the TVARM method is smoother than that obtained by the MARM method.

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