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

New Methods for Nonlinear Damping Identification of Damping Alloy

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.

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

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

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.