Numerical method for nonlinear complex eigenvalues problems depending on two parameters: Application to three-layered viscoelastic composite structures

Authors

K. Akoussan, H. Boudaoud, E. M. Daya, Y. Koutsawa, and E. Carrera

Reference

Mechanics of Advanced Materials and Structures, vol. 25, no. 15-16, pp. 1361-1373, 2018

Description

The design of high damping composite viscoelastic sandwich structures (CVSS) requires continuous study of damping properties according to some parameters. The common design parameters which directly affect the damping properties of composite viscoelastic sandwich structures are the fibers orientation and the thicknesses of the composite layers. However, until now there is no method for studying continuously the influences of any design parameter on the damping properties of CVSS. Also, to study the influence of a design parameter on damping properties of CVSS, computations are made for various discrete values of this parameter. These calculations qualified incremental are very expensive in computation time and do not allow to follow continuously the effects of the parameter on the damping properties of CVSS. In order to tackle these problems, we propose in this paper, a numerical method for studying the damping properties variation of CVSS according to a chosen modeling parameter, through the resolution of a generic residual complex nonlinear eigenvalues problems having frequency dependence and the modeling parameter which describes a study interval. This method is based on the asymptotic numerical method, automatic differentiation, homotopy technic and continuation. An application is performed to study the variation of the damping properties of a three layered symmetric viscoelastic sandwich plates according to the fibers orientation of their orthotropic faces layers.

Link

doi:10.1080/15376494.2017.1286418