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

Komlan Akoussan

doi:10.1080/15376494.2017.1286418

Return

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

2017-03-17

PRE

DOI：10.1080/15376494.2017.1286418

Original

Original request for help

Save

Abstract

En 中文

The design of high-damping composite viscoelastic sandwich structures (CVSS) requires continuous study of damping properties according to some parameters. The common design parameters that directly affect the damping properties of CVSS are the fibers' orientation and the thicknesses of the composite layers. However, until now there has been no method for continuously studying the influences of any design parameter on the damping properties of CVSS. Also, to study the influence of a design parameter on the damping properties of CVSS, computations are made for various discrete values of this parameter. These calculations are qualified incrementally, and 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 article 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 a modeling parameter that describes a study interval. This method is based on the asymptotic numerical method, automatic differentiation, homotopy technique 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.

Keywords:

Nonlinear eigenvalue problem

asymptotic numerical method

automatic differentiation

homotopy

continuation

viscoelastic structures

AI Summary

Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.