Nonlinear vibrations of variable thickness curved panels made of multi-scale epoxy/fiberglass/CNT material using Jacobi elliptic functions

Abstract

This article deals with nonlinear vibration study of variable thickness cylindrical panels made of multi-scale composite materials containing epoxy matrix, glass fibers, and carbon nanotubes (CNTs). The elastic properties of multi-scale material have been defined in the context of 3D Mori-Tanaka scheme considering unidirectional aligned macro-fibers and randomly oriented CNTs. It is considered that the panel thickness is varying in axial direction and may have linear and parabolic changes. The governing equations of variable thickness curved panel have been stablished using thin shell theory containing geometric nonlinearity. Then, Jacobi elliptic functions are proposed for solving the governing equations since they leads to exact frequency-amplitude curves of the curved panels. It is reported that frequency-amplitude curves are varying with the changes of CNT weight fraction, fiber orientation, fiber volume, variable thickness parameters, panel curvature radius, and length-to-radius ratio of CNTs.

Keywords:

• Nonlinear vibration
• cylindrical shell
• shell theory
• nano-composite material
• curved panel
• Jacobi elliptic functions

Acknowledgment

The first and second authors would like to thank FPQ (Fidar project Qaem) for providing the fruitful and useful help.