Primary resonance of double-curved nanocomposite shells using nonlinear theory and multi-scales method: Modeling and analytical solution

Avey M., Sofiyev A., Fantuzzi N., KURUOĞLU N.

International Journal of Non-Linear Mechanics, vol.137, 2021 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 137
  • Publication Date: 2021
  • Doi Number: 10.1016/j.ijnonlinmec.2021.103816
  • Journal Name: International Journal of Non-Linear Mechanics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Computer & Applied Sciences, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Damping, Excitation, Multi-scales method, Nanocomposite shells, Nonlinear forced frequency, Primary resonance
  • Uşak University Affiliated: Yes

Abstract

In this article, the forced vibration of double-curved nanocomposite shells under a time dependent excitation is studied using nonlinear shell theory and multi-scales method in primary resonance. The nanocomposite representative volume element consists of two phases, including carbon nanotube (CNT) and matrix. By generalizing the Ambartsumyan's first order shear deformation shell theory (FSDT) to the heterogeneous nanocomposite shells, the nonlinear partial differential equations are derived. Then, the problem is reduced to the nonlinear forced vibration of damped nanocomposite shells with quadratic and cubic nonlinearities. For the occurrence of the primary resonance, the damping, nonlinearity, and excitation terms in the disturbance circuit are reduced to the same order. Applying the multi-scales method to nonlinear ordinary differential equation, nonlinear frequency–amplitude dependence in primary resonance is obtained.