Nonlinear Dynamic Behavior of Hyperbolic Paraboloidal Shells Reinforced by Carbon Nanotubes with Various Distributions

YUSUFOĞLU E., Avey M.

Journal of Applied and Computational Mechanics, vol.7, no.2, pp.913-921, 2021 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.22055/jacm.2021.36043.2783
  • Journal Name: Journal of Applied and Computational Mechanics
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Directory of Open Access Journals
  • Page Numbers: pp.913-921
  • Keywords: Amplitude-frequency relationship, CNTs, Hyperbolic paraboloidal shallow shells, Nonlinear dynamics
  • Uşak University Affiliated: Yes

Abstract

The analytical solution of the nonlinear dynamic behavior of CNT based hyperbolic paraboloidal shallow shells (HYPARSSs) with various distribution shapes is presented. A theoretical model was created for HYPARSSs reinforced with CNTs using the von Kármán -type nonlinearity. Then the nonlinear basic equations are reduced to ordinary nonlinear differential equations using Galerkin methods and the correlation for frequency-amplitude relationship is obtained using the Grigolyuk method. In addition, the nonlinear frequency/linear frequency (NL/L) ratio is determined as a function of amplitude. Comparisons with reliable results in the literature were made to test the accuracy of the formulas. Finally, a systematic investigate is performed to control the influences of CNTs in the matrix, CNT distribution types and nonlinearity on the vibration frequency-amplitude relationship.