On the nonlinear vibration of heterogenous orthotropic shallow shells in the framework of the shear deformation shell theory


Sofiyev A. H. , Turan F.

THIN-WALLED STRUCTURES, vol.161, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 161
  • Publication Date: 2021
  • Doi Number: 10.1016/j.tws.2020.107181
  • Title of Journal : THIN-WALLED STRUCTURES

Abstract

In this study, the nonlinear vibration of heterogeneous orthotropic shallow shells (HTOSSs) is investigated. The first order shear deformation theory (FSDT) is generalized to the non-linear vibration problem of HTOSSs for the first time. After the presentation of visual and mathematical models of HTOSSs, the von-Karman type nonlinear basic relations of HTOSSs are created and then the non-linear equations of motion are derived depending on the rotation angles, Airy stress and deflection functions. Then, applying superposition, Galerkin and semi-inverse methods to the nonlinear differential equations, the frequency-amplitude relation of non-linear vibration of HTOSSs is obtained. The frequency-amplitude relation within the classical shell theory (CST) is obtained in a special case. After checking the reliability of the proposed formulation and the accuracy of the results in accordance with the available literature, a systematic study is aimed at checking the sensitivity of the dynamic response to the shear stresses, nonlinearity, heterogeneity, orthotropy and different geometric characteristics.