On the Nonlinear Vibration of Heterogenous Orthotropic Shallow Shells in the Framework of the Shear Deformation Shell Theory

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.