Analytical solution of stability and vibration problem of clamped cylindrical shells containing functionally graded layers within shear deformation theory

Abstract

The aim of the study is to present a new approach to the analytical solution of the vibration and stability problem of clamped sandwich cylindrical shells (SCSs) covered by functionally graded (FG) coatings under an axial compressive load in the framework of shear deformation theory (ST). After modeling the micro and macro mechanical properties of FG coated SCSs with various configurations, the constitutive relations and basic equations are derived depending on the stress, deflection and two angles of rotation functions using modified Donnell type theory. An attempt is made to analytically solve the fundamental differential equations for SCSs covered by FG coatings using novel approximation functions satisfying the clamped boundary conditions. Three different shear stress functions (SSFs) such as parabolic shear stress function (Par-SSF), cosine-hyperbolic shear stress function (Cos-Hyp-SSF) and uniform shear stress function (U-SSF) are used in the analysis. After confirming the accuracy of the obtained results, the influences of coating profiles, volume fractions and layer arrangement variations on the critical parameters for three different transverse shear stress functions are investigated in detail.