Modeling and solution of eigenvalue problems of laminated cylindrical shells consisting of nanocomposite plies in thermal environments

• Published in: Archive of applied mechanics (1991) Vol. 94; no. 10; pp. 3071 - 3099
• Main Author: Sofiyev, Abdullah H.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2024; Springer Nature B.V
• Subjects: Axial loads; Classical Mechanics; Closed form solutions; Cylindrical shells; Eigenvalues; Engineering; Functionally gradient materials; Kirchhoff theory; Laminates; Layers; Material properties; Mathematical analysis; Molecular dynamics; Nanocomposites; Original; Parameter estimation; Partial differential equations; Shear deformation; Temperature dependence; Theoretical and Applied Mechanics; Thermal environments; Thickness; Time dependence; Shear deformation theory; Axial critical load; Thermal effect; Nanocomposite plies; Laminated cylindrical shells; Frequency parameter
• ISSN: 0939-1533; 1432-0681
• DOI: 10.1007/s00419-024-02658-7

This work is dedicated to the modeling and solution of eigenvalue problems within shear deformation theory (SDT) of laminated cylindrical shells containing nanocomposite plies subjected to axial compressive load in thermal environments. In this study, the shear deformation theory for homogeneous laminated shells is extended to laminated shells consisting of functionally graded (FG) nanocomposite layers. The nanocomposite plies of laminated cylindrical shells (LCSs) are arranged in a piecewise FG distribution along the thickness direction. Temperature-dependent material properties of FG-nanocomposite plies are estimated through a micromechanical model, and CNT efficiency parameters are calibrated based on polymer material properties obtained from molecular dynamics simulations. After mathematical modeling, second-order time-dependent and fourth-order coordinate-dependent partial differential equations are derived within SDT, and a closed-form solution for the dimensionless frequency parameter and critical axial load is obtained for first time. After the accuracy of the applied methodology is confirmed by numerical comparisons, the unique influences of ply models, the number and sequence of plies and the temperature on the critical axial load and vibration frequency parameter within SDT and Kirchhoff–Love theory (KLT) are presented with numerical examples.