Vibration response of shear deformable laminated truncated conical shells formed by nano-composite laminae in thermal environments

There are very few studies on modeling and solution of eigenvalue problems of truncated conical shells formed by functionally graded nanocomposite (FG-NC) laminae in thermal environments. One of the biggest difficulties is to adapt the theories proposed for homogeneous laminated truncated conical shells to the FG-NC laminated truncated conical shells (LTCSs), i.e. to extend this theory. In this study, extended shear deformation theory (ST) is proposed for the formulation and modeling of the vibration problem of LTCSs formed by FG-NC laminae in thermal environments. In this sense, the presented work is not only original, but the proposed extended theory can also be used to solve different problems for laminated conical shells. LTCSs are made of perfectly bonded carbon nanotubes (CNTs) reinforced composite laminae. Fundamental relationships and equations of the motion for LTCSs composed of NC laminae in thermal environments are derived and the expressions of dimensionless frequencies within ST and classical theory (CT) are obtained. Numerical comparisons with published results are made to validate the correctness of the present approach. Detailed analysis and interpretations are performed by comparing with CT.