A unified Fourier series solution for vibration analysis of FG-CNTRC cylindrical, conical shells and annular plates with arbitrary boundary conditions

This research paper presents a unified Fourier series solution to solve the vibration problem of functionally graded carbon nanotube-reinforcement composite (FG-CNTRC) cylindrical shells, conical shells and annular plates subjected to general boundary conditions, so as to enrich the existing research results on FG-CNTRC structures. Utilizing a micro-mechanical model based on the developed rule of mixtures, the effective material properties of the FG-CNTRC structures which is strengthened by single-walled carbon nanotubes (SWCNTs) are scrutinized. The first-order shear deformation theory (FSDT) and the virtual boundary method are applied to achieve the energy expressions of FG-CNTRC structures. On the basis of that, the unified Fourier series solution in conjugation with the modified Fourier series and Ritz method, is utilized to receive characteristic equation of the structural vibration. The correctness, convergence and several advantages of the present methodology are verified by numerous numerical examples. Furthermore, some novel numerical results, including the vibration results of FG-CNTRC cylindrical shells, conical shells and annular plates accompanied with classical boundary, elastic boundary, classical-elastic mixed boundary and parameterized results of structure and material parameters, will be presented for future researchers.