A unified formulation for free vibration of functionally graded carbon nanotube reinforced composite spherical panels and shells of revolution with general elastic restraints by means of the Rayleigh-Ritz method

In this article, the free vibration of the functionally graded carbon nanotube reinforced composite spherical panels and shells of revolution with general elastic restraints is analyzed on the basis of the first-order shear deformation theory. First, the general boundary condition is simulated by using a set of artificial springs along all the edges and the general is obtained by changing the stiffness of the corresponding kinds of springs. Then, the admissible function is expressed by the improved Fourier series which is the combination of a standard double cosine Fourier series and several auxiliary functions introduced to remove all potential discontinuities of the original displacement and its derivatives at the edges. Finally, the equations of motion of the FG-CNT reinforced composite spherical panels and shells of revolution with general boundary conditions are derived by extending the Rayleigh-Ritz method. For the validation of the present method, several comparison studies are conducted and its convergence is also checked meanwhile. In addition, the effect of the volume fraction of CNTs, distribution type of CNTs, boundary restraint parameters on the vibration characteristics are also presented. POLYM. COMPOS., 39:E924-E944, 2018. (c) 2017 Society of Plastics Engineers