A semi-analytical method for vibration analysis of functionally graded carbon nanotube reinforced composite doubly-curved panels and shells of revolution

The object of this paper is to present a novel semi-analytical method and its associated applications for linear vibration analyses of functionally graded carbon nanotube reinforced composite (FG-CNTRC) doubly-curved panels and shells of revolution on with arbitrary boundary conditions. Distribution of the carbon nanotubes through the thickness of the structures may be uniform or functionally graded and four types of the CNTs distribution are considered in this paper. Properties of the composite media are determined by a refined rule of mixtures approach which contains the efficiency parameters. The translation and rotation displacements of the doubly-curved structures are uniformly expressed as the superposition of a standard cosine Fourier series and several auxiliary functions introduced to eliminate all potential discontinuities of the original displacement function and its derivatives at the edges. Based on that, the energy expression of the FG-CNTRC doubly-curved panels and shells of revolution is examined where the first-order shear deformation elasticity theory is considered. Lastly, to solve the natural frequencies as well as the associated mode shapes by means of the Ritz-variational energy method. Unlike other existing methods, the proposed method is capable of handling various combinations of boundary constraints in a unified fashion, including free, simply-supported, clamped and elastic-supported boundary conditions. Comprehensive studies on the convergence, accuracy, stability and efficiency of the method are derived via the comparison with existing results reported in publications. The parametric studies concerning the influence of the geometrical parameters, CNTs distributions, volume fraction of CNTs as well as boundary restraint parameters on free vibration of FG-CNTRC doubly-curved panels and shells of revolution is also investigated in detail.