FGM and laminated doubly curved shells and panels of revolution with a free-form meridian: A 2-D GDQ solution for free vibrations

Free vibrations of non-uniform CNT/fiber/polymer nanocomposite beams

“…GDQ technique, as an efficient numerical technique, is implemented for solving partial differential equations, especially in the field of solid mechanics [37][38][39][40][41]. Here, this method is utilized to obtain the natural frequencies of non-uniform CNTFPC beam.…”

Free Vibration Analysis of Functionally Graded Porous Doubly-Curved Shells Based on the First-Order Shear Deformation Theory

“…A brief review is presented here for the sake of completeness. Tornabene [11] and Tornabene et al [12,13] investigated the free vibrations of anisotropic doubly-curved shells of revolution defined by free-form meridians. Viola et al [14] and Tornabene et al [15,16] employed a higher-order formulation, based on an equivalent single layer approach, for the mechanical analysis of laminated composite shell structures characterized by curved surfaces as reference domains.…”

Free vibration of functionally graded parabolic and circular panels with general boundary conditions

“…Pradyumna and Bandyopadhyay [12] used the finite element method to study the free vibration of functionally graded curved panels with classical boundary conditions by using a higher-order shear deformation theory. Tornabene and his team [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] extended the generalized differential quadrature (GDQ) method for the free vibration analysis of functionally graded circular and parabolic panels and shells of revolution with classical boundary conditions. Other related research results with the layered composite parabolic and circular panels can be seen in Refs [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46].…”