A Dynamic Analysis of Randomly Oriented Functionally Graded Carbon Nanotubes/Fiber-Reinforced Composite Laminated Shells with Different Geometries

Abstract

The present study demonstrates the free vibration behavior of composite laminated shells reinforced by both randomly oriented single-walled carbon nanotubes (SWCNTs) and functionally graded fibers. The shell structures with different principal radii of curvature are considered, such as cylindrical, spherical, elliptical–paraboloid shell, hyperbolic–paraboloid shell, and plate. The volume fraction of the fibers has a linear variation along the shell thickness from layer to layer, while the volume fraction of CNTs is constant in all shell layers and uniformly distributed. The fiber-reinforced elements are distributed with three functions which are V-distribution, O-distribution, and X-distribution in addition to the uniform distribution. A numerical analysis was carried out systematically to validate the proposed solution. A new analytical solution is presented based on the Galerkin approach for shells and is exploited to illustrate the influence of some factors on the free vibration behavior of CNTs/fibe-reinforced composite (CNTs/F-RC) laminated shells, including the distributions and volume fractions, various boundary conditions, and geometrical properties of the reinforcement materials. The proposed solution is shown to be an effective theoretical tool to analyze the free vibration response of shells.

Vibrations of Nonlocal Polymer-GPL Plates at Nanoscale: Application of a Quasi-3D Plate Model

“…A similar conclusion is reported by [48,49]. Another deduction can be stated that, due to the fact that, in X model, GPL-rich layers are located at a greater distance from the middle layer, X-GPLRC nanoplates have greater flexural rigidity and, as a result, higher frequencies [50][51][52][53][54]. On the other hand, in the O- Another deduction can be stated that, due to the fact that, in X model, GPL-rich layers are located at a greater distance from the middle layer, X-GPLRC nanoplates have greater flexural rigidity and, as a result, higher frequencies [50][51][52][53][54].…”

“…Another deduction can be stated that, due to the fact that, in X model, GPL-rich layers are located at a greater distance from the middle layer, X-GPLRC nanoplates have greater flexural rigidity and, as a result, higher frequencies [50][51][52][53][54]. On the other hand, in the O- Another deduction can be stated that, due to the fact that, in X model, GPL-rich layers are located at a greater distance from the middle layer, X-GPLRC nanoplates have greater flexural rigidity and, as a result, higher frequencies [50][51][52][53][54]. On the other hand, in the O-GPLRC plate, the arrangement of the GPL-rich and GPL-poor layers is the opposite of the X model, as a result of which the lowest flexural rigidity is obtained, and that is why we see the lowest frequencies in association with the O model.…”

Analysis of torsional buckling of a cylindrical sandwich shell with a magnetorheological fluid core layer

“…where σ i xx and σ i θθ indicate the initial normal stresses in the x and θ axes, respectively, and τ i xθ is the initial shear stress. The variation in the external loads applied to the top and bottom face sheets are defined as equation ( 14) [42]: (14) where N xxj i and N θθj i are the in-plane loads per unit length applied to the edge of the top and bottom face sheets, and N xθj i is the critical shear load. If initial stresses are eliminated, the governing equations are reduced to equation ( 15) below:…”

“…Abdelhaffez et al [13] analyzed the buckling of unidirectional, bidirectional, and tridirectional spherical FGM-coated nano shells under biaxial loads. Melaibari et al [14] studied the free vibration of laminated composite shells reinforced by both randomly oriented single-walled carbon nanotubes and FGM fibers.…”

Free Vibration Analysis of Composite Cylindrical Shell Reinforced with Silicon Nano-Particles: Analytical and FEM Approach

“…The composite materials investigation in previous years in different applications was due to the high strength to weight ratio; therefore, this investigation for composite materials being modified for mechanical properties for composite materials by reinforcement with different fibers, and then modified for composite by reinforcement with varying concentrations of powder, [1][2][3]. Then, the investigated different composite materials structures are as a beam, plate, and other facilities with various applications, such as the vibration of the plate with different parameters, [4][5], buckling for a plate with multiple parameters, [6][7][8], stress analysis for other structures, fatigue characterization with different applications, [9], and prosthetic and orthotics structures.…”