Vibration analysis of cantilever FG-CNTRC trapezoidal plates

Abstract

In this paper, a numerical solution is presented for free vibration analysis of cantilever functionally graded carbon nanotubereinforced trapezoidal plates. The plate is modeled based on the first-order shear deformation theory, effective mechanical properties are estimated according to extended rule of mixture, and the set of governing equations and boundary conditions are derived using Hamilton's principle. Generalized differential quadrature method is employed, and natural frequencies and corresponding mode shapes are derived numerically. Convergence and accuracy of the solution are confirmed, and effect of various parameters on the natural frequencies is investigated including geometrical characteristics, volume fraction and distribution of carbon nanotubes. Because of similarity of the studied model with the wing, tail and fin of aircrafts and missiles, results of this paper can be useful in design and analysis of aeronautic vehicles in the near future. It is worth mentioning that results of this paper may serve as benchmarks for future studies.

Free Vibration Analysis of Trapezoidal Bi-Stable Laminates Supported at the Elastic Midpoint of the Median Line

“…Traditional numerical methods can only compute the modes of square laminated plates and cannot generate mode shapes for complex shapes such as trapezoidal plates. To address this limitation, the original trapezoidal shape in a physical coordinate system is mapped onto a square in the ξ-η coordinate system [31]; see Figure 2.…”

“…Traditional numerical methods can only compute the modes of square laminated plates and cannot generate mode shapes for complex shapes such as trapezoidal plates. To address this limitation, the original trapezoidal shape in a physical coordinate system is mapped onto a square in the ξ-η coordinate system [31]; see Figure 2. Assuming the image before mapping is H(x, y) and the image after mapping is H ( x, ȳ), the following transformation relationship exists between the images before and after mapping:…”

Effects of non-uniformity in thickness and volume fraction of nanofillers on the flutter characteristics of nanocomposite cantilever trapezoidal plates

“…It was revealed by them that a higher volume fraction of ceramic brings about better aeroelastic stability. Majidi et al 27,28 studied the free vibration and supersonic flutter analyses of a cantilever polymeric trapezoidal plate enriched with CNTs. They discovered that subjoining a low percentage of CNTs increases the natural frequencies and enhances the aeroelastic stability.…”

Four-node quadrilateral C 0-element based on cell-based smoothed strains strategy and third-order shear deformation theory for functionally graded carbon nanotube reinforced composite plates

“…In the past few decades, carbon nanotubes (CNTs) with their outstanding features have made a big step forward for materials science. They have some advantages related to their remarkable mechanical, thermal and electrical properties [1][2][3][4][5][6][7]. From the structural review, their material properties are listed as high strength, low density, stiffness, etc.…”