Free vibration analysis of FG-CNT reinforced composite straight-sided quadrilateral plates resting on elastic foundations using the IMLS-Ritz method

Abstract

The vibration behavior was investigated of thin-to-moderately thick functionally graded carbon nanotube (FG-CNT) reinforced composite quadrilateral plates resting on elastic foundations. In the study, transverse shear and rotatory inertia were incorporated through first-order shear deformation theory. The improved moving least-squares-Ritz method was employed to derive the eigenvalue equation of the plate vibration. The study examined the effects of the elastic Winkler medium, CNT ratios, distributions of CNTs, boundary conditions, side angles, thickness-to-width ratios, and the relative plate aspect ratios on the vibration response of the FG-CNT reinforced composite plates. A set of vibration frequencies and mode shapes for the FG-CNT reinforced composite quadrilateral plates is presented. Additionally, a comprehensive parametric study and vivid mode shape plots demonstrate details of the vibration spectrum of the FG-CNT reinforced composite plates.

Vibratory response and acoustic radiation behavior of laminated functionally graded composite plates in thermal environments

“…The expressions are as follows [15,16] where E11cnt, G12cnt, Em and Gm are Young’s modulus and shear modulus of CNT and matrix, η1, η2 and η3 are CNT efficiency parameters, Vm is the volume fraction of matrix. In addition, the total volume of the composite is taken as the sum of the individual constituent of the CNT and the polymer matrix volume fractions and can be conceded as [14] …”

“…Zhang et al. [14] employed the IMLS-Ritz method to study the free vibration of FG-CNT reinforced composite straight-sided quadrilateral plates resting on elastic foundations. Following the work of Zhang et al., Selim et al.…”

Frequency optimization of laminated functionally graded carbon nanotube reinforced composite quadrilateral plates using smoothed FEM and evolution algorithm

“…The quadrilateral plate with a single CNTRC layer was previously analyzed by some researchers in literature 6,12,13 and the angle-ply [45 o /−45 o /45 o /−45 o /45 o ] laminated quadrilateral plate was studied by Malekzadeh and Zarei. 12 The geometric parameters of these plates are given by a/h = 10, b/a = 0.8, c/a = 0.7, γ=75∘,β=70∘ and the material parameters of these plates are referred to in the previous studies.…”

“…In this section, several examples are implemented to validate the efficiency and reliability of the proposed approach. First, the accuracy and convergence of the CS-DSG3 method for analyzing the free vibration of the laminated FG- The quadrilateral plate with a single CNTRC layer was previously analyzed by some researchers in literature 6,12,13 and the angle-ply [45 o /À45 o /45 o /À45 o /45 o ] laminated quadrilateral plate was studied by Malekzadeh and Zarei. 12 The geometric parameters of these plates are given by a/h ¼ 10, b/a ¼ 0.8, c/ a ¼ 0.7, ¼ 75 , ¼ 70 and the material parameters of these plates are referred to in the previous studies.…”

“…4 In the last few years, many studies relating to the CNTreinforced composite (CNTRC) structures have been published in the literature. For example, free vibration analysis of CNTRC beams and plates, [5][6][7][8][9][10][11][12][13][14][15][16] buckling analysis of CNTRC beams and plates, [17][18][19][20] static and free vibration analysis of laminated CNTRC plates, 1,21 free vibration of CNTRC cylindrical panels, beams and plates integrated with piezoelectric layers. [22][23][24] A comprehensive review of the mechanical analysis of CNTRC structures is reported by Lei et al 25 Most of the previous studies focused on the mechanical analysis of the CNTRC structures with simple models, e.g.…”