The Effect of Volume Fraction of Single-Walled Carbon Nanotubes on Natural Frequencies of Polymer Composite Cone-Shaped Shell Made from Poly(Methyl Methacrylate)

A H Meysami,V Bagheri,I Fakhari Golpayegani,H Razavi

doi:10.1155/2017/7345438

Abstract

In this paper, the effect of volume fraction of single-walled carbon nanotubes on natural frequencies of polymer composite cone-shaped shells made from Poly(Methyl Methacrylate) (PMMA) is studied. In order to determine the characterization of materials reinforced with nanoparticles, the molecular dynamics and mixture rule has been used. The motion equations of composite shell based on the classical thin shells theory using Hamilton’s principle are obtained. Then, using the Ritz method, approximate analytical solution of the natural frequency is presented. Results indicate that the nanotubes have a noticeable effect on the natural frequencies.

Highlights

One of the most important phenomena in shells sciences is vibration due to dynamic loading, either one cyclic or impact loading
Composite plates and shells reinforced with single-walled carbon nanotube (SWCNT) are used widely in industry
In general the vibration solution for polymer composite cone-shaped shell made from Poly(Methyl Methacrylate) (PMMA) is hard

Summary

Introduction

One of the most important phenomena in shells sciences is vibration due to dynamic loading, either one cyclic or impact loading. Newly fabricated composites based on PMMA (whereas PMMA is used as matrix) are of high concern to the researchers In this regard, Ke et al [33] and Ansari et al [34] have investigated, respectively, the nonlinear free vibration and nonlinear forced vibration behavior of nanocomposite beams reinforced with singlewalled carbon nanotube (SWCNT) based on Timoshenko beam theory. Zhang and Liew [37] have proposed an improved moving least-squares (IMLS) approximation for the field variables in the functionally graded CNT plates They [38] have studied that using the element-free kp-Ritz method based on first-order shear deformation theory. Formica et al [44] have studied the vibrational properties of composites reinforced with carbon nanotubes (CNTs), using a continuum model, based on the view of Mori et al.’s theory [45, 46]. The effect of volume fraction of nanotubes and the effect of vertex angle of the cone on the natural frequencies are investigated

Theoretical Approach

Material Properties of Carbon Nanotubes

Results and Validation

Conclusion