Vibration analysis of single-walled carbon nanotubes using wave propagation approach

Perspective of Carbon Nanotubes

2019

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This chapter deals with the vibrational properties of single-walled carbon nanotubes (SWCNTs), based on nonlocalized theory of elasticity (NLT). The nanotube pilot control with nonlinear parameters was derived from Euler's beam theory. The wave propagation (WPA) approach was used to derive the frequency equation describing the natural frequencies of vibration in SWCNTs. Complex exponentials depend on the boundary conditions given at the edges of the carbon nanotubes used. Vibration frequency spectra were obtained and evaluated for different physical parameters such as diameter ratio for single chiral carbon nanotubes and flexural strength for chiral SWCNT. The results show that the natural frequencies are significantly reduced by increasing the nonlocal parameters, but by increasing the ratio of the diameter length (aspect ratio), the natural frequency increases. The frequency of SWCNTs is calculated with the help of MATLAB computer software. These results are compared to previously known numerical simulations.

Section: Application Of Wpamentioning

confidence: 99%

“…where q m denoted the wave number in axial direction and used for support conditions of SWCNTs [29]. ω =2π f is the angular frequency.…”

Section: Application Of Wpamentioning

confidence: 99%

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Vibration Characteristics of Single-Walled Carbon Nanotubes Based on Nonlocal Elasticity Theory Using Wave Propagation Approach (WPA) Including Chirality

Perspective of Carbon Nanotubes

2019

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“…Before this, present method has been successively used for the study of shell vibrations [25][26][27]. The axial coordinate and time variable are denoted by x, t correspondingly and the circumferential coordinate signifies by θ.…”

Section: Applications Of the Wave Propagation Approachmentioning

confidence: 99%

Vibrational Behavior of Single-Walled Carbon Nanotubes Based on Donnell Shell Theory Using Wave Propagation Approach

Novel Nanomaterials - Synthesis and Applications

2018

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This chapter is concerned with the vibration analysis of single-walled carbon nanotubes (SWCNTs). This analysis is based on the Donnell thin shell theory. The wave propagation approach in standard eigenvalue form has been employed in order to derive the characteristic frequency equation describing the natural frequencies of vibration in SWCNTs. The axial modal dependence is measured by the complex exponential functions implicating the axial modal numbers. Vibration frequency spectra are gained and evaluated for physical parameter like length-to-diameter ratios. The dimensionless frequency is also investigated in armchair and zigzag SWCNTs with in-plane rigidity and mass density per unit lateral area for armchair and zigzag SWCNTs. These frequencies of the SWCNTs are computed with the aid of the computer software MATLAB. These results are compared with those obtained using molecular dynamics (MD) simulation and the results are somewhat in agreement.

“…The WPA was found to be a very popular tool to compute the vibrational properties of plates. Recently, the strong formulation of WPA has been applied for investigations fundamental frequencies of single-walled carbon nanotubes and detailed discussion is given in our earlier published work [30][31][32]. The present model based on WPA is, therefore, another choice of powerful numerical technique, whose results are appropriate in the limit of acceptable statistical errors than the earlier used Raleigh-Ritz [19] and Galerkin'st e c hniques [16,21].…”

Section: Introductionmentioning

confidence: 99%

Effect of Various Edge Conditions on Free-Vibration Characteristics of Isotropic Square and Rectangular Plates

Advanced Engineering Testing

2018

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In this chapter, vibrations of isotropic rectangular plates have been analyzed by applying the wave propagation approach. The plate problem has been expressed in integral form by considering the strain and kinetic energies. The Hamilton's principle has been applied to transform the integral form into the partial differential equation of second order. The classical method namely product method has been used to separate independent variables. The partial differential equation has converted into the ordinary differential equations. The axial wave numbers are associated with particular boundary conditions. This is an approximate technique, which is based on eigenvalues of characteristic beam functions. The natural frequencies of plates are investigated versus modal numbers by varying the length and width of the plates with simply supported-simply supported (SS-SS), clamped-clamped (CC-CC), and simply supported-clamped (SS-CC) boundary conditions. The frequencies of the plates increase by increasing the modal number, and CC-CC frequencies are greater than the frequencies of other boundary conditions. Computational computer software MATLAB is engaged to characterize the frequencies. The results are compared with the earlier simulation work in order to test the accuracy and efficiency of the present method.