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

Hussain, Muzamal

doi:10.5772/intechopen.80672

Cited by 7 publications

(3 citation statements)

References 19 publications

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“…Several techniques [78,79,80] have been proposed to analyze the vibration of CNT, but here, Galerkin's method to discretize the governing equation of motion. The coordinate system ,,…”

Section: Application Of Galerkin's Methodsmentioning

confidence: 99%

Effect of Power Law-Index for Accurate Natural Frequencies of Rotating Isotropic SWCNTs with Ring Supports

Hussain¹

2019

Preprint

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Vibration analysis of carbon nanotubes (CNTs) is very essential field owing to their many promising applications in tiny instruments. The unique and interesting properties of CNTs, particularly their mechanical and electrical features, have fascinated industries and researchers to implement CNTs for production of different electromechanical devices. Research on vibration behavior of CNTs was done for a few decades ago. Vibrations of isotropic rotating zigzag and chiral single-walled carbon nanotube (SWCNTs) with ring supports are established using the Love’s shell theory. To discretize the governing equations of current model, Galerkin’s method is utilized for frequency equations of single-walled carbon nanotubes (SWCNTs). The unknown axial functions have assumed by characteristic beam functions which fulfill boundary conditions applied at the tube ends. Effects of different parameters with ring supports on the fundamental natural frequencies versus ratio of length-to-radius, angular speed and height-to-radius ratio have been investigated. The frequencies curves decrease as the length-to-diameter ratio increases. With the increase of angular speed the frequency curve of backward waves increases and forward wave decreases for rotating zigzag and chiral tubes. On the other hand, the phenomena of frequency versus height-to-radius ratio are counterpart of length-to-radius ratio for rotating boundary conditions. The frequency phenomena have been observed very pronounced with ring support. Frequency value of C-C end condition is higher than those of C-F computations. The results of single-walled carbon nanotube are computed by using MATLAB software. To validate the accuracy of present model, the results have been compared with earlier modeling/simulations.

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“…Several techniques [78,79,80] have been proposed to analyze the vibration of CNT, but here, Galerkin's method to discretize the governing equation of motion. The coordinate system ,,…”

Section: Application Of Galerkin's Methodsmentioning

confidence: 99%

Effect of Power Law-Index for Accurate Natural Frequencies of Rotating Isotropic SWCNTs with Ring Supports

Hussain¹

2019

Preprint

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“…Here, Galerkin’s method is used to solve the CNT problem of differential equations in an efficient and comprehensive way [71–79]. The analysis of vibration of SWCNTs as a theoretical work is very necessary before their practical applications.…”

Section: Theoretical Formulationsmentioning

confidence: 99%

Mass density effect on vibration of zigzag and chiral SWCNTs: A theoretical study

Hussain

2020

Jnl of Sandwich Structures & Materials

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Carbon nanotubes fascinate new materials with astonishing mechanical, optical, and electrical properties. In fact, carbon nanotubes are kinds of rolled graphene sheets, and the rolling manner shows the basic properties of the tube, and that is actually the main reason for the extraordinary feature of the carbon nanotubes. This paper aims to presents formulation of Love’s shell theory for single-wall carbon nanotubes (SWCNTs) using Galerkin’s method. For this system, the governing equation is developed with proposed method. It is assumed that C–C and C–F support conditions are applied on the edge of carbon nanotube. Zigzag and chiral structures are considered for the vibrational analysis to investigate the effect of different mode and in-plane rigidity with end conditions. Moreover, the influence of mass density per unit lateral area on the same structure is also developed. It is also concluded that the fundamental frequencies of chiral tubes are lower than that of zigzag tubes frequencies. By increasing values of in-plane rigidity, resulting frequencies also increase and frequencies decrease on increasing mass density per unit lateral area. Though the trends of frequency values of both mass density per unit lateral area and in-plane rigidity are converse to each other. It is shown that variation in mass density has a significant effect on the vibration of SWCNTs. To generate the fundamental natural frequencies and for better accuracy and effectiveness, the computer software MATLAB is used. Tube dynamical equations for the present problem are taken in the integral form energy expressions for a carbon nanotube. The axial modal deformations are approximated by making use of the beam functions. The proposed model is continuum-model for getting the dynamic character of SWCNTs and to validate the results by earlier methods.

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“…Prior to this, many techniques have been sequentially used to study the vibration of CNTs [41][42][43]. Previously, the current approach was used continuously to study the vibration of carbon nanotubes [27,29,[44][45][46][47].…”

Section: Application Of Wpamentioning

confidence: 99%

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

Hussain¹

2019

Perspective of Carbon Nanotubes

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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.

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

Cited by 7 publications

References 19 publications

Effect of Power Law-Index for Accurate Natural Frequencies of Rotating Isotropic SWCNTs with Ring Supports

Effect of Power Law-Index for Accurate Natural Frequencies of Rotating Isotropic SWCNTs with Ring Supports

Mass density effect on vibration of zigzag and chiral SWCNTs: A theoretical study

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

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