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

Hussain, Muzamal

doi:10.5772/intechopen.73503

Cited by 13 publications

(10 citation statements)

References 40 publications

(43 reference statements)

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“…Continuum mechanics models depicted that thickness plays a significant role for vibrational analysis of tubes [31,32]. Taking the transducer of metal prestressed tube as steel and piezoelectric ceramic tube as PZT-4 as an example, the relationship between natural frequency and structure sizes is given by programming with MATLAB.…”

Section: Relationship Between Natural Frequencies and Structural Dimementioning

confidence: 99%

Radial Vibration Characteristics of Piezoelectric Ceramic Composite Ultrasonic Transducer

Yao

Zhang

et al. 2020

Shock and Vibration

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Different from the existing equivalent circuit analysis method of the transducer, based on the vibration theory of the mechanical system and combined with the constitutive equation, this paper analyzes the radial vibration characteristics of the transducer. The piezoelectric ceramic composite ultrasonic transducer is simplified as a mechanical model of a composite thick wall tube composed of a piezoelectric ceramic tube and a metal prestressed tube. The mathematical model of radial vibration of the transducer is established, which consists of the wave equation of radial coupling vibration of the piezoelectric ceramic tube and the metal prestressed tube, the continuity conditions, and the boundary conditions of radial vibration of composite thick wall tube. The characteristic equation and the mode function of radial vibration are derived. The calculated results of natural frequency are in good agreement with the existing experimental results. Based on the analytical method and the difference method, the numerical simulation models of radial vibration are established, and the amplitude-frequency characteristic curves and the displacement responses are given. The simulation results show that the amplitude-frequency characteristic curves and the displacement responses of the two methods are the same, which verifies the correctness of simulation results. Through the simulation analysis, the influence rule of the transducer’s structure sizes on its radial vibration natural frequency is given: when the thickness of the metal prestressed tube and the piezoelectric ceramic tube are constant, the natural frequency decreases with the increase of the inner diameter of the piezoelectric ceramic tube; when the outer diameter of the metal prestressed tube and the inner diameter of the piezoelectric ceramic tube are constant, the natural frequency decreases with the increase of the thickness-to-wall ratio. The calculation method of natural frequency based on elastic vibration theory is clear in concept and simple in calculation, and the simulation models can analyze the mechanical vibration of the transducer.

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Section: Relationship Between Natural Frequencies and Structural Dimementioning

confidence: 99%

Radial Vibration Characteristics of Piezoelectric Ceramic Composite Ultrasonic Transducer

Yao

Zhang

et al. 2020

Shock and Vibration

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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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“…This concept leads to develop a new technique which is more efficient and simple and provides accurate results. It has been seen that in the recent years, the wave propagation approach has been employed successfully to solve a number of shell and tube problems [28,[30][31][32]. Application of this approach reduces the differential equations in simple algebraic equations.…”

Section: Application Of Wave Propagation Approachmentioning

confidence: 99%

“…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

Hussain¹

2018

Advanced Engineering Testing

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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.

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

Cited by 13 publications

References 40 publications

Radial Vibration Characteristics of Piezoelectric Ceramic Composite Ultrasonic Transducer

Radial Vibration Characteristics of Piezoelectric Ceramic Composite Ultrasonic Transducer

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

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

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