Nonlinear ultrasonic waves in a magneto-flexo-thermally actuated single walled armchair carbon nanotube embedded on polymer matrix

2020 ◽  
Vol 18 (1) ◽  
pp. 1-13
Author(s):  
Rajendran Selvamani ◽  
M. Mahaveer Sree Jayan ◽  
Farzad Ebrahimi
Keyword(s):  
Mathematical Model ◽  
Carbon Nanotube ◽  
Boundary Conditions ◽  
Polymer Matrix ◽  
Ultrasonic Waves ◽  
Dimensionless Frequency ◽  
Single Walled Carbon Nanotube ◽  
Content Type ◽  
Analytical Formulation ◽  
Nonlinear Ultrasonic

Purpose The purpose of this paper is concerned with the study of nonlinear ultrasonic waves in a magneto-flexo-thermo (MFT) elastic armchair single-walled carbon nanotube (ASWCNT) resting on polymer matrix. Design/methodology/approach A mathematical model is developed for the analytical study of nonlinear ultrasonic waves in a MFT elastic armchair single walled carbon nanotube rested on polymer matrix using Euler beam theory. The analytical formulation is developed based on Eringen’s nonlocal elasticity theory to account small scale effect. After developing the formal solution of the mathematical model consisting of partial differential equations, the frequency equations have been analysed numerically by using the nonlinear foundations supported by Winkler-Pasternak model. The solution is obtained by ultrasonic wave dispersion relations. Findings From the literature survey, it is evident that the analytical formulation of nonlinear ultrasonic waves in an MFT elastic ASWCNT embedded on polymer matrix is not discussed by any researchers. So, in this paper the analytical solutions of nonlinear ultrasonic waves in an MFT elastic ASWCNT embedded on polymer matrix are studied. Parametric studies is carried out to scrutinize the influence of the nonlocal scaling, magneto-electro-mechanical loadings, foundation parameters, various boundary condition and length on the dimensionless frequency of nanotube. It is noticed that the boundary conditions, nonlocal parameter and tube geometrical parameters have significant effects on dimensionless frequency of nanotubes. Originality/value This paper contributes the analytical model to find the solution of nonlinear ultrasonic waves in an MFT elastic ASWCNT embedded on polymer matrix. It is observed that the increase in the foundation constants raises the stiffness of the medium and the structure is able to attain higher frequency once the edge condition is C-C followed by S-S. Further, it is noticed that the natural frequency is arrived below 1% in both local and nonlocal boundary conditions in the presence of temperature coefficients. Also, it is found that the density and Poisson ratio variation affects the natural frequency with below 2%. The results presented in this study can provide mechanism for the study and design of the nano devices such as component of nano oscillators, micro wave absorbing, nano-electron technology and nano-electro--magneto-mechanical systems that make use of the wave propagation properties of ASWCNTs embedded on polymer matrix.

scholarly journals Nonlinear magneto-thermo-elastic vibration of mass sensor armchair carbon nanotube resting on an elastic substrate

2020 ◽  
Vol 7 (1) ◽  
pp. 153-165
Author(s):  
Rajendran Selvamani ◽  
M. Mahaveer Sree Jayan ◽  
Rossana Dimitri ◽  
Francesco Tornabene ◽  
Farzad Ebrahimi
Keyword(s):  
Carbon Nanotube ◽  
Mechanical Response ◽  
Scale Effects ◽  
Nonlocal Elasticity Theory ◽  
Wave Dispersion ◽  
Elastic Vibration ◽  
Ultrasonic Waves ◽  
Small Scale ◽  
Dimensionless Frequency ◽  
Mass Sensors

AbstractThe present paper aims at studying the nonlinear ultrasonic waves in a magneto-thermo-elastic armchair single-walled (SW) carbon nanotube (CNT) with mass sensors resting on a polymer substrate. The analytical formulation accounts for small scale effects based on the Eringen’s nonlocal elasticity theory. The mathematical model and its differential equations are solved theoretically in terms of dimensionless frequencies while assuming a nonlinear Winkler-Pasternak-type foundation. The solution is obtained by means of ultrasonic wave dispersion relations. A parametric work is carried out to check for the effect of the nonlocal scaling parameter, together with the magneto-mechanical loadings, the foundation parameters, the attached mass, boundary conditions and geometries, on the dimensionless frequency of nanotubes. The sensitivity of the mechanical response of nanotubes investigated herein, could be of great interest for design purposes in nano-engineering systems and devices.

Forced Axial Vibration of a Single-Walled Carbon Nanotube Embedded in Elastic Medium under Various Moving Forces

2020 ◽  
Vol 63 ◽  
pp. 112-133 ◽  
Author(s):  
Farshad Khosravi ◽  
Seyyed Amirhosein Hosseini ◽  
Abdelouahed Tounsi
Keyword(s):  
Carbon Nanotube ◽  
Boundary Conditions ◽  
Elastic Medium ◽  
Time Domain ◽  
Natural Frequencies ◽  
Moving Load ◽  
Nonlocal Parameter ◽  
Single Walled Carbon Nanotube ◽  
Single Walled Carbon ◽  
The Time Domain

The dynamic free and forced axial vibrations subjected to moving exponential and harmonic axial forces of a single-walled carbon nanotube (SWCNT) embedded in an elastic medium, are studied in this paper. Two different boundary conditions of SWCNT, including clamped-clamped and clamped-free, are taken into account. Eringen’s nonlocal elasticity theory is used to show the nonlocality for the model. The constitutive equations and their boundary conditions are derived by Hamilton’s principle. Employing the general solution, the derived equations are analytically solved to obtain two items. Firstly, the axial natural frequencies, secondly, the time-domain axial displacements at the middle of the carbon nanotube (CNT), and then the maximum axial displacements. The responses are validated with previous works, and the results demonstrates good agreement to them to verify the influence of the nonlocal parameter on the nondimensional natural frequencies for three various mode numbers. In the time-domain section, the effects of the nonlocal parameter, length, nondimensional stiffness of the elastic medium, and velocity of the moving load on the axial displacement are investigated. Also, the influences of the excitation frequency to natural frequency for the harmonic moving load, as well as the time constant for the exponential moving load on the axial displacement, are illustrated. Finally, the effect of the nonlocal parameter on the maximum axial deflection versus velocity parameter is schematically indicated.

Nonlinear vibration properties of a zigzag single-walled carbon nanotube embedded in a polymer matrix

2015 ◽  
Vol 3 (1) ◽  
pp. 29-37 ◽  
Author(s):  
Abderrahmane Besseghier ◽  
Houari Heireche ◽  
Abdelmoumen Anis Bousahla ◽  
Abdelouahed Tounsi ◽  
Abdelnour Benzair
Keyword(s):  
Carbon Nanotube ◽  
Nonlinear Vibration ◽  
Polymer Matrix ◽  
Single Walled Carbon Nanotube ◽  
Single Walled Carbon ◽  
Vibration Properties

RMVT-Based Nonlocal Timoshenko Beam Theory for Stability Analysis of Embedded Single-Walled Carbon Nanotube with Various Boundary Conditions

2016 ◽  
Vol 16 (10) ◽  
pp. 1550068 ◽  
Author(s):  
Chih-Ping Wu ◽  
Jyun-Yu Liou
Keyword(s):  
Carbon Nanotube ◽  
Stability Analysis ◽  
Boundary Conditions ◽  
Critical Load ◽  
Elastic Medium ◽  
Timoshenko Beam ◽  
Beam Theory ◽  
Single Walled Carbon Nanotube ◽  
Various Boundary Conditions ◽  
Nonlocal Timoshenko Beam Theory

On the basis of Reissner’s mixed variational theorem (RMVT), a nonlocal Timoshenko beam theory (TBT) is developed for the stability analysis of a single-walled carbon nanotube (SWCNT) embedded in an elastic medium, with various boundary conditions and under axial loads. Eringen’s nonlocal elasticity theory is used to account for the small length scale effect. The strong formulations of the RMVT-based nonlocal TBT and its associated possible boundary conditions are presented. The interaction between the SWCNT and its surrounding elastic medium is simulated using the Pasternak foundation models. The critical load parameters of the embedded SWCNT with different boundary conditions are obtained by using the differential quadrature (DQ) method, in which the locations of [Formula: see text] sampling nodes are selected as the roots of [Formula: see text]-order Chebyshev polynomials. The results of the RMVT-based nonlocal TBT are compared with those obtained using the principle of virtual displacement (PVD)-based nonlocal TBT available in the literature. The influences of some crucial effects on the critical load parameters of the embedded SWCNT are examined, such as different boundary conditions, Winkler stiffness and shear modulus of the foundation, aspect ratios, and the nonlocal parameter.

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