Nonlocal continuum mechanics formulation for axial, flexural, shear and contraction coupled wave propagation in single walled carbon nanotubes

Narendar, S.; Gopalakrishnan, S.

doi:10.1590/s1679-78252012000400005

Cited by 9 publications

(4 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The influences of long range interatomic and intermolecular cohesive forces on the static and dynamic properties become significant in small scale [29]. In the following, the nonlocal Eringen theory is utilized in differential form [30] (1…”

Section: Problem Formulation -Governing Differential Equations Of The...mentioning

confidence: 99%

See 1 more Smart Citation

Application of HOHWM for Vibration Analysis of Nanobeams

Kirs

Eerme

Bassir³

et al. 2019

KEM

View full text Add to dashboard Cite

The higher order Haar wavelet method (HOHWM) introduced recently by workgroup is utilized for vibration analysis of nanobeams. The results obtained are compared with widely used Haar wavelet method. It has been observed that the absolute error has been reduced several magnitudes depending on number of collocation points used and the numerical rate of convergence was improved from two to four. These results are obtained in the case of the simplest higher order approach where expansion parameter k is equal to one. The complexity issues of the HOHWM are discussed.

show abstract

Section: Problem Formulation -Governing Differential Equations Of The...mentioning

confidence: 99%

“…In ( 2) 0 e and nonlocal parameter 𝑎𝑎 stand for the material properties and internal characteristic length, respectively. Proceeding from Eringen nonlocal elasticity theory the governing differential equations of the Euler-Bernoulli nanobeam can be derived as [30,31]…”

Section: Problem Formulation -Governing Differential Equations Of The...mentioning

confidence: 99%

Application of HOHWM for Vibration Analysis of Nanobeams

Kirs

Eerme

Bassir³

et al. 2019

KEM

View full text Add to dashboard Cite

show abstract

“…The effect of the aspect ratio, the elastic boundary conditions and the nonlocal parameter is presented. A forced vibration of a single-and double-walled carbon nanotube under excitation of a moving harmonic load has been analyzed using nonlocal elasticity theory by Rahmani et al (2017Rahmani et al ( , 2018.…”

Section: Introductionmentioning

confidence: 99%

The computation of bending eigenfrequencies of single-walled carbon nanotubes based on the nonlocal theory

Bocko

Lengvarský

Huňady³

et al. 2018

Mech. Sci.

View full text Add to dashboard Cite

Abstract. In this work, a recently proposed nonlocal theory of bending is used in the analysis of eigenfrequencies of single-walled carbon nanotubes (SWCNTs). The nanotube vibration is analyzed in the form of a homogenized continuum. Classical treatment where a nanotube is approximated by standard beam theory, is replaced by the more sophisticated nonlocal method of material interactions where a nonlocal parameter is used. The eigenfrequencies are computed by the combination of analytical as well as numerical methods for four different carbon nanotube (CNT) supports. Various types of supports are considered for the analysis: fixed–simply supported, fixed–free, simply–simply supported and fixed–fixed. Due to the huge amount of computed data, only outcomes of eigenfrequency computations for the nanobeams of armchair type with fixed and simply supported ends, and different nonlocal parameters are represented in the form of graphs at the end of the article. The study shows how the nanotube eigenfrequencies depend on nonlocal parameters as well as on the length and diameter of CNTs. The obtained results are in good agreement with the results published in papers which were gained by different procedures.

show abstract

“…modified continuum mechanics approaches) is required as they are relatively simple to be applied with less time-consuming without compromising the accuracy of the results. Eringen (1983) proposed the nonlocal elasticity theory which has been widely used for continuum mechanics modeling of CNTs (Wang et al, 2008;Murmu and Pradhan, 2010;Wang et al, 2010;Murmu and Adhikari, 2011;Narendar and Gopalakrishnan, 2012;Thai, 2012;Thai and Vo, 2012;Şimşek and Yurtcu, 2013;Tounsi et al, 2013, Asemi et al, 2014. In this theory, the effects of small scaling parameter on the mechanical analysis of nanostructures are taken into account.…”

Section: Introductionmentioning

confidence: 99%

DQ thermal buckling analysis of embedded curved carbon nanotubes based on nonlocal elasticity theory

Setoodeh

Derahaki

Bavi

2015

Lat. Am. j. solids struct.

View full text Add to dashboard Cite

To investigate the thermal buckling of curved carbon nanotubes (CCNTs) embedded in an elastic medium, nonlocal elasticity theory is employed in combination with the theory of thin curved beams. Differential quadrature (DQ) method is implemented to discretize the resulted governing equations. Solving these equations enables us to estimate the critical temperature and the critical axial buckling load for CCNTs surrounded by an elastic medium and under the effect of a uniform temperature change. The elastic interaction between the nanotube and its surrounding medium is modeled as a Winkler-Pasternak elastic foundation. The fast convergence of the DQ method is demonstrated and also its accuracy is verified by comparing the results with available solutions in the literature. The effects of various parameters such as different boundary conditions, nonlocal parameter, Winkler and Pasternak elastic modulus, temperature and nanotube curvature on the critical buckling temperature and load are successfully studied. The results reveal that the critical buckling load depends significantly on the curvature of the CCNT. KeywordsCurved carbon nanotubes; thermal buckling; nonlocal elasticity theory; differential quadrature method.DQ thermal buckling analysis of embedded curved carbon nanotubes based on nonlocal elasticity theory 1 INTRODUCTION Nano-electro-mechanical systems (NEMS) are among fast growing technologies which deal with the production of nano-scale machines. These devices are being extensively used in many advanced industries such as aerospace, automotive, biotechnology, and audiometric equipment (Dai et al., 1996). Among the nanostructures, carbon nanotubes (CNTs) are one of the most important structures

show abstract

Nonlocal continuum mechanics formulation for axial, flexural, shear and contraction coupled wave propagation in single walled carbon nanotubes

Cited by 9 publications

References 29 publications

Application of HOHWM for Vibration Analysis of Nanobeams

Application of HOHWM for Vibration Analysis of Nanobeams

The computation of bending eigenfrequencies of single-walled carbon nanotubes based on the nonlocal theory

DQ thermal buckling analysis of embedded curved carbon nanotubes based on nonlocal elasticity theory

Contact Info

Product

Resources

About