Bending and Vibration Analysis of Curved FG Nanobeams via Nonlocal Timoshenko Model

In nano-dimension, the strength of the material is considerable, and the failure is unavoidable in a torsional mode. Because of this reason, the free and forced torsional vibrations of single-walled carbon nanotube (SWCNT) are investigated in this paper. For dynamic analysis, the moving harmonic torsional load is exerted to SWCNT. The related boundary condition and equation of motion are derived by Hamilton’s principle, and the equation is discretized by the Galerkin method. In order to demonstrate the nonlocality and small–scale effect, Eringen’s theory based on nonlocal elasticity theory is applied. A clamped-clamped (C-C) boundary condition is fitted for the end supports. The influences of the aspect ratio and mode number on the free natural frequency are investigated. Furthermore, the dynamic effects of nonlocal parameter, velocity, thickness, length, and excitation-to-natural frequencies on dimensional and nondimensional angular displacements are indicated. Moreover, the natural frequency was investigated due to the variation of the aspect ratio.

show abstract

“…The related studies considering the nonlocal elasticity theory include the Refs. [31][32][33][34][35][36][37][38][39][40][41][42].…”

Section: Introductionmentioning

confidence: 99%

Effect of External Moving Torque on Dynamic Stability of Carbon Nanotube

Hosseini

Khosravi

Ghadiri

2020

JNanoR

Self Cite

View full text Add to dashboard Cite

show abstract

“…The nonlocal Eringen's elasticity theory [15][16][17][18][19] has been established to show the small-scale effect and the torsional behavior of the nanorods. In this way, many studies are devoted to the vibration of the nanostructure via the mentioned nonlocal approach [20][21][22][23][24][25][26][27][28][29][30][31]. Meanwhile, there are some investigations that are carried out via the other theories such as Refs.…”

Section: Introductionmentioning

confidence: 99%

Analytical investigation on free torsional vibrations of noncircular nanorods

Khosravi

Hosseini

Hamidi

2020

J Braz. Soc. Mech. Sci. Eng.

View full text Add to dashboard Cite

This paper is devoted to the free torsional behavior of the nanorods containing noncircular cross sections. The rectangular cross section is chosen to be the case of the study. Three various boundary conditions, namely the clamped-clamped (C-C), clamped-free (C-F), and clamped-torsional spring (C-T) boundary conditions, are used to model the nanorod. Hamilton's principle is utilized to derive the equation of motion along with associated boundary conditions. The derived equation is reformulated by Eringen's nonlocal elasticity approach to exhibit the small-scale effect. An analytical method is established to discretize and analyze the equation of motion. The novelty of this work is the analysis of the torsional vibration in rectangular nanorods, which are not observed in previous works. For the results, the influences of the horizontal and vertical aspect ratios ( a∕b and b∕a ) (for C-C and C-F boundary conditions) and the influences of the nonlocal parameter and stiffness of the boundary spring (for C-T boundary condition) are illustrated schematically and tabularly.

show abstract

“…Other than nanoscale beams, nanoscale shells and plates were the focus of many researchers [21][22][23][24][25][26][27][28]. Two-dimensional general equations of piezoelectric shells with nano-thickness were suggested by Zhang et al [29] considering the surface effects.…”

Section: Introductionmentioning

confidence: 99%

Archive of Mechanical Engineering

Bastanfar¹,

Hosseini²,

Sourki³

et al. 2019

View full text Add to dashboard Cite

A nanoscale beam model containing defect under the piezoelectricity considering the surface effects and flexoelectricity is established on the framework of Euler-Bernoulli theory. The governing equations of motion and related boundary conditions are derived by using Hamilton's principle. The imperfect nanobeam is modeled by dividing the beam into two separate parts that are connected by a rotational and a longitude spring at the defect location. Analytical results on the free vibration response of the imperfect piezoelectric nanobeam exhibit that the flexoelectricity and the surface effects are sensitive to the boundary conditions, defect position, and geometry of the nanobeam. Numerical results are provided to predict the mechanical behavior of a weakened piezoelectric nanobeam considering the flexoelectric and surface effects. It is also revealed that the voltage, defect severity, and piezoelectric material have a critical role on the resonance frequency. The work is envisaged to underline the influence of surface effects and flexoelectricity on the free vibration of a cracked piezoelectric nanobeam for diverse boundary conditions. It should be mentioned, despite our R. Sourkiprevious works, an important class of piezoelectric materials used nowadays and called piezoelectric ceramics is considered in the current study.

show abstract

Bending and Vibration Analysis of Curved FG Nanobeams via Nonlocal Timoshenko Model

Cited by 12 publications

References 4 publications

Effect of External Moving Torque on Dynamic Stability of Carbon Nanotube

Effect of External Moving Torque on Dynamic Stability of Carbon Nanotube

Analytical investigation on free torsional vibrations of noncircular nanorods

Archive of Mechanical Engineering

Contact Info

Product

Resources

About