Vibration modeling of carbon-nanotube-based biosensors incorporating thermal and nonlocal effects

In the present article, the total potential energy principle and the nonlocal integral elasticity theory have been used to develop a novel finite element method for studying the free vibration behavior of nano-scaled beams. The formulations are based on Euler-Bernoulli beam theory and this method is able to properly analyze the free vibration of beams with various boundary conditions. By implementing the variational statements, the eigenvalue problem of the free vibration is obtained. The validation investigation is pursued by comparing the results of the current study with those available in the literature. The effects of nonlocal parameter, geometry parameters and boundary conditions on the free vibration of the Euler-Bernoulli beam are then studied.

Section: Introductionmentioning

confidence: 99%

Free vibration characteristics of nanoscaled beams based on nonlocal integral elasticity theory

Naghinejad

Ovesy

2017

“…Since the CNT was invented by Iijima (1991), it has attracted researchers’ attention due to its unique physical, mechanical, and electronic properties. A lot of research has been carried out on the buckling (Wang et al., 2008), wave propagation (Narendar et al., 2012), linear vibration (Wang and Wang, 2014), and nonlinear vibration (Fakhrabadi et al., 2014) of CNTs. Kazemi-Lari et al.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal instability of cantilever piezoelectric carbon nanotubes by considering surface effects subjected to axial flow

Hosseini

Bahaadini

Jamali

2016

In this study, the divergence and flutter instability of a cantilever piezoelectric carbon nanotube (CNT) conveying flowing fluid is investigated by considering surface effects. The size-dependent governing differential equation of a piezoelectric CNT is derived using a Newtonian method based on the Eringen nonlocal elasticity theory and in conjunction with the Euler–Bernoulli beam model. The extended Galerkin method is employed to transform the partial differential equation into a set of ordinary differential equations. The resulting eigenvalue problem is solved numerically to determine the effect of nonlocal parameter, various values of piezoelectric voltage, and surface effects on the divergence and flutter instability of a CNT conveying a fluid. Results show that by increasing the voltage from negative values to positive values, the nondimensional critical velocity of the fluid flow decreases. In addition, it should be noted that the effects of the nonlocal parameter lead to a reduction of the flutter and divergence stability of the CNT. Finally, this research can be used to design fluid-conveying nanodevices based on piezoelectric CNTs.

“…In the classical theories of continuum mechanics, the stress in a point is related only to the strain in that specific point; however, in the nonlocal elasticity theory, the stress is also dependent on the strains at all points in the domain. The scientific literature includes many papers based on nonlocal elasticity theory on the mechanical analysis of micro- and nano-sized structures such as micro/nanorod (Aydogdu, 2009a; Murmu and Adhikari, 2010; Narendar and Gopalakrishnan, 2011; Aydogdu, 2012a, 2012b; Chang, 2012; Danesh et al., 2012; Huang, 2012; Şimşek, 2012; Adhikari et al., 2013; Aydogdu and Elishakoff, 2014; Karličić et al., 2015; Bahrami, 2017a; Numanoğlu et al., 2018), and micro/nanobeam (Aydogdu, 2009b; Demir et al., 2010; Wang and Wang, 2014; Bahrami and Teimourian 2015; Karami and Farid, 2015; Bahrami and Teimourian, 2016; Barretta et al., 2016; Mercan and Civalek, 2016; Bahrami, 2017b; Demir and Civalek, 2017; Mercan and Civalek, 2017; Naghinejad and Ovesy, 2019).…”

Section: Introductionmentioning

confidence: 99%

Size-dependent free vibration of axially functionally graded tapered nanorods having nonlinear spring constraint with a tip nanoparticle

Bahrami

Zargaripoor

Shiri

et al. 2019

According to the present literature review, the axial vibration of the axially functionally graded (FG) tapered nanorod with attached nonlinear spring has not been addressed so far. In this study, the axial vibration of the FG tapered nanorod is studied based on Eringen’s nonlocal theory, in which one end of the nanorod is clamped and the other end is attached to a nonlinear spring and a nanoparticle. The influence of different parameters such as the nonlinear spring constant, mass of the nanoparticle, and the nonlocal parameter on the natural frequencies is presented in detail. The solutions via Tables can be utilized as a reliable reference for evaluating the validity of future researches. The presented nonlocal solutions can be helpful for those who are interested in designing micro/nano electromechanical systems.