• Advances in nano research
• /
• v.5 no.2
• /
• pp.179-192
• /
• 2017

The transverse vibration of double walled carbon nanotube (DWCNT) embedded in elastic medium with an initial imperfection is considered. In this paper, Timoshenko beam theory is employed. However the nonlocal theory is used for modeling the nano scale of nanotube. In addition, the governing Equations of motion are obtained utilizing the Hamilton's principle and simply-simply boundary conditions are assumed. Furthermore, the Navier method is used for determining the natural frequencies of DWCNT. Hence, some parameters such as nonlocality, curvature amplitude, Winkler and Pasternak elastic foundations and length of the curved DWCNT are analyzed and discussed. The results show that, the curvature amplitude causes to increase natural frequency. However, nonlocal coefficient and elastic foundations have important role in vibration behavior of DWCNT with imperfection.

• Structural Engineering and Mechanics
• /
• v.71 no.1
• /
• pp.89-98
• /
• 2019

In this study, the mechanical bending behaviors of functionally graded porous nanobeams are investigated. Four types of porosity which are, the classical power porosity function, the symmetric with mid-plane cosine function, bottom surface distribution and top surface distribution are proposed in analysis of nanobeam for the first time. A comparison between four types of porosity are illustrated. The effect of nano-scale is described by the differential nonlocal continuum theory of Eringen by adding the length scale into the constitutive equations as a material parameter comprising information about nanoscopic forces and its interactions. The graded material is designated by a power function through the thickness of nanobeam. The beam is simply-supported and is assumed to be thin, and hence, the kinematic assumptions of Euler-Bernoulli beam theory are held. The mathematical model is solved numerically using the finite element method. Numerical results show effects of porosity type, material graduation, and nanoscale parameters on the static deflection of nanobeam.

• Structural Engineering and Mechanics
• /
• v.68 no.6
• /
• pp.701-711
• /
• 2018

Herein, the thermo-magneto-elastic wave dispersion answers of functionally graded (FG) double-nanobeam systems (DNBSs) are surveyed implementing a nonlocal strain gradient theory (NSGT). The kinematic relations are derived employing the classical beam theory. Also, scale influences are covered precisely in the framework of NSGT. Moreover, Mori-Tanaka homogenization model is introduced in order to obtain the effective material properties of FG nanobeams. Meanwhile, effects of external forces such as thermal and Lorentz forces are included in this research. Also, based upon the Hamilton's principle, the Euler-Lagrange equations are developed; afterwards, these equations are incorporated with those of NSGT to reach the nonlocal governing equations of FG-DNBSs. Furthermore, according to an analytical approach, the governing equations are solved to obtain the wave frequencies and phase velocities of FG-DNBSs. At the end, some illustrations are rendered to clarify the influences of a wide range of involved parameters.

• Advances in nano research
• /
• v.7 no.5
• /
• pp.325-335
• /
• 2019

In the present study, nonlocal strain gradient theory (NSGT) is developed for wave propagation of functionally graded (FG) nanoscale plate in the thermal environment by considering the porosity effect. $Si_3N_4$ as ceramic phase and SUS304 as metal phase are regarded to be constitutive material of FG nanoplate. The porosity effect is taken into account on the basis of the newly extended method which considers coupling influence between Young's modulus and mass density. The motion relation is derived by applying Hamilton's principle. NSGT is implemented in order to account for small size effect. Wave frequency and phase velocity are obtained by solving the problem via an analytical method. The effects of different parameters such as porosity coefficient, gradient index, wave number, scale factor and temperature change on phase velocity and wave frequency of FG porous nanoplate have been examined and been presented in a group of illustrations.

• Advances in nano research
• /
• v.7 no.2
• /
• pp.135-143
• /
• 2019

The important effect of porosity on the mechanical behaviors of a continua makes it necessary to account for such an effect while analyzing a structure. motivated by this fact, a new two-step porosity dependent homogenization scheme is presented in this article to investigate the wave propagation responses of functionally graded (FG) porous nanobeams. In the introduced homogenization method, which is a modified form of the power-law model, the effects of porosity distributions are considered. Based on Hamilton's principle, the Navier equations are developed using the Euler-Bernoulli beam model. Thereafter, the constitutive equations are obtained employing the nonlocal elasticity theory of Eringen. Next, the governing equations are solved in order to reach the wave frequency. Once the validity of presented methodology is proved, a set of parametric studies are adapted to put emphasis on the role of each variant on the wave dispersion behaviors of porous FG nanobeams.

• Advances in Computational Design
• /
• v.7 no.2
• /
• pp.99-112
• /
• 2022

This research has been devoted to examine nonlinear static bending analysis of smart beams with nano dimension exposed to thermal environment. The beam elastic properties are corresponding to piezo-magnetic material of different compositions. The large deflection analysis of the beam has been performed assuming that the beam is exposed to transverse uniform pressure. Based on the rule of Hamilton, the governing equations have been derived for a nonlocal thin beam and solved using differential quadrature method. Temperature variation effect on nonlinear deflection of the smart beams has been studied. Also, the beam deflection is shown to be affected by electric voltage, magnetic intensity and material composition.

• Advances in nano research
• /
• v.14 no.2
• /
• pp.179-193
• /
• 2023

Physical activities enhance blood flow in the vessels, which may increase the quality of medicine delivery. The emergence of revolutionary technologies such as nanoscience, made it possible to treat the incurable illnesses such as cancer. This paper investigates the impact of sport and physical exercises on the quality and quantity of the drug-delivery based on the mathematical modeling of a nanomotor made by nanotubes carrying the nano-drug capsules. Accordingly, the mathematical equations of rotating nanomotor are generated by considering the both of higher-order beam model and nonlocal strain gradient model, as a comprehensive continuum theory. Next, through the generalized differential quadrature together with Newmark-beta methods, the differential relations are discretized and solved. Finally, the impact of varied parameters on the dynamical behavior of the nanomotor is examined in detail. The outcomes of this investigation can be useful to achieve an excellent design of nanomotors carrying nano-drugs.

• Steel and Composite Structures
• /
• v.46 no.1
• /
• pp.143-152
• /
• 2023

In this paper, static and dynamic bending of nanocomposite micro beam armed with CNTs considering agglomeration effect is studied. The structural damping is considered by Kelvin-Voigt model. The agglomeration effects are assumed using Mori-Tanaka model. The micro beam is modeled by third order shear deformation theory (TSDT). The motion equations are derived by principle of Hamilton's and energy method assuming size effects on the basis of Eringen theory. Using differential quadrature method (DQM) and Newmark method, the static and dynamic deflections of the structure are obtained. The effects of agglomeration and CNTs volume percent, damping of structure, nonlocal parameter, length and thickness of micro-beam are presented on the static and dynamic deflections of the nanocomposite structure. Results show that with increasing CNTs volume percent, the static and dynamic deflections are decreased. In addition, enhancing the nonlocal parameter yields to higher static and dynamic deflections.

• Steel and Composite Structures
• /
• v.45 no.4
• /
• pp.535-546
• /
• 2022

The memory response of nonlocal systematical formulation size-dependent coupling of viscoelastic deformation and thermal fields for piezoelectric materials with dual-phase lag heat conduction law is constructed. The method of the matrix exponential, which constitutes the basis of the state-space approach of modern control theory, is applied to the non-dimensional equations. The resulting formulation together with the Laplace transform technique is applied to solve a problem of a semi-infinite piezoelectric rod subjected to a continuous heat flux with constant time rates. The inversion of the Laplace transforms is carried out using a numerical approach. Some comparisons of the impacts of nonlocal parameters and time-delay constants for various forms of kernel functions on thermal spreads and thermo-viscoelastic response are illustrated graphically.

• Advances in nano research
• /
• v.15 no.3
• /
• pp.203-213
• /
• 2023

The possibility of energy harvesting as well as vibration of a three-layered beam consisting of two piezoelectric layers and one core layer made of nonpiezoelectric material is investigated using nonlocal strain gradient theory. The three-layered nanobeam is resting on an elastic foundation. Hamilton's principle is used to derive governing equations and associated boundary conditions. The generalized differential quadrature method (GDQM) was used to discretize the equations, and the Newmark beta method was used to solve them. The size-dependency of the elastic foundation is considered using two-phase elasticity. The equations, as well as the solution procedure, are validated utilizing some compassion studies. This work can be a basis for future studies on energy harvesting of small scales.