• 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.13 no.3
• /
• pp.297-312
• /
• 2022

Coughing and breath shortness are common symptoms of nano (small) cell lung cancer. Smoking is main factor in causing such cancers. The cancer cells form on the soft tissues of lung. Deformation behavior and wave vibration of lung affected when cancer cells exist. Therefore, in the current work, phase velocity behavior of the small cell lung cancer as a main part of the body via an exact size-dependent theory is presented. Regarding this problem, displacement fields of small cell lung cancer are obtained using first-order shear deformation theory with five parameters. Besides, the size-dependent small cell lung cancer is modeled via nonlocal stress/strain gradient theory (NSGT). An analytical method is applied for solving the governing equations of the small cell lung cancer structure. The novelty of the current study is the consideration of the five-parameter of displacement for curved panel, and porosity as well as NSGT are employed and solved using the analytical method. For more verification, the outcomes of this reports are compared with the predictions of deep neural network (DNN) with adaptive optimization method. A thorough parametric investigation is conducted on the effect of NSGT parameters, porosity and geometry on the phase velocity behavior of the small cell lung cancer structure.

• Structural Engineering and Mechanics
• /
• v.72 no.1
• /
• pp.71-81
• /
• 2019

The objective of this paper is to develop a size-dependent nonlinear model of beams for fluid-conveying nanotubes with an initial deflection. The nonlinear frequency response of the nanotube is analysed via an Euler-Bernoulli model. Size influences on the behaviour of the nanosystem are described utilising the nonlocal strain gradient theory (NSGT). Relative motions at the inner wall of the nanotube is taken into consideration via Beskok-Karniadakis model. Formulating kinetic and elastic energies and then employing Hamilton's approach, the nonlinear motion equations are derived. Furthermore, Galerkin's approach is employed for discretisation, and then a continuation scheme is developed for obtaining numerical results. It is observed that an initial deflection significantly alters the frequency response of NSGT nanotubes conveying fluid. For small initial deflections, a hardening nonlinearity is found whereas a softening-hardening nonlinearity is observed for large initial deflections.

• 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.

• Structural Engineering and Mechanics
• /
• v.65 no.6
• /
• pp.645-656
• /
• 2018

Importance of procuring adequate knowledge about the mechanical behavior of double-layered graphene sheets (DLGSs) incensed the authors to investigate wave propagation responses of mentioned element while rested on a visco-Pasternak medium under hygro-thermal loading. A nonlocal strain gradient theory (NSGT) is exploited to present a more reliable size-dependent mechanical analysis by capturing both softening and hardening effects of small scale. Furthermore, in the framework of a classical plate theory the kinematic relations are developed. Incorporating kinematic relations with the definition of Hamilton's principle, the Euler-Lagrange equations of each of the layers are derived separately. Afterwards, combining Euler-Lagrange equations with those of the NSGT the nonlocal governing equations are written in terms of displacement fields. Interaction of the each of the graphene sheets with another one is regarded by the means of vdW model. Then, a widespread analytical solution is employed to solve the derived equations and obtain wave frequency values. Subsequently, influence of each participant variable containing nonlocal parameter, length scale parameter, foundation parameters, temperature gradient and moisture concentration is studied by plotting various figures.

• Advances in nano research
• /
• v.7 no.3
• /
• pp.157-167
• /
• 2019

In this paper, a classical plate model is utilized to formulate the wave propagation problem of magnetostrictive sandwich nanoplates (MSNPs) while subjected to hygrothermal loading with respect to the scale effects. Herein, magnetostriction effect is considered and controlled on the basis of a feedback control system. The nanoplate is supposed to be embedded on a visco-Pasternak substrate. The kinematic relations are derived based on the Kirchhoff plate theory; also, combining these obtained equations with Hamilton's principle, the local equations of motion are achieved. According to a nonlocal strain gradient theory (NSGT), the small scale influences are covered precisely by introducing two scale coefficients. Afterwards, the nonlocal governing equations can be derived coupling the local equations with those of the NSGT. Applying an analytical solution, the wave frequency and phase velocity of propagated waves can be gathered solving an eigenvalue problem. On the other hand, accuracy and efficiency of presented model is verified by setting a comparison between the obtained results with those of previous published researches. Effects of different variants are plotted in some figures and the highlights are discussed in detail.

• Advances in nano research
• /
• v.16 no.2
• /
• pp.187-200
• /
• 2024

This study focuses on wave propagation analysis in the curved nanobeam exposed to different thermal loadings based on the Nonlocal Strain Gradient Theory (NSGT). Mechanical properties of the constitutive materials are assumed to be temperature-dependent and functionally graded. For modeling, the governing equations are derived using Hamilton's principle. Using the proposed model, the effects of small-scale, geometrical, and thermo-mechanical parameters on the dynamic behavior of the curved nanobeam are studied. A small-scale parameter, Z, is taken into account that collectively represents the strain gradient and the nonlocal parameters. When Z<1 or Z>1, the phase velocity decreases/increases, and the stiffness-softening/hardening phenomenon occurs in the curved nanobeam. Accordingly, the phase velocity depends more on the strain gradient parameter rather than the nonlocal parameter. As the arc angle increases, more variations in the phase velocity emerge in small wavenumbers. Furthermore, an increase of ∆T causes a decrease in the phase velocity, mostly in the case of uniform temperature rise rather than heat conduction. For verification, the results are compared with those available for the straight nanobeam in the previous studies. It is believed that the findings will be helpful for different applications of curved nanostructures used in nano-devices.

• Structural Monitoring and Maintenance
• /
• v.7 no.2
• /
• pp.69-84
• /
• 2020

Based on differential quadrature method (DQM) and nonlocal strain gradient theory (NSGT), forced vibrations of a porous functionally graded (FG) scale-dependent beam in thermal environments have been investigated in this study. The nanobeam is assumed to be in contact with a moving point load. NSGT contains nonlocal stress field impacts together with the microstructure-dependent strains gradient impacts. The nano-size beam is constructed by functionally graded materials (FGMs) containing even and un-even pore dispersions within the material texture. The gradual material characteristics based upon pore effects have been characterized using refined power-law functions. Dynamical deflections of the nano-size beam have been calculated using DQM and Laplace transform technique. The prominence of temperature rise, nonlocal factor, strain gradient factor, travelling load speed, pore factor/distribution and elastic substrate on forced vibrational behaviors of nano-size beams have been explored.

• Coupled systems mechanics
• /
• v.9 no.3
• /
• pp.201-217
• /
• 2020

This paper employs differential quadrature method (DQM) and nonlocal strain gradient theory (NSGT) for studying free vibrational characteristics of porous functionally graded (FG) nanoplates coupled by visco-elastic foundation. A secant function based refined plate theory is used for mathematical modeling of the nano-size plate. Two scale factors are included in the formulation for describing size influences based on NSGT. The material properties for FG plate are porosity-dependent and defined employing a modified power-law form. Visco-elastic foundation is presented based on three factors including a viscous layer and two elastic layers.The governing equations achieved by Hamilton's principle are solved implementing DQM. The nanoplate vibration is shown to be affected by porosity, temperature rise,scale factors and viscous damping.

• Structural Engineering and Mechanics
• /
• v.75 no.6
• /
• pp.659-674
• /
• 2020

The present paper employs nonlocal strain gradient theory (NSGT) to study buckling behavior of functionally graded magneto-electro-thermo-elastic (FG-METE) nanoshells under various physical fields. NSGT modeling of the nanoshell contains two size parameters, one related to nonlocal stress field and another related to strain gradients. It is considered that mechanical, thermal, electrical and magnetic loads are exerted to the nanoshell. Temperature field has uniform and linear variation in nanoshell thickness. According to a power-law function, piezo-magnetic, thermal and mechanical properties of the nanoshell are considered to be graded in thickness direction. Five coupled governing equations have been obtained by using Hamilton's principle and then solved implementing Galerkin's method. Influences of temperature field, electric voltage, magnetic potential, nonlocality, strain gradient parameter and FG material exponent on buckling loads of the FG-METE nanoshell have been studied in detail.