• Advances in nano research
• /
• v.8 no.3
• /
• pp.191-202
• /
• 2020

The article brings the study of nonlocal, surface and the couple stress together to apparent the frequency retaliation of FG nanobeams (Functionally graded). For the examination of frequency retaliation, the article considers the accurate spot of neutral axis. This article aims to enhance the coherence of proposed model to accurately encapsulate the significant effects of the nonlocal stress field, size effects together with material length scale parameters. These considered parameters are assimilated through what are referred to as modified couple stress as well as nonlocal elasticity theories, which encompasses the stiffness-hardening and softening influence on the nanobeams frequency characteristics. Power-law distribution is followed by the functional gradation of the material across the beam width in the considered structure of the article. Following the well-known Hamilton's principle, fundamental basic equations alongside their correlated boundary conditions are solved analytically. Validation of the study is also done with published result. Distinct parameters (such as surface energy, slenderness ratio, as nonlocal material length scale and power-law exponent) influence is depicted graphically following the boundary conditions on non-dimensional FG nanobeams frequency.

• Advances in nano research
• /
• v.6 no.2
• /
• pp.113-133
• /
• 2018

In this work, free vibration characteristics of functionally graded piezoelectric (FGP) nanobeams based on third order parabolic shear deformation beam theory are studied by presenting a Navier type solution as the first attempt. Electro-mechanical properties of FGP nanobeam are supposed to change continuously throughout the thickness based on power-law model. To capture the small size effects, Eringen's nonlocal elasticity theory is adopted. Using Hamilton's principle, the nonlocal governing equations for third order shear deformable piezoelectric FG nanobeams are obtained and they are solved applying analytical solution. By presenting some numerical results, it is demonstrated that the suggested model presents accurate frequency results of the FGP nanobeams. The influences of several parameters including, external electric voltage, power-law exponent, nonlocal parameter and mode number on the natural frequencies of the size-dependent FGP nanobeams is discussed in detail.

• Advances in nano research
• /
• v.13 no.1
• /
• pp.47-61
• /
• 2022

The present research investigates the dynamic behavior of a rotating functionally graded (FG) nonlocal cylindrical beam. The cylindrical beam is mathematically modeled via third-order beam theory linked with nonlocal strain gradient theory. The tube structure is made of functionally graded materials composed of Aluminum oxide coated on the Nickel, which the mechanical properties vary in the tube radius direction according to the power law. The bending harmonic force is applied in the tube length middle. The nonlocal spinning equations of the tube are derived via the energy method of the Hamilton principle, and they are solved via a robust numerical procedure for different boundary conditions. The main application of the rotating nanostructures is for the production of small-scale motors and devices and the drug-delivery application, the presented results can help the researcher have a better view regarding the different conditions.

• Structural Engineering and Mechanics
• /
• v.82 no.5
• /
• pp.629-641
• /
• 2022

This study deals with the spinning impact on flap-wise vibration characteristics of nonlocal functionally graded (FG) cylindrical beam based on the Hyperbolic shear deformation beam theory. The nonlocal strain gradient theory is used to investigate the small-scale impact on the nonlocal motion equation as well as corresponding nonlocal boundary conditions. Based on the mathematical simulation and according to the Hamilton principle, the computerized modeling of a rotating functionally graded nanotube is generated, and then, via a numerical approach, the obtained mathematical equations are solved. The calculated outcomes are helpful to the production of Nano-electro-mechanical-systems (NEMS) by investigating some designed parameters such as rotating speed, hub radius, length-scale parameters, volume fraction parameters, etc.

• Advances in nano research
• /
• v.16 no.2
• /
• pp.201-215
• /
• 2024

The present research study emphasizes the utilization of mathematical simulation on a nanoelectromechanical systems (NEMS) sensor to facilitate the detection of injuries in players and equipment. Specifically, an investigation is conducted on the thermal buckling behavior of a small-scale truncated conical, cylindrical beam, which is fabricated using porous functionally graded (FG) material. The beam exhibits non-uniform characteristics in terms of porosity, thickness, and material distribution along both radial and axial directions. To assess the thermal buckling performance under various environmental heat conditions, classical and first-order nonlocal beam theories are employed. The governing equations for thermal stability are derived through the application of the energy technique and subsequently numerically solved using the extended differential quadratic technique (GDQM). The obtained results are comprehensively analyzed, taking into account the diverse range of effective parameters employed in this meticulous study.

• Advances in nano research
• /
• v.17 no.4
• /
• pp.323-334
• /
• 2024

This paper deals with the effect of non-linear volume fraction distribution of carbon nanotube in the FG-CNTRC beams on the critical buckling via a hyperbolic shear deformation theory. Here, different boundary condition was considered including hinged hinged, clamped clamped and clamped-free. Single-walled carbon nanotubes are aligned and distributed in the polymer matrix in different ways to reinforce it and the material properties of (CNTRC) beams are assumed to vary gradually along the thickness direction, following a new exponential power law distribution of (CNT). The effective material properties of nanocomposite beams are estimated using the rule of mixture. The governing equations of the mathematical models are obtained by applying Hamilton's principle. The results provided of mathematical models in this work are compared and validated with similar ones in the literature. The critical buckling loads of nanocomposite beams with different boundary conditions of linear and non-linear distribution of CNT volume fraction were obtained. The effects of several parameters, including the type of beam, the volume fraction of carbon nanotubes (CNTs), the exponent degree (n), and the aspect ratio, were investigated. The distribution non-linearity of CNT volume fraction in the beam has a significant impact on the mechanical properties, particularly in buckling behavior with different boundary conditions.

• Advances in nano research
• /
• v.7 no.4
• /
• pp.223-231
• /
• 2019

In this article the frequency response of magneto-flexo-electric rotary porous (MFERP) nanobeams subjected to thermal loads has been investigated through nonlocal strain gradient elasticity theory. A quasi-3D beam model beam theory is used for the expositions of the displacement components. With the aid of Hamilton's principle, the governing equations of MFERP nanobeams are obtained. Further, administrating an analytical solution the frequency problem of MFERP nanobeams are solved. In addition the numerical examples are also provided to evaluate the effect of nonlocal strain gradient parameter, hygro thermo environment, flexoelectric effect, in-plane magnet field, volume fraction of porosity and angular velocity on the dimensionless eigen frequency.

• Advances in nano research
• /
• v.16 no.3
• /
• pp.251-263
• /
• 2024

This article investigates the free vibration behavior of carbon nanotube reinforced composite (CNTRC) beams embedded using variational analytical methods and artificial neural networks (ANN). The material properties of layered functionally graded CNTRC (FG-CNTRC) beams are estimated using nonlocal parameters modified power-law with different types of CNT distributions through the thickness direction of the beam. Adopting Eringen's nonlocal elasticity theory to capture the small size effects, the nonlocal governing equations are derived and solved using the analytical method. And also, the problem was analyzed using the ANN method. The architecture of the proposed ANN model is 3-9-1. In the experiments, we used 112 different data to predict the natural frequency using ANN. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion as well as the boundary conditions of the beam are derived using Hamilton's principle. The classical beam theory is used to formulate a governing equation for predicting the free vibration of laminated CNTRC beams. According to the experimental results, the prediction ability of the ANN model is very good and the natural frequency can be predicted in ANN without attempting any experiments.

• Advances in nano research
• /
• v.5 no.2
• /
• pp.141-169
• /
• 2017

In this paper, a nanobeam connected to a rotating molecular hub is considered. The vibration behavior of rotating functionally graded nanobeam based on Eringen's nonlocal theory and Euler-Bernoulli beam model is investigated. Furthermore, axial preload and porosity effect is studied. It is supposed that the material attributes of the functionally graded porous nanobeam, varies continuously in the thickness direction according to the power law model considering the even distribution of porosities. Porosity at the nanoscopic length scale can affect on the rotating functionally graded nanobeams dynamics. The equations of motion and the associated boundary conditions are derived through the Hamilton's principle and generalized differential quadrature method (GDQM) is utilized to solve the equations. In this paper, the influences of some parameters such as functionally graded power (FG-index), porosity parameter, axial preload, nonlocal parameter and angular velocity on natural frequencies of rotating nanobeams with pure ceramic, pure metal and functionally graded materials are examined and some comparisons about the influence of various parameters on the natural frequencies corresponding to the simply-simply, simplyclamped, clamped-clamped boundary conditions are carried out.

• Steel and Composite Structures
• /
• v.36 no.3
• /
• pp.293-305
• /
• 2020

This article presented a nanoscale modified continuum model to investigate the free vibration of functionally graded (FG) porous nanobeam by using finite element method. The main novelty of this manuscript is presenting effects of four different porosity models on vibration behaviors of nonlocal nanobeam structure including size effect, that not be discussed before The proposed porosity models are, uniform porosity distribution, symmetric with mid-plane, bottom surface distribution and top surface distribution. The nano-scale effect is included in modified model by using the differential nonlocal continuum theory of Eringen that adding the length scale into the constitutive equations as a material parameter constant. The graded material is distributed through the beam thickness by a generalized power law function. The beam is simply supported, and it is assumed to be thin. Therefore, the kinematic assumptions of Euler-Bernoulli beam theory are held. The mathematical model is solved numerically using the finite element method. Results demonstrate effects of porosity type, material gradation, and nanoscale parameters on the free vibration of nanobeam. The proposed model is effective in vibration analysis of NEMS structure manufactured by porous functionally graded materials.