• Wind and Structures
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• v.27 no.6
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• pp.431-438
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• 2018

This paper presents a free vibration analysis of size-dependent functionally graded (FG) nanobeams with all surface effects considerations on the basis of modified couple stress theory. The material properties of FG nanobeam are assumed to vary according to power law distribution. Based on the Euler-Bernoulli beam theory, the modeled nanobeam and its equations of motion are derived using Hamilton's principle. An analytical method is used to discretize the model and the equation of motion. The model is validated by comparing the benchmark results with the obtained results. Results show that the vibration behavior of a nanobeam is significantly influenced by surface density, surface tension and surface elasticity. Also, it is shown that by increasing the beam size, influence of surface effect reduces to zero, and the natural frequency tends to its classical value.

• Computers and Concrete
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• v.30 no.4
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• pp.243-256
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• 2022

The static analysis of spinning functionally graded (FG) nanotube on the basis of the nonlocal strain gradient theory (NSGT) is presented. The high-order beam theory is employed for mathematical modeling of the tube structures according to the Sinusoidal shear deformation beam theory. The energy conservation principle is operated to generate the equations. The centrifugal force is assumed along the tube length due to the rotating of the tube, moreover, the nanotube is made of functionally graded material (FGM) composed of ceramic and metal phases along the tube radius direction. The generalized differential quadratic method (GDQM) is utilized to solve the formulations. Finally, the numerical results are discussed in detail to examine the impact of different relevant parameters on the bending the buckling behavior of the rotating nanotube.

• Advances in nano research
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• v.12 no.6
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• pp.617-627
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• 2022

In the current study, the nonlinear impact of the Von-Kármán theory on the vibrational response of nonhomogeneous structures of functionally graded (FG) nano-scale tubes is investigated according to the nonlocal theory of strain gradient theory as well as high-order Reddy beam theory. The inhomogeneous distributions of temperature-dependent material consist of ceramic and metal phases in the radial direction of the tube structure, in which the thermal stresses are applied due to the temperature change in the thickness of the pipe structure. The general motion equations are derived based on the Hamilton principle, and eventually, the acquired equations are solved and modeled by the Meshless approach as well as a computer simulation via intelligent mathematical methodology. The attained results are helpful to dissect the stability of the MEMS and NEMS.

• Geomechanics and Engineering
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• v.32 no.5
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• pp.541-551
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• 2023

Snap-buckling is one of the main failure modes of structures, because it will lead to the reduction of structural bearing capacity, durability loss and even structural damage. Boundary condition plays an important role in the research of engineering mechanics. Further discussion on the boundary conditions problems will help to analyze the dynamic and static behavior of structures more accurately. Therefore, in order to understand the dynamic and static behavior of curved beams more comprehensively, this paper mainly studies the nonlinear snap-through buckling and forced vibration characteristics of functionally graded graphene reinforced composites (FG-GPLRCs) curved beams with two different boundary conditions (including clamped-hinged and hinged-hinged) using Euler-Bernoulli beam theory (E-BBT). In addition, the effects of the curved beam radius, the GLPs distributions, number of GLPs layers, the mass fraction of GLPs and elastic foundation parameters on the nonlinear snap-through buckling and forced vibration behavior are discussed respectively.

• Computers and Concrete
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• v.31 no.2
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• pp.139-149
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• 2023

This article investigates the statically analysis regarding the thermal buckling behavior of a nonuniform small-scale nanobeam made of functionally graded material based on classic beam theories along with the nonlocal Eringen elasticity. The material distribution of functionally graded structures is composed of temperature-dependent ceramic and metal phases in axial and thickness directions, called two-dimensional functionally graded (2D-FG). The partial differential (PD) formulations and end conditions are extracted by using to the conservation energy method. The porosity voids are assumed in the nonuniform functionally graded (FG) structure. The thermal loads are in the axial direction of the beam. The extracted nonlocal PD equations are also solved by employing generalized differential quadrature method (GDQM). Last but not least, the information acquired is used to produce miniature sensors, providing a unique perspective on the growth of nanoelectromechanical systems (NEMS).

• Earthquakes and Structures
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• v.15 no.4
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• pp.369-382
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• 2018

A free vibration analysis and wave propagation of functionally graded porous beams has been presented in this work using a high order hyperbolic shear deformation theory. Unlike other conventional shear deformation theories, a new displacement field that introduces indeterminate integral variables has been used to minimize the number of unknowns. The constituent materials of the beam are assumed gradually variable along the direction of height according to a simple power law distribution in terms of the volume fractions of the constituents. The variation of the pores in the direction of the thickness influences the mechanical properties. It is therefore necessary to predict the effect of porosity on vibratory behavior and wave velocity of FG beams in this study. A new function of the porosity factor has been developed. Hamilton's principle is used for the development of wave propagation equations in the functionally graded beam. The analytical dispersion relationship of the FG beam is obtained by solving an eigenvalue problem. Illustrative numerical examples are given to show the effects of volume fraction distributions, beam height, wave number, and porosity on free vibration and wave propagation in a functionally graded beam.

• Coupled systems mechanics
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• v.6 no.2
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• pp.207-227
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• 2017

In this paper Timoshenko beam theory is employed to investigate the vibration characteristics of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) Beams with a stiff core in thermal environment. The material characteristic of carbon nanotubes (CNT) are supposed to change in the thickness direction in a functionally graded form. They can also be calculated through a micromechanical model where the CNT efficiency parameter is determined by matching the elastic modulus of CNTRCs calculated from the rule of mixture with those gained from the molecular dynamics simulations. The differential transform method (DTM) which is established upon the Taylor series expansion is one of the effective mathematical techniques employed to the differential governing equations of sandwich beams. Effects of carbon nanotube volume fraction, slenderness ratio, core-to-face sheet thickness ratio, different thermal environment and various boundary conditions on the free vibration characteristics of FG-CNTRC sandwich beams are studied. It is observed that vibration response of FG-CNTRC sandwich beams is prominently influenced by these parameters.

• Advances in nano research
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• v.6 no.3
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• pp.201-217
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• 2018

In the present research, wave propagation characteristics of a rotating FG nanobeam undergoing rotation is studied based on nonlocal strain gradient theory. Material properties of nanobeam are assumed to change gradually across the thickness of nanobeam according to Mori-Tanaka distribution model. The governing partial differential equations are derived for the rotating FG nanobeam by applying the Hamilton's principle in the framework of Euler-Bernoulli beam model. An analytical solution is applied to obtain wave frequencies, phase velocities and escape frequencies. It is observed that wave dispersion characteristics of rotating FG nanobeams are extremely influenced by angular velocity, wave number, nonlocal parameter, length scale parameter, temperature change and material graduation.

• Steel and Composite Structures
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• v.36 no.2
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• pp.179-186
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• 2020

In this paper, the forced resonance vibration of porous functionally graded (FG) curved nanobeam is examined. In order to capture the hardening and softening mechanisms of nanostructure, the nonlocal strain gradient theory is employed to build the size-dependent model. Using the Timoshenko beam theory together with the Hamilton principle, the equations of motion for the curved nanobeam are derived. Then, Navier series are used in order to obtain the dynamical deflections of the porous FG curved nanobeam with simply-supported ends. It is found that the resonance position of the nanobeam is very sensitive to the nonlocal and strain gradient parameters, material variation, porosity coefficient, as well as geometrical conditions. The results indicate that the resonance position is postponed by increasing the strain gradient parameter, while the nonlocal parameter has the opposite effect on the results. Furthermore, increasing the opening angle or length-to-thickness ratio will result in resonance position moves to lower-load frequency.

• Smart Structures and Systems
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• v.17 no.5
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• pp.837-857
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• 2016

In the present study, for first time the size dependent vibration behavior of a rotating functionally graded (FG) Timoshenko nanobeam based on Eringen's nonlocal theory is investigated. It is assumed that the physical and mechanical properties of the FG nanobeam are varying along the thickness based on a power law equation. The governing equations are determined using Hamilton's principle and the generalized differential quadrature method (GDQM) is used to obtain the results for cantilever boundary conditions. The accuracy and validity of the results are shown through several numerical examples. In order to display the influence of size effect on first three natural frequencies due to change of some important nanobeam parameters such as material length scale, angular velocity and gradient index of FG material, several diagrams and tables are presented. The results of this article can be used in designing and optimizing elastic and rotary type nano-electro-mechanical systems (NEMS) like nano-motors and nano-robots including rotating parts.