• Advances in nano research
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• 제5권2호
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• pp.113-126
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• 2017

This paper proposes a new nonlocal higher-order hyperbolic shear deformation beam theory (HSBT) for the static bending and vibration of nanoscale-beams. Eringen's nonlocal elasticity theory is incorporated, in order to capture small size effects. In the present model, the transverse shear stresses account for a hyperbolic distribution and satisfy the free-traction boundary conditions on the upper and bottom surfaces of the nanobeams without using shear correction factor. Employing Hamilton's principle, the nonlocal equations of motion are derived. The governing equations are solved analytically for the edges of the beam are simply supported, and the obtained results are compared, as possible, with the available solutions found in the literature. Furthermore, the influences of nonlocal coefficient, slenderness ratio on the static bending and dynamic responses of the nanobeam are examined.

• Advances in materials Research
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• 제9권1호
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• pp.33-48
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• 2020

With the use of differential quadrature method (DQM), forced vibrations and resonance frequency analysis of functionally graded (FG) nano-size beams rested on elastic substrate have been studied utilizing a shear deformation refined beam theory which contains shear deformations influence needless of any correction coefficient. The nano-size beam is exposed to uniformly-type dynamical loads having partial length. The two parameters elastic substrate is consist of linear springs as well as shear coefficient. Gradation of each material property for nano-size beam has been defined in the context of Mori-Tanaka scheme. Governing equations for embedded refined FG nano-size beams exposed to dynamical load have been achieved by utilizing Eringen's nonlocal differential law and Hamilton's rule. Derived equations have solved via DQM based on simply supported-simply supported edge condition. It will be shown that forced vibrations properties and resonance frequency of embedded FG nano-size beam are prominently affected by material gradation, nonlocal field, substrate coefficients and load factors.

• Advances in nano research
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• 제8권1호
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• pp.49-58
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• 2020

This paper investigates the vibration characteristics of flexoelectric nanobeams resting on viscoelastic foundation and subjected to magneto-electro-viscoelastic-hygro-thermal (MEVHT) loading. In this regard, the Nonlocal strain gradient elasticity theory (NSGET) is employed. The proposed formulation accommodates the nonlocal stress and strain gradient parameter along with the flexoelectric coefficient to accurately predict the frequencies. Further, with the aid of Hamilton's principle the governing differential equations are derived which are then solved through Galerkin-based approach. The variation of the natural frequency of MEVHT nanobeams under the influence of various parameters such as the nonlocal strain gradient parameter, different field loads, power-law exponent and slenderness ratio are also investigated.

• Advances in nano research
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• 제7권4호
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• pp.223-231
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• 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.

• Steel and Composite Structures
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• 제32권3호
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• pp.293-304
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• 2019

In the present paper, the element free Galerkin (EFG) method is developed for geometrically nonlinear analysis of deep beams considering small scale effect. To interpret the behavior of structure at the nano scale, the higher-order gradient elasticity nonlocal theory is taken into account. The radial point interpolation method with high order of continuity is used to construct the shape functions. The nonlinear equation of motion is derived using the principle of the minimization of total potential energy based on total Lagrangian approach. The Newmark method with the small time steps is used to solve the time dependent equations. At each time step, the iterative Newton-Raphson technique is applied to minimize the residential forces caused by the nonlinearity of the equations. The effects of nonlocal parameter and aspect ratio on stiffness and dynamic parameters are discussed by numerical examples. This paper furnishes a ground to develop the EFG method for large deformation analysis of structures considering small scale effects.

• Geomechanics and Engineering
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• 제17권2호
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• pp.175-180
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• 2019

This research is concerned with post-buckling investigation of nano-scaled beams constructed from porous functionally graded (FG) materials taking into account geometrical imperfection shape. Hence, two types of nanobeams which are perfect and imperfect have been studied. Porous FG materials are classified based on even or uneven porosity distributions. A higher order nonlinear refined beam theory is used in the present research. Both perfect and imperfect nanobeams are formulated based on this refined theory. A detailed study is provided to understand the effects of geometric imperfection, pore distribution, material distribution and small scale effects on buckling of FG nanobeams.

• Advances in nano research
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• 제7권5호
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• pp.351-364
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• 2019

In this work, dynamic behavior of functionally graded (FG) porous nano-beams is studied based on nonlocal nth-order shear deformation theory which takes into the effect of shear deformation without considering shear correction factors. It has been observed that during the manufacture of "functionally graded materials" (FGMs), micro-voids and porosities can occur inside the material. Thus, in this work, the investigation of the dynamic analysis of FG beams taking into account the influence of these imperfections is established. Material characteristics of the FG beam are supposed to be vary continuously within thickness direction according to a "power-law scheme" which is modified to approximate material characteristics for considering the influence of porosities. A comparative study with the known results in the literature confirms the accuracy and efficiency of the current nonlocal nth-order shear deformation theory.

• Structural Monitoring and Maintenance
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• 제6권2호
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• pp.147-159
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• 2019

In present article, a size-dependent refined thick beam element has been established based upon nonlocal elasticity theory. Next, it is used to explore vibration response of porous metal foam nanobeams on elastic medium. The established beam element introduces ten degrees of freedom. Different porosity distributions called uniform, symmetric and asymmetric will be employed. Herein, introduced thick beam element contains shear deformations without using correction factors. Convergence and verification studies of obtained results from finite element method are also provided. The impacts of nonlocality factor, foundation factors, shear deformation, slenderness ratio, porosity kinds and porosity factor on vibration frequencies of metal foam nano-sized beams have been explored.

• Structural Engineering and Mechanics
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• 제82권5호
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• pp.629-641
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• 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
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• 제14권1호
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• pp.67-80
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• 2023

Economic investigation is one of the main issues regarding the design and production of small-scale structures. This paper concerns the creation, implementation, and economic aspects of the cross-section profile of small-scale structures regarding the dynamic response of the free and forced vibration behavior of spinning nanoscale beams based on big data analysis. According to the financial analysis, the three practical non-uniform functions of cross-sections are compared to the uniform beam in the same weight and the equal material used. The previous studies reported that the uniform beams are more stable and contain a better frequency response based on the mechanical analysis. Still, concerning the economic investigation, which means the considered structures should have equal length and have the same weight in the aspect of material used, the conclusion can be different from the mechanical aspect. Consequently, in the current paper, the dynamic response along with computer technology as well as the big data analysis of the free and forced vibration of the nanobeam regarding the economic shape of the cross-section is scrutinized.