• Advances in nano research
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• v.7 no.3
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• pp.145-155
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• 2019

In this article, the influence of small scale effects on the free vibration response of curved magneto-electro-elastic functionally graded (MEE-FG) nanobeams has been investigated considering nonlocal elasticity theory. Power-law is used to judge the through thickness material property distribution of MEE nanobeams. The Euler-Bernoulli beam model has been adopted and through Hamilton's principle the Nonlocal governing equations of curved MEE-FG nanobeam are obtained. The analytical solutions are obtained and validated with the results reported in the literature. Several parametric studies are performed to assess the influence of nonlocal parameter, magnetic potential, electric voltage, opening angle, material composition and slenderness ratio on the dynamic behaviour of MEE curved nanobeams. It is believed that the results presented in this article may serve as benchmark results in accurate analysis and design of smart nanostructures.

• Steel and Composite Structures
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• v.38 no.3
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• pp.293-304
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• 2021

The aim of this paper is to analyze the nonlinear bending of functionally graded (FG) curved nanobeams reinforced by carbon nanotubes (CNTs) in thermal environment. Chen-Yao's surface elastic theory and geometric nonlinearity are also considered. The nanobeams are subjected to uniform loadings and placed on three-parameter substrates. The Euler-Lagrange equations are employed to deduce the equations of equilibrium. Then, the asymptotic solutions and boundary value problems are analytically determined by utilizing the two-step perturbation technique. Finally, the effects of the surface parameters, geometric factors, foundation stiffness, volume fraction, thermal effects and layout type of CNTs on the nonlinear bending of the nanobeams are discussed.

• Advances in nano research
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• v.7 no.6
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• pp.391-403
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• 2019

In this article the frequency response analysis of curved magneto-electro-viscoelastic functionally graded (CMEV-FG) nanobeams resting on viscoelastic foundation has been carried out. To this end, the study incorporates the Euler-Bernoulli beam model in association with Eringen's nonlocal theory to incorporate the size effects. The viscoelastic foundation in the current investigation is assumed to be the combination of Winkler-Pasternak layer and viscous layer of infinite parallel dashpots. The equations of motion are derived with the aid of Hamilton's principle and the solution to vibration problem of CMEV-FG nanobeams are obtained analytically. The material gradation is considered to follow Power-law rule. This study thoroughly investigates the influence of prominent parameters such as linear, shear and viscous layers of foundation, structural damping coefficient, opening angle, magneto-electrical field, nonlocal parameter, power-law exponent and slenderness ratio on the frequencies of FG nanobeams.

• Structural Engineering and Mechanics
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• v.59 no.3
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• pp.475-502
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• 2016

Nanobeams are widely used as a structural element for nanodevices and nanomachines. The development of nano-sized machines depends on proper understanding of mechanical behavior of these nano-sized beam elements. Small length scales such as lattice spacing between atoms, surface properties, grain size etc. are need to be considered when applying any classical continuum model. In this study, Eringen's nonlocal elasticity theory is incorporated into classical beam model considering the effects of axial extension and the shear deformation to capture unique static behavior of the nanobeams under continuum mechanics theory. The governing differential equations are obtained for curved beams and solved exactly by using the initial value method. Circular uniform beam with concentrated loads are considered. The displacements, slopes and the stress resultants are obtained analytically. A detailed parametric study is conducted to examine the effect of the nonlocal parameter, mechanical loadings, opening angle, boundary conditions, and slenderness ratio on the static behavior of the nanobeam.

• Structural Engineering and Mechanics
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• v.64 no.1
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• pp.1-10
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• 2017

The present paper deals with the free vibration and buckling problem with consideration of surface properties of circular nanobeams and nanoarches. The Gurtin-Murdach theory is used for investigating the surface effects parameters including surface tension, surface density and surface elasticity. Both linear and nonlinear elastic foundation effect are considered on the circular curved nanobeam. The analytically Navier solution is employed to solve the governing equations. It is obviously detected that the natural frequencies of a curved nanobeams is substantially influenced by the elastic foundations. Besides, it is revealed that by increasing the thickness of curved nanobeam, the influence of surface properties and elastic foundations reduce to vanished, and the natural frequency and critical buckling load turns into to the corresponding classical values.

• Coupled systems mechanics
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• v.5 no.3
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• pp.255-267
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• 2016

To investigate the surface effects on vibration of embedded circular curved nanosize beams, nonlocal elasticity model is used in combination with surface properties including surface elasticity, surface tension and surface density for modeling the nano scale effect. The governing equations are determined via the energy method. Analytically Navier method is utilized to solve the governing equations for simply supported at both ends. Solving these equations enables us to estimate the natural frequency for circular curved nanobeam including Winkler and Pasternak elastic foundations. The results determined are verified by comparing the results by available ones in literature. The effects of various parameters such as nonlocal parameter, surface properties, Winkler and Pasternak elastic foundations and opening angle of circular curved nanobeam on the natural frequency are successfully studied. The results reveal that the natural frequency of circular curved nanobeam is significantly influenced by these effects.

• Smart Structures and Systems
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• v.20 no.3
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• pp.351-368
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• 2017

To peruse the free vibration of curved functionally graded piezoelectric (FGP) nanosize beam in thermal environment, nonlocal elasticity theory is applied for modeling the nano scale effect. The governing equations are obtained via the energy method. Analytically Navier solution is employed to solve the governing equations for simply supported boundary conditions. Solving these equations enables us to estimate the natural frequency for curved FGP nanobeam under the effect of a uniform temperature change and external electric voltage. The results determined are verified by comparing the results by available ones in literature. The effects of various parameters such as nonlocality, uniform temperature changes, external electric voltage, gradient index, opening angle and aspect ratio of curved FGP nanobeam on the natural frequency are successfully discussed. The results revealed that the natural frequency of curved FGP nanobeam is significantly influenced by these effects.

• 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.

• Steel and Composite Structures
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• v.29 no.5
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• pp.579-590
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• 2018

Size-dependent free vibration responses and magneto-electro-elastic bending results of a three layers piezomagnetic curved beam rest on Pasternak's foundation are presented in this paper. The governing equations of motion are derived based on first-order shear deformation theory and nonlocal piezo-elasticity theory. The curved beam is containing a nanocore and two piezomagnetic face-sheets. The piezomagnetic layers are imposed to applied electric and magnetic potentials and transverse uniform loadings. The analytical results are presented for simply-supported curved beam to study influence of some parameters on vibration and bending results. The important parameters are spring and shear parameters of foundation, applied electric and magnetic potentials, nonlocal parameter and radius of curvature of curved beam. It is concluded that the increase in radius of curvature tends to an increase in the stiffness of curved beam and consequently natural frequencies increase and bending results decrease. In addition, it is concluded that with increase of nonlocal parameter of curved beam, the stiffness of structure is decreased that leads to decrease of natural frequency and increase of bending results.

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