• Advances in aircraft and spacecraft science
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• v.7 no.6
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• pp.517-536
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• 2020

The present study investigates axial vibration of a FG nanobeam using nonlocal elasticity theory under clamped-clamped and clamped-free boundary conditions. Power law, exponential law and sigmoid law are applied as grading laws to examine the effect of the material distribution on axial vibration of the FG nanobeam. A parametric study was done to examine the effect of length scale on the dynamic behavior of the structure and the results are presented. It was observed that consideration of the nonlocal length scale is essential when analyzing the free vibration of a FG nanobeam. The results of the present study can be used as benchmarks in future studies of FG nanostructures.

• 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.55 no.2
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• pp.281-298
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• 2015

In this study, nonlinear transverse vibrations of tensioned Euler-Bernoulli nanobeams are studied. The nonlinear equations of motion including stretching of the neutral axis and axial tension are derived using nonlocal beam theory. Forcing and damping effects are included in the equations. Equation of motion is made dimensionless via dimensionless parameters. A perturbation technique, the multiple scale methods is employed for solving the nonlinear problem. Approximate solutions are applied for the equations of motion. Natural frequencies of the nanobeams for the linear problem are found from the first equation of the perturbation series. From nonlinear term of the perturbation series appear as corrections to the linear problem. The effects of the various axial tension parameters and different nonlocal parameters as well as effects of different boundary conditions on the vibrations are determined. Nonlinear frequencies are estimated; amplitude-phase modulation figures are presented for simple-simple and clamped-clamped cases.

• Steel and Composite Structures
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• v.11 no.1
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• pp.59-76
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• 2011

Dynamic analysis of an embedded single-walled carbon nanotube (SWCNT) traversed by a moving nanoparticle, which is modeled as a moving load, is investigated in this study based on the nonlocal Timoshenko beam theory, including transverse shear deformation and rotary inertia. The governing equations and boundary conditions are derived by using the principle of virtual displacement. The Galerkin method and the direct integration method of Newmark are employed to find the dynamic response of the SWCNT. A detailed parametric study is conducted to study the influences of the nonlocal parameter, aspect ratio of the SWCNT, elastic medium constant and the moving load velocity on the dynamic responses of SWCNT. For comparison purpose, free vibration frequencies of the SWCNT are obtained and compared with a previously published study. Good agreement is observed. The results show that the above mentioned effects play an important role on the dynamic behaviour of the SWCNT.

• Structural Engineering and Mechanics
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• v.76 no.3
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• pp.413-420
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• 2020

Considering inverse cotangential shear strain function, the present paper studies nonlinear stability of nonlocal higher-order refined beams made of metal foams based on Chebyshev-Ritz method. Based on inverse cotangential beam model, it is feasible to incorporate shear deformations needless of shear correction factor. Metal foam is supposed to contain different distributions of pores across the beam thickness. Also, presented Chebyshev-Ritz method can provide a unified solution for considering various boundary conditions based on simply-supported and clamped edges. Nonlinear effects have been included based upon von-karman's assumption and nonlinear elastic foundation. The buckling curves are shown to be affected by pore distribution, geometric imperfection of the beam, nonlocal scale factor, foundation and geometrical factors.

• Advances in nano research
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• v.7 no.2
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• pp.99-108
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• 2019

Higher-order theories are very important to investigate the mechanical properties and behaviors of nanoscale structures. In this study, a free vibration behavior of SiNW resting on elastic foundation is investigated via Eringen's nonlocal elasticity theory. Silicon Nanowire (SiNW) is modeled as simply supported both ends and clamped-free Euler-Bernoulli beam. Pasternak two-parameter elastic foundation model is used as foundation. Finite element formulation is obtained nonlocal Euler-Bernoulli beam theory. First, shape function of the Euler-Bernoulli beam is gained and then Galerkin weighted residual method is applied to the governing equations to obtain the stiffness and mass matrices including the foundation parameters and small scale parameter. Frequency values of SiNW is examined according to foundation and small scale parameters and the results are given by tables and graphs. The effects of small scale parameter, boundary conditions, foundation parameters on frequencies are investigated.

• Advances in nano research
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• v.7 no.1
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• pp.63-75
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• 2019

This article represents a quasi-3D theory for the buckling investigation of magneto-electro-elastic functionally graded (MEE-FG) nanoplates. All the effects of shear deformation and thickness stretching are considered within the presented theory. Magneto-electro-elastic material properties are considered to be graded in thickness direction employing power-law distribution. Eringen's nonlocal elasticity theory is exploited to describe the size dependency of such nanoplates. Using Hamilton's principle, the nonlocal governing equations based on quasi-3D plate theory are obtained for the buckling analysis of MEE-FG nanoplates including size effect and they are solved applying analytical solution. It is found that magnetic potential, electric voltage, boundary conditions, nonlocal parameter, power-law index and plate geometrical parameters have significant effects on critical buckling loads of MEE-FG nanoscale plates.

• Advances in Computational Design
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• v.7 no.3
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• pp.211-227
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• 2022

In this research, the size-dependent impact of an embedded piezoelectric nanoplate subjected to in-plane loading on free vibration characteristic is studied. The foundation is two-parameter viscoelastic. The nonlocal elasticity is employed in order to capture the influence of size of the plate. By utilizing Hamilton's principle as well as the first- order shear deformation theory, the governing equation and boundary conditions are achieved. Then, using Navier method the equations associated with the free vibration of a plate constructed piezoelectric material under in-plane loads are solved analytically. The presented formulation and solution procedure are validated using other papers. Also, the impacts of nonlocal parameter, mode number, constant of spring, electric potential, and geometry of the nanoplate on the vibrational frequency are examined. As this paper is the first research in which the vibration associated with piezoelectric nanoplate on the basis of FSDT and nonlocal elasticity is investigated analytically, this results can be used in future investigation in this area.

• Advances in nano research
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• v.12 no.1
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• pp.37-47
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• 2022

In this paper, the non-linear static analysis of Timoshenko nanobeams consisting of bi-directional functionally graded material (BFGM) with immovable ends is investigated. The scratching in the FG nanobeam mid-plane, is the source of nonlinearity of the bending problems. The nonlocal theory is used to investigate the non-linear static deflection of nanobeam. In order to simplify the formulation, the problem formulas is derived according to the physical middle surface. The Hamilton principle is employed to determine governing partial differential equations as well as boundary conditions. Moreover, the differential quadrature method (DQM) and direct iterative method are applied to solve governing equations. Present results for non-linear static deflection were compared with previously published results in order to validate the present formulation. The impacts of the nonlocal factors, beam length and material property gradient on the non-linear static deflection of BFG nanobeams are investigated. It is observed that these parameters are vital in the value of the non-linear static deflection of the BFG nanobeam.

• Advances in materials Research
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• v.12 no.4
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• pp.309-330
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• 2023

The humid thermal vibration characteristics of a nonhomogeneous thermopiezoelectric nonlocal plate of polygonal shape are addressed in the purview of generalized nonlocal thermoelasticity. The plate is initially stressed, and the three-dimensional linear elasticity equations are taken to form motion equations. The problem is solved using the Fourier expansion collocation method along the irregular boundary conditions. The numerical results of physical variables have been discussed for the triangle, square, pentagon, and hexagon shapes of the plates and are given as dispersion curves. The amplitude of non-dimensional frequencies is tabulated for the longitudinal and flexural symmetric modes of the thermopiezoelectric plate via moisture and thermal constants. Also, a comparison of numerical results is made with existing literature, and good agreement is reached.