• Structural Engineering and Mechanics
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• v.64 no.4
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• pp.391-402
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• 2017

In this paper, a new nonlocal trigonometric shear deformation theory is proposed for thermal buckling response of nanosize functionally graded (FG) nano-plates resting on two-parameter elastic foundation under various types of thermal environments. This theory uses for the first time, undetermined integral variables and it contains only four unknowns, that is even less than the first shear deformation theory (FSDT). It is considered that the FG nano-plate is exposed to uniform, linear and sinusoidal temperature rises. Mori-Tanaka model is utilized to define the gradually variation of material properties along the plate thickness. Nonlocal elasticity theory of Eringen is employed to capture the size influences. Through the stationary potential energy the governing equations are derived for a refined nonlocal four-variable shear deformation plate theory and then solved analytically. A variety of examples is proposed to demonstrate the importance of elastic foundation parameters, various temperature fields, nonlocality, material composition, aspect and side-to-thickness ratios on critical stability temperatures of FG nano-plate.

• Structural Engineering and Mechanics
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• v.66 no.5
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• pp.621-629
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• 2018

By employing the nonlocal continuum field theory of Eringen and Von Karman nonlinear strains, this paper presents an analytical model for linear and nonlinear dynamics analysis of single-walled carbon nanotubes (SWNTs) conveying fluid with different boundary conditions. In the linear analysis the natural frequencies and critical flow velocities of SWNTs are computed. However, in the nonlinear analysis the effect of nonlocal parameter on nonlinear dynamics of cantilevered SWNTs conveying fluid is investigated by using bifurcation diagram, phase plane and Poincare map. Numerical results confirm existence of chaos as well as a period-doubling transition to chaos.

• 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.20 no.5
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• pp.963-981
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• 2016

A nonlocal trigonometric shear deformation beam theory based on neutral surface position is developed for bending, buckling, and vibration of functionally graded (FG) nanobeams using the nonlocal differential constitutive relations of Eringen. The present model is capable of capturing both small scale effect and transverse shear deformation effects of FG nanobeams, and does not require shear correction factors. The material properties of the FG nanobeam are assumed to vary in the thickness direction. The equations of motion are derived by employing Hamilton's principle, and the physical neutral surface concept. Analytical solutions are presented for a simply supported FG nanobeam, and the obtained results compare well with those predicted by the nonlocal Timoshenko beam theory.

• Smart Structures and Systems
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• v.26 no.1
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• pp.77-87
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• 2020

By employing a quasi-3D plate formulation, the present research studies static stability of magneto-electro-thermo-elastic functional grading (METE-FG) nano-sized plates. Accordingly, influences of shear deformations as well as thickness stretching have been incorporated. The gradation of piezo-magnetic and elastic properties of the nano-sized plate have been described based on power-law functions. The size-dependent formulation for the nano-sized plate is provided in the context of nonlocal elasticity theory. The governing equations are established with the usage of Hamilton's rule and then analytically solved for diverse magnetic-electric intensities. Obtained findings demonstrate that buckling behavior of considered nanoplate relies on the variation of material exponent, electro-magnetic field, nonlocal coefficient and boundary conditions.

• Advances in nano research
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• v.9 no.4
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• pp.277-294
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• 2020

In current paper, nonlocal (NLT), nonlocal strain gradient (NSGT) and Gurtin-Murdoch surface/interface (GMSIT) theories with classical theory (CT) are utilized to investigate vibration and stability analysis of Double Walled Piezoelectric Nanosensor (DWPENS) based on cylindrical nanoshell. DWPENS simultaneously subjected to direct electrostatic voltage DC and harmonic excitations, structural damping, two piezoelectric layers and also nonlinear van der Waals force. For this purpose, Hamilton's principle, Galerkin technique, complex averaging and with arc-length continuation methods are used to analyze nonlinear behavior of DWPENS. For this work, three nonclassical theories compared with classical theory CT to investigate Dimensionless Natural Frequency (DNF), pull-in voltage, nonlinear frequency response and stability analysis of the DWPENS considering the nonlocal, material length scale, surface/interface (S/I) effects, electrostatic and harmonic excitation.

• Structural Engineering and Mechanics
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• v.76 no.1
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• pp.27-56
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• 2020

In this paper, the deflection and buckling analyses of porous nano-composite piezoelectric plate reinforced by carbon nanotube (CNT) are studied. The equations of equilibrium using energy method are derived from principle of minimum total potential energy. In the research, the non-local strain gradient theory is employed to consider size dependent effect for porous nanocomposite piezoelectric plate. The effects of material length scale parameter, Eringen's nonlocal parameter, porosity coefficient and aspect ratio on the deflection and critical buckling load are investigated. The results indicate that the effect of porosity coefficient on the increase of the deflection and critical buckling load is greatly higher than the other parameters effect, and size effect including nonlocal parameter and the material length scale parameter have a lower effect on the deflection increase with respect to the porosity coefficient, respectively and vice versa for critical buckling load. Porous nanocomposites are used in various engineering fields such as aerospace, medical industries and water refinery.

• 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.

• Steel and Composite Structures
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• v.32 no.2
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• pp.281-292
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• 2019

Nonlocal elasticity and Reddy plant theory are used to study the vibration response of functionally graded (FG) nanoplates resting on two parameters elastic medium called Pasternak foundation. Nonlocal higher order theory accounts for the effects of both scale and the effect of transverse shear deformation, which becomes significant where stocky and short nanoplates are concerned. It is assumed that the properties of FG nanoplate follow a power law through the thickness. In addition, Poisson's ratio is assumed to be constant in this model. Both Winkler-type and Pasternak-type foundation models are employed to simulate the interaction of nanoplate with surrounding elastic medium. Using Hamilton's principle, size-dependent governing differential equations of motion and corresponding boundary conditions are derived. A differential quadrature approach is being utilized to discretize the model and obtain numerical solutions for various boundary conditions. The model is validated by comparing the results with other published results.

• 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.