• 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.5
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• pp.619-629
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• 2020

In current study, surface/interface effects for pull-in voltage and viscous fluid velocity effects on dimensionless natural frequency (DNF) of fluid-conveying piezoelectric nanosensor (FCPENS) subjected to direct electrostatic voltage DC with nonlinear excitation, harmonic force and also viscoelastic foundation (visco-pasternak medium and structural damping) are investigated using Gurtin-Murdoch surface/interface (GMSIT) theory. For this analysis, Hamilton's principles, the assumed mode method combined with Lagrange-Euler's are used for the governing equations and boundary conditions. The effects of surface/interface parameters of FCPENS such as Lame's constants (λI,S, μI,S), residual stress (τ0I,S), piezoelectric constants (e31psk,e32psk) and mass density (ρI,S) are considered for analysis of dimensionless natural frequency respect to viscous fluid velocity u̅f and pull-in voltage V̅DC.

• Smart Structures and Systems
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• v.21 no.1
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• pp.65-74
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• 2018

In this article, an analytic non-classical model for the free vibrations of nanobeams accounting for surface stress effects is developed. The classical continuum mechanics fails to capture the surface energy effects and hence is not directly applicable at nanoscale. A general beam model based on Gurtin-Murdoch continuum surface elasticity theory is developed for the analysis of thin and thick beams. Thus, surface energy has a significant effect on the response of nanoscale structures, and is associated with their size-dependent behavior. To check the validity of the present analytic solution, the numerical results are compared with those obtained in the scientific literature. The influences of beam thickness, surface density, surface residual stress and surface elastic constants on the natural frequencies of nanobeams are also investigated. It is indicated that the effect of surface stress on the vibrational response of a nanobeam is dependent on its aspect ratio and thickness.

• Advances in aircraft and spacecraft science
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• v.5 no.6
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• pp.691-729
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• 2018

In this paper the hygro-thermo-mechanical vibration and buckling behavior of embedded FG nano-plates are investigated. The Eringen's and Gurtin-Murdoch theories are applied to study the small scale and surface effects on frequencies and critical buckling loads. The effective material properties are modeled using Mori-Tanaka homogenization scheme. On the base of RPT and HSDPT plate theories, the Hamilton's principle is employed to derive governing equations. Using iterative and GDQ methods the governing equations are solved and the influence of different parameters on natural frequencies and critical buckling loads are studied.

• Interaction and multiscale mechanics
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• v.4 no.2
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• pp.123-137
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• 2011

We review a series of crack problems arising in the general deformations of a linearly elastic solid (Mode-I, Mode-II and Mode-III crack) and, perhaps more significantly, when the contribution of surface effects are taken into account. The surface mechanics are incorporated using the continuum based surface/interface model of Gurtin and Murdoch. We show that the deformations of an elastic solid containing a single crack can be decoupled into in-plane (Mode-I and Mode-II crack) and anti-plane (Mode-III crack) parts, even when the surface mechanics is introduced. In particular, it is shown that, in contrast to classical fracture mechanics (where surface effects are neglected), the incorporation of surface elasticity leads to the more accurate description of a finite stress at the crack tip. In addition, the corresponding stress fields exhibit strong dependency on the size of crack.

• Multiscale and Multiphysics Mechanics
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• v.1 no.1
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• pp.15-33
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• 2016

In this paper, an asymptotic method is employed to formulate nano- or micro-beams based on strain gradient elasticity. Although a basic theory for the strain gradient elasticity has been well established in literature, a systematic approach is relatively rare because of its complexity and ambiguity of higher-order elasticity coefficients. In order to systematically identify the strain gradient effect, an asymptotic approach is adopted by introducing the small parameter which represents the beam geometric slenderness and/or the internal atomistic characteristic. The approach allows us to systematically split the two-dimensional strain gradient elasticity into the microscopic one-dimensional through-the-thickness analysis and the macroscopic one-dimensional beam analysis. The first-order beam problem turns out to be different from the classical elasticity in terms of the bending stiffness, which comes from the through-the-thickness strain gradient effect. This subsequently affects the second-order transverse shear stress in which the surface shear stress exists. It is demonstrated that a careful derivation of a first strain gradient elasticity embraces "Gurtin-Murdoch traction" as the surface effect of a one-dimensional Euler-Bernoulli-like beam model.

• Interaction and multiscale mechanics
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• v.4 no.2
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• pp.85-105
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• 2011

The influence of surface elasticity and surface residual stress on the elastic field of an isotropic nanoscale elastic layer of finite thickness bonded to a rigid material base is considered by employing the Gurtin-Murdoch continuum theory of elastic material surfaces. The fundamental solutions corresponding to buried vertical and horizontal line loads are obtained by using Fourier integral transform techniques. Selected numerical results are presented for the cases of a finite elastic layer and a semi-infinite elastic medium to portray the influence of surface elasticity and residual surface stress on the bulk stress field. It is found that the bulk stress field depends significantly on both surface elastic constants and residual surface stress. The consideration of out-of-plane terms of the surface stress yields significantly different solutions compared to previous studies. The solutions presented in this study can be used to examine a variety of practical problems involving nanoscale/soft material systems and to develop boundary integral equations methods for such systems.

• Steel and Composite Structures
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• v.37 no.5
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• pp.551-569
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• 2020

Vibration of vertically aligned-monolayered-nonuniform nanorods consist of functionally graded materials with elastic supports has not been investigated yet. To fill this gap, the problem is examined using the elasticity theories of Eringen and Gurtin-Murdoch. The geometrical and mechanical properties of the surface layer and the bulk are allowed to vary arbitrarily across the length. The nonlocal-surface energy-based governing equations are established using differential-type and integro-type formulations, and solved by employing the Galerkin method by exploiting admissible modes approach and element-free Galerkin (EFG). Through various comparison studies, the effectiveness of the EFG in capturing both nonlocal-differential/integro-based frequencies is proved. A constructive parametric study is also conducted, and the roles of nanorods' diameter, length, stiffness of both inter-rod's elastic layer and elastic supports, power-law index of both constituent materials and geometry, nonlocal and surface effects on the dominant frequencies are revealed.

• Steel and Composite Structures
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• v.35 no.4
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• pp.555-566
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• 2020

This paper aims to present an analytical methodology to investigate influences of nanoscale and surface energy on buckling stability behavior of perforated nanobeam structural element, for the first time. The surface energy effect is exploited to consider the free energy on the surface of nanobeam by using Gurtin-Murdoch surface elasticity theory. Thin and thick beams are considered by using both classical beam of Euler and first order shear deformation of Timoshenko theories, respectively. Equivalent geometrical constant of regularly squared perforated beam are presented in simplified form. Problem formulation of nanostructure beam including surface energies is derived in detail. Explicit analytical solution for nanoscale beams are developed for both beam theories to evaluate the surface stress effects and size-dependent nanoscale on the critical buckling loads. The closed form solution is confirmed and proven by comparing the obtained results with previous works. Parametric studies are achieved to demonstrate impacts of beam filling ratio, the number of hole rows, surface material characteristics, beam slenderness ratio, boundary conditions as well as loading conditions on the non-classical buckling of perforated nanobeams in incidence of surface effects. It is found that, the surface residual stress has more significant effect on the critical buckling loads with the corresponding effect of the surface elasticity. The proposed model can be used as benchmarks in designing, analysis and manufacturing of perforated nanobeams.

• Steel and Composite Structures
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• v.37 no.2
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• pp.229-251
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• 2020

In this paper, dynamic buckling of a smart sandwich nanotube is studied. The nanostructure is composed of a carbon-nanotube with inner and outer surfaces coated with ZnO piezoelectric layers, which play the role of sensor and actuator. Nanotube is under magnetic field and ZnO layers are under electric field. The nanostructure is located in a viscoelastic environment, which is assumed to obey Visco-Pasternak model. Non-local piezo-elasticity theory is used to consider the small-scale effect, and Kelvin model is used to describe the structural damping effects. Surface stresses are taken into account based on Gurtin-Murdoch theory. Hamilton principle in conjunction with zigzag shear-deformation theory is used to obtain the governing equations. The governing equations are then solved using the differential quadrature method, to determine dynamic stability region of the nanostructure. To validate the analysis, the results for simpler case studies are compared with others reported in the literature. Then, the effect of various parameters such as small-scale, surface stresses, Visco-Pasternak environment and electric and magnetic fields on the dynamic stability region is investigated. The results show that considering the surface stresses leads to an increase in the excitation frequency and the dynamic stability region happens at higher frequencies.