• Steel and Composite Structures
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• v.32 no.2
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• pp.213-223
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• 2019

For the first time, longitudinal and transverse wave propagation of triclinic nanobeam is investigated via a size-dependent shear deformation theory including stretching effect. Furthermore, the influence of initial stress is studied. To consider the size-dependent effects, the nonlocal strain gradient theory is used in which two small scale parameters predict the behavior of wave propagation more accurately. The Hamiltonian principle is adopted to obtain the governing equations of wave motion, then an analytic technique is applied to solve the problem. It is demonstrated that the wave characteristics of the nanobeam rely on the wave number, nonlocal parameter, strain gradient parameter, initial stress, and elastic foundation. From this paper, it is concluded that the results of wave dispersion in isotropic and anisotropic nanobeams are almost the same in the presented case study. So, in this case, triclinic nanobeam can be approximated with isotropic model.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.7
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• pp.3207-3215
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• 2012

In this paper, we study the bending and free vibration analysis of nano plate, using a nonlocal elasticity theory of Eringen with a third-order shear deformation theory. This theory has ability to capture the both small scale effects and quadratic variation of shear strain and consequently shear stress through the plate thickness. Analytical solutions of bending and vibration of a laminated composite nano plate are presented using this theory to illustrate the effect of nonlocal theory on deflection of the nano plates. The relations between nonlocal third-order and local theories are discussed by numerical results. Further, effects of (i) nonlocal parameters, (ii) laminate schemes, (iii) directions of the fiber angle and (iv) number of layers on nondimensional deflections are investigated. In order to validate the present solutions, the reference solutions are used and discussed. The results of anisotropic nano plates using the nonlocal theory may be the benchmark test for the bending analysis.

• Coupled systems mechanics
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• v.7 no.4
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• pp.373-393
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• 2018

This paper is concerned with the wave propagation behavior of rotating functionally graded temperature-dependent nanoscale beams subjected to thermal loading based on nonlocal strain gradient stress field. Uniform, linear and nonlinear temperature distributions across the thickness are investigated. Thermo-elastic properties of FG beam change gradually according to the Mori-Tanaka distribution model in the spatial coordinate. The nanobeam is modeled via a higher-order shear deformable refined beam theory which has a trigonometric shear stress function. The governing equations are derived by Hamilton's principle as a function of axial force due to centrifugal stiffening and displacement. By applying an analytical solution and solving an eigenvalue problem, the dispersion relations of rotating FG nanobeam are obtained. Numerical results illustrate that various parameters including temperature change, angular velocity, nonlocality parameter, wave number and gradient index have significant effect on the wave dispersion characteristics of the understudy nanobeam. The outcome of this study can provide beneficial information for the next generation researches and exact design of nano-machines including nanoscale molecular bearings and nanogears, etc.

• Structural Engineering and Mechanics
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• v.55 no.5
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• pp.1001-1014
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• 2015

Bending analysis of functionally graded (FG) nano-plates is investigated in the present work based on a new sinusoidal shear deformation theory. The theory accounts for sinusoidal distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. The material properties of nano-plate are assumed to vary according to power law distribution of the volume fraction of the constituents. The size effects are considered based on Eringen's nonlocal theory. Governing equations are derived using energy method and Hamilton's principle. The closed-form solutions of simply supported nano-plates are obtained and the results are compared with those of first-order shear deformation theory and higher-order shear deformation theory. The effects of different parameters such as nano-plate length and thickness, elastic foundation, orientation of foundation orthtotropy direction and nonlocal parameters are shown in dimensionless displacement of system. It can be found that with increasing nonlocal parameter, the dimensionless displacement of nano-plate increases.

• Advances in aircraft and spacecraft science
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• v.10 no.3
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• pp.257-279
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• 2023

This manuscript is dedicated to deriving the closed form solutions of free vibration of viscoelastic nanobeam embedded in an elastic medium using nonlocal differential Eringen elasticity theory that not considered before. The kinematic displacements of Euler-Bernoulli and Timoshenko theories are developed to consider the thin nanobeam structure (i.e., zero shear strain/stress) and moderated thick nanobeam (with constant shear strain/stress). To consider the internal damping viscoelastic effect of the structure, Kelvin/Voigt constitutive relation is proposed. The perforation geometry is intended by uniform symmetric squared holes arranged array with equal space. The partial differential equations of motion and boundary conditions of viscoelastic perforated nonlocal nanobeam with elastic foundation are derived by Hamilton principle. Closed form solutions of damped and natural frequencies are evaluated explicitly and verified with prestigious studies. Parametric studies are performed to signify the impact of elastic foundation parameters, viscoelastic coefficients, nanoscale, supporting boundary conditions, and perforation geometry on the dynamic behavior. The closed form solutions can be implemented in the analysis of viscoelastic NEMS/MEMS with perforations and embedded in elastic medium.

• Structural Engineering and Mechanics
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• v.90 no.6
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• pp.569-575
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• 2024

The objective of this study is to investigate the influence of an inclined load, location, and time on the behavior of a fiber-reinforced visco-thermoelastic half-space. The displacement, stress, and temperature distributions are derived from the normal mode analysis. The problem is analyzed using a three-phase-lag model. MATLAB programming is employed to ascertain the physical fields with appropriate boundary conditions and to perform numerical computations. The outcomes are then examined with different inclination loads, time, and location settings.

• Structural Engineering and Mechanics
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• v.75 no.6
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• pp.659-674
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• 2020

The present paper employs nonlocal strain gradient theory (NSGT) to study buckling behavior of functionally graded magneto-electro-thermo-elastic (FG-METE) nanoshells under various physical fields. NSGT modeling of the nanoshell contains two size parameters, one related to nonlocal stress field and another related to strain gradients. It is considered that mechanical, thermal, electrical and magnetic loads are exerted to the nanoshell. Temperature field has uniform and linear variation in nanoshell thickness. According to a power-law function, piezo-magnetic, thermal and mechanical properties of the nanoshell are considered to be graded in thickness direction. Five coupled governing equations have been obtained by using Hamilton's principle and then solved implementing Galerkin's method. Influences of temperature field, electric voltage, magnetic potential, nonlocality, strain gradient parameter and FG material exponent on buckling loads of the FG-METE nanoshell have been studied in detail.

• Steel and Composite Structures
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• v.25 no.1
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• pp.67-78
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• 2017

In this study, free vibration of functionally graded (FG) micro/nanobeams based on nonlocal third-order shear deformation theory and under different boundary conditions is investigated by applying the differential quadrature method. Third-order shear deformation theory can consider the both small-scale effects and quadratic variation of shear strain and hence shear stress along the FG nanobeam thickness. The governing equations are obtained by using the Hamilton's principle, based on third-order shear deformation beam theory. The differential quadrature (DQ) method is used to discretize the model and attain the natural frequencies and mode shapes. The properties of FG micro/nanobeam are assumed to be chanfged along the thickness direction based on the simple power law distribution. The effects of various parameters such as the nonlocal parameter, gradient index, boundary conditions and mode number on the vibration characteristics of FG micro/nanobeams are discussed in detail.

• Advances in nano research
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• v.11 no.6
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• pp.581-593
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• 2021

This model is proposed to describe the buckling behavior of Carbon Nanotubes (CNTs) embedded in an elastic medium taking into account the combined effects of the magnetic field, the temperature, the nonlocal parameter, the number of walls. Using Eringen's nonlocal elasticity theory, thin cylindrical shell theory and Van der Waal force (VdW) interactions, we develop a system of partial differential equations governing the buckling response of CNTs embedded on Winkler, Pasternak, and Kerr foundations in a thermal-magnetic environment. The pre-buckling stresses are obtained by applying airy's stress function and an adjacent equilibrium criterion. To estimate the nonlocal critical buckling load of CNTs under the simultaneous effects of the magnetic field, the temperature change, and the number of walls, an optimization technique is proposed. Furthermore, analytical formulas are developed to obtain the buckling behavior of SWCNTs embedded in an elastic medium without taking into account the effects of the nonlocal parameter. These formulas take into account VdW interactions between adjacent tubes and the effect of terms involving differences in tube radii generally neglected in the derived expressions of the critical buckling load published in the literature. Most scientific research on modeling the effects of magnetic fields is based on beam theories, this motivation pushes me to develop a cylindrical shell model for studying the effect of the magnetic field on the static behavior of CNTs. The results show that the magnetic field has significant effects on the static behavior of CNTs and can lead to slow buckling. On the other hand, thermal effects reduce the critical buckling load. The findings in this work can help us design of CNTs for various applications (e.g. structural, electrical, mechanical and biological applications) in a thermal and magnetic environment.

• Steel and Composite Structures
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• v.36 no.6
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• pp.643-656
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• 2020

This article presents a comprehensive static analysis of simply supported cross-ply carbon nanotubes reinforced composite (CNTRC) laminated nanobeams under various loading profiles. The nonlocal strain gradient constitutive relation is exploited to present the size-dependence of nano-scale. New higher shear deformation beam theory with hyperbolic function is proposed to satisfy the zero-shear effect at boundaries and parabolic variation through the thickness. Carbon nanotubes (CNTs), as the reinforced elements, are distributed through the beam thickness with different distribution functions, which are, uniform distribution (UD-CNTRC), V- distribution (FG-V CNTRC), O- distribution (FG-O CNTRC) and X- distribution (FG-X CNTRC). The equilibrium equations are derived, and Fourier series function are used to solve the obtained differential equation and get the response of nanobeam under uniform, linear or sinusoidal mechanical loadings. Numerical results are obtained to present influences of CNTs reinforcement patterns, composite laminate structure, nonlocal parameter, length scale parameter, geometric parameters on center deflection ad stresses of CNTRC laminated nanobeams. The proposed model is effective in analysis and design of composite structure ranging from macro-scale to nano-scale.