Size-dependent vibration in two-directional functionally graded porous nanobeams under hygro-thermo-mechanical loading

Ebrahimi-Nejad, Salman; Shaghaghi, Gholam Reza; Miraskari, Fatemeh; Kheybari, Majid

doi:10.1140/epjp/i2019-12795-6

Cited by 18 publications

(9 citation statements)

References 39 publications

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“…Structures and components in advanced machines such as aerospace shuttles and craft require advanced composites whose properties vary continuously in more than one direction to satisfy the requirements of temperature and stress distributions in two or more directions [27]. By the rapid advancement in nanomechanics, the static and dynamic characteristics of bi-directional functionally graded (BDFG) micro/nanosized beams have been modelled and investigated based on the differential nonlocal elasticity theory "DNET" ( [6,[28][29][30][31][32][33][34]), MCST ( [35][36][37][38][39][40][41][42]), and the differential nonlocal strain gradient theory "DNSGT" ( [43][44][45]).…”

Section: Introductionmentioning

confidence: 99%

On the dynamic response of bi-directional functionally graded nanobeams under moving harmonic load accounting for surface effect

Attia

Shanab

2022

Acta Mech

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This paper presents an investigation of the dynamic behavior of bi-directionally functionally graded (BDFG) micro/nanobeams excited by a moving harmonic load. The formulation is established in the context of the surface elasticity theory and the modified couple stress theory to incorporate the effects of surface energy and microstructure, respectively. Based on the generalized elasticity theory and the parabolic shear deformation beam theory, the nonclassical governing equations of the problem are obtained using Lagrange’s equation accounting for the physical neutral plane concept. The material properties of the beam smoothly change along both the axial and thickness directions according to power-law distribution, accounting for the gradation of the material length scale parameter and the surface parameters, i.e., residual surface stress, two surface elastic constants, and surface mass density. Using trigonometric Ritz method (TRM), the trial functions denoting transverse, axial deflections, and rotation of the cross sections of the beam are expressed in sinusoidal form. Then, with the aid of Lagrange’s equation, the system of equations of motion are derived. Finally, Newmark method is employed to find the dynamic responses of BDFG subjected to a moving harmonic load. To validate the present formulation and solution method, some comparisons of the obtained fundamental frequency and dynamic response with those available in the literature are performed. A parametric study is performed to extensively explore the impact of the key parameters such as the gradient indices in both directions, moving speed, and excitation frequency of the acting load on the dynamic response of BDFG nanobeams. The obtained results can serve as a guideline for assessing the multi-functional and optimal design of micro/nanobeams acted upon by a moving load.

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Section: Introductionmentioning

confidence: 99%

On the dynamic response of bi-directional functionally graded nanobeams under moving harmonic load accounting for surface effect

Attia

Shanab

2022

Acta Mech

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“…Now, by using Hamilton’s principle [ 49 ], the equations of motion can be derived as:

with the corresponding boundary conditions at x = [ 0 , L ]:

where

, and

denote the local axial force, the bending moment resultant and the equivalent shear force, respectively. In Equations (7) and (8),

and

are, respectively, the temperature-dependent rotary inertia and the effective cross-sectional mass of the porous FG nano-beam, expressed as follow:

and

denote the hygro-thermal axial force resultants, defined as:

in which

and

are the thermal and moisture expansion temperature-dependent coefficients, respectively, previously defined, and

…”

Section: Problem Formulationmentioning

confidence: 99%

“…The motivation of the present paper is to extend the analysis on the hygro-thermal bending behavior of porous FG nano-beams, developed in [ 46 ] by using the aforementioned consistent nonlocal gradient formulations, to their dynamic response, against of many articles on the topic in which the hygro-thermal effects on the size-dependent behavior of nanostructures have been analyzed by making recourse to Eringen’s nonlocal model [ 47 , 48 , 49 , 50 , 51 , 52 , 53 ] or Lim’s nonlocal strain gradient theory in [ 54 , 55 , 56 ], more popularities due to their simply differential formulation.…”

Section: Introductionmentioning

confidence: 99%

Hygro-Thermal Vibrations of Porous FG Nano-Beams Based on Local/Nonlocal Stress Gradient Theory of Elasticity

et al. 2021

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In this manuscript the dynamic response of porous functionally-graded (FG) Bernoulli–Euler nano-beams subjected to hygro-thermal environments is investigated by the local/nonlocal stress gradient theory of elasticity. In particular, the influence of several parameters on both the thermo-elastic material properties and the structural response of the FG nano-beams, such as material gradient index, porosity volume fraction, nonlocal parameter, gradient length parameter, mixture parameter is examined. It is shown how the proposed approach is able to capture the dynamic behavior of porous functionally graded Bernoulli–Euler nano-beams under hygro-thermal loads and leads to well-posed structural problems of nano-mechanics.

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“…In order to overcome the complexity of the experimental tests at nanoscale and the high computational cost of the atomistic simulations, several higher-order continuum mechanics theories have been developed in the last years. The two milestones on this topic are Eringen's strain-driven nonlocal integral model (Eringen's StrainDM) [21,22] and Lim's nonlocal strain gradient theory (Lim's NStrainGT) [23], which have been widely used in a large number of investigations, respectively, in [24][25][26][27][28][29] and [30][31][32][33][34][35], due to their simply differential formulation.…”

Section: Introductionmentioning

confidence: 99%

Application of the Higher-Order Hamilton Approach to the Nonlinear Free Vibrations Analysis of Porous FG Nano-Beams in a Hygrothermal Environment Based on a Local/Nonlocal Stress Gradient Model of Elasticity

et al. 2022

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Nonlinear transverse free vibrations of porous functionally-graded (FG) Bernoulli–Euler nanobeams in hygrothermal environments through the local/nonlocal stress gradient theory of elasticity were studied. By using the Galerkin method, the governing equations were reduced to a nonlinear ordinary differential equation. The closed form analytical solution of the nonlinear natural flexural frequency was then established using the higher-order Hamiltonian approach to nonlinear oscillators. A numerical investigation was developed to analyze the influence of different parameters both on the thermo-elastic material properties and the structural response, such as material gradient index, porosity volume fraction, nonlocal parameter, gradient length parameter, mixture parameter, and the amplitude of the nonlinear oscillator on the nonlinear flexural vibrations of metal–ceramic FG porous Bernoulli–Euler nano-beams.

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Size-dependent vibration in two-directional functionally graded porous nanobeams under hygro-thermo-mechanical loading

Cited by 18 publications

References 39 publications

On the dynamic response of bi-directional functionally graded nanobeams under moving harmonic load accounting for surface effect

On the dynamic response of bi-directional functionally graded nanobeams under moving harmonic load accounting for surface effect

Hygro-Thermal Vibrations of Porous FG Nano-Beams Based on Local/Nonlocal Stress Gradient Theory of Elasticity

Application of the Higher-Order Hamilton Approach to the Nonlinear Free Vibrations Analysis of Porous FG Nano-Beams in a Hygrothermal Environment Based on a Local/Nonlocal Stress Gradient Model of Elasticity

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