Pull-in and freestanding instability of actuated functionally graded nanobeams including surface and stiffening effects

Abo-bakr, Rasha M.; Eltaher, Mohamed A.; Attia, Mohamed A.

doi:10.1007/s00366-020-01146-0

Cited by 31 publications

(7 citation statements)

References 84 publications

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“…Gurtin and Murdoch ([23,24]) proposed a surface elasticity theory to approximate the contribution of surface energy by assuming an elastic body with elastic surface layers of zero thickness that is perfectly bonded to the surface of the bulk continuum. The Gurtin and Murdoch surface elasticity theory (GM-SET) has been successfully employed in conjunction with the other nonclassical continuum theories in the analysis of homogeneous and one-dimensional FG structures, i.e., GM-SET combined with the DNET ( [47][48][49]), GM-SET combined with the SGT ( [50]), GM-SET combined with the DNSGT ( [51]), GM-SET combined with the MCST ( [52][53][54][55][56][57][58][59][60][61][62][63][64]), and GM-SET combined with the MCST in the framework of DNET ( [65,66]). Based on these studies, it has been shown that incorporating the influence of surface energy may show a stiffness-hardening or stiffness-softening of the studied nanostructures depending on whether the signs of the surface elastic constants are positive or negative.…”

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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“…If not properly addressed, these issues have the potential to adversely affect the system's performance and even destroy the stability of the whole system. As a result, various control approaches have been proposed in the literature to overcome these issues [1][2][3]. These approaches can be classified into intelligent methods, classical approaches and combination of both.…”

Section: Background and Motivationmentioning

confidence: 99%

“…The following conditions should be satisfied:3-a |d(x, t)| + |x k (t)| < ρ where ρ is a positive constant.3-b There exist continuous and positive-definite functions ν and μ such that:ℓ 1 ‖x‖ 2 < ν(x) < ℓ 2 ‖x‖ 2 , ℓ 3 ‖x‖ 2 < μ(x) < ℓ 4 ‖x‖2 where x = (x 1 , . .…”

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confidence: 99%

Adaptive Integral-Type Terminal Sliding Mode Tracker Based on Active Disturbance Rejection for Uncertain Nonlinear Robotic Systems With Input Saturation

Karami

Alattas

Mobayen³

et al. 2021

IEEE Access

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This paper proposes an adaptive integral-type terminal sliding mode tracking control approach based on the active disturbance rejection for uncertain nonlinear systems subject to input saturation and external disturbances. Its main objective is to achieve zero tracking error in the presence of external disturbances, parametric uncertainties and input saturation; ubiquitous problems in most practical engineering systems. The proposed approach combines the robustness and chattering-free dynamics of adaptive integraltype sliding mode control with the estimation properties of a nonlinear extended state observer. It also assumes the bounds of the input saturation to be unknown. The asymptotic stability of the closed-loop system in the presence of disturbances, uncertainties and input saturation is proven using the Lyapunov theorem. The effectiveness of the proposed approach is assessed using a flexible-link robotic manipulator. The obtained results confirmed the robustness and god tracking performance of the proposed approach. Robustness, chattering-free dynamics and good tracking performance albeit input saturation are among the main features INDEX TERMS Active disturbance rejection; nonlinear system; terminal sliding mode control; input saturation; flexible-link manipulator.

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“…Thermal and magnetic fields have been considered in the solution. Furthermore, there are some important papers related to static and dynamic analyses of FG beams [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Buckling analysis of functionally graded beams with periodic nanostructures using doublet mechanics theory

Gül

Aydoğdu

2021

J Braz. Soc. Mech. Sci. Eng.

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Buckling analysis of functionally graded (FG) nanobeams is examined using doublet mechanics theory. The material properties of FG nanobeams change with the thickness coordinate. A periodic nanostructure model is considered in FG nanobeams which has a simple crystal square lattice type and Euler-Bernoulli beam theory is used in the formulation. Softening or hardening material behaviour has been observed by changing chiral angle of the considered FG periodic nanobeams in the present doublet mechanics theory. Unlike other size dependent theories such as nonlocal stress gradient elasticity theory, couple stress theory, strain gradient theory, this mechanical response (softening or hardening) is seen for the first time in doublet mechanics theory. Mechanical material responses are directly affected by the atomic structure of the considered material in the doublet mechanics theory. Firstly, micro-stress and micro-strain relations are obtained for the considered nanostructure model in doublet mechanics theory. Then, these microequations are transformed to macroequations in the present doublet mechanics theory. Thus, more physical and accurate mechanical results can be obtained in nanostructures using the doublet mechanics theory. After developing the mathematical formulations of FG periodic nanobeams, Ritz method is applied to obtain the critical buckling loads for different boundary conditions. Comparison of example studies with the present doublet mechanics model is presented for verification, and effects of chiral angle on stability response of periodic FG nanobeams are discussed.

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Pull-in and freestanding instability of actuated functionally graded nanobeams including surface and stiffening effects

Cited by 31 publications

References 84 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

Adaptive Integral-Type Terminal Sliding Mode Tracker Based on Active Disturbance Rejection for Uncertain Nonlinear Robotic Systems With Input Saturation

Buckling analysis of functionally graded beams with periodic nanostructures using doublet mechanics theory

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