Post-buckling and vibration of post-buckled rotating pre-twisted FG microbeams in thermal environment

Shenas, Amin Ghorbani; Ziaee, Sima; Malekzadeh, P.

doi:10.1016/j.tws.2019.02.012

Cited by 37 publications

(5 citation statements)

References 65 publications

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“…The modified strain gradient and couple stress theories are frequently applied to study the mechanical response of structures at the microscale [44,61]. Subsequently, many scholars applied these size-dependent theories to study the nonlinear statics and dynamics of the FG microstructures in terms of beams [62,63], circular [64,65], and rectangular plates [66]. For instance, employing the parabolic shear deformation beam model and the MCST, Hendi et al [67] anticipated the nonlinear thermo-mechanical vibration behavior of the tapered two-directional graded microbeams around the pre/post-buckling domains.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamic buckling and vibration of thermally post-buckled temperature-dependent FG porous nanobeams based on the nonlocal theory

Salari

Ashoori²,

Vanini³

et al. 2022

Phys. Scr.

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In this paper, nonlinear dynamic snap-through buckling and vibration behavior of the thermally post-buckled functionally graded (FG) porous nanobeams subjected to static and sudden mechanical loads are investigated utilizing the nonlocal elasticity theory. The physical properties of the nanobeam are considered to be functions of temperature based on the Touloukian model. In addition, to describe the FG porous materials, two different patterns of porosity distribution are adopted using trigonometric functions through the thickness of the nanobeam. The equations of motion in conjunction with the von-K ́arm ́an nonlinear assumption are established in the framework of Hamilton’s principle. By employing the Chebyshev-Ritz procedure, the nonlinear equations are discretized for three types of edge supports. Following that, the cylindrical arc-length technique is employed to assess the vibrational responses of the post-buckled nanobeam during static snap-through buckling. To evaluate the nonlinear dynamic buckling of the graded nanobeam under a sudden dynamic load, the Newmark time integration scheme together with the Newton-Raphson iterative method are utilized. Next, by means of the Budiansky-Roth criterion and the phase-plane approach, the dynamic snap-through loads are identified. After validating the developed mathematical model, a comprehensive investigation is carried out to determine the role of various physical and geometrical parameters on the dynamic snap-through buckling and vibration characteristics of the post-buckled FG nanobeams.

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Section: Introductionmentioning

confidence: 99%

Nonlinear dynamic buckling and vibration of thermally post-buckled temperature-dependent FG porous nanobeams based on the nonlocal theory

Salari

Ashoori²,

Vanini³

et al. 2022

Phys. Scr.

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“…Ghommem et al [ 11 ] presented a study on nonlinear dynamic characteristics of rotary nano crystalline material microbeams under electric excitation. Shenas et al [ 12 ] examined the thermal effect on the post-buckling behavior of a spinning pre-twisted microbeam. Yao et al [ 13 ] investigated the transverse free vibration and wave propagation of Timoshenko microbeams with an axial motion.…”

Section: Introductionmentioning

confidence: 99%

Wave Propagation in Rotating Functionally Graded Microbeams Reinforced by Graphene Nanoplatelets

Zhao

Zhou

et al. 2021

Molecules

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This paper presents a study on wave propagation in rotating functionally graded (FG) microbeams reinforced by graphene nanoplatelets (GPLs). The graphene nanoplatelets (GPLs) are considered to distribute in the diameter direction of the micro-beam in a gradient pattern, which leads to the functionally graded structure. By using the Halpin-Tsai micromechanics model and the rule of mixture, the effective material properties of the microbeam are determined. According to the Euler-Bernoulli beam theory and nonlocal elasticity theory, the rotating microbeams are modeled. A comprehensive parametric study is conducted to examine the effects of rotating speed, GPL distribution pattern, GPL length-to-thickness ratio, GPL length-to-width ratio, and nonlocal scale on the wavenumber, phase speed and group speed of the microbeam. The research findings can play an important role on the design of rotating graphene nanoplatelet (GPL) reinforced microbeams for better structural performance.

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“…Such long range interactions occur between charged atoms or molecules in a solid. Recently, many works have been focused on mechanical analysis of micro‐and nanostructures namely: static, vibration, bucking and postbuckling, dynamic and thermomechanical behavior based on the non‐classical continuum theories.…”

Section: Introductionmentioning

confidence: 99%

“…Such long range interactions occur between charged atoms or molecules in a solid. Recently, many works have been focused on mechanical analysis of micro-and nanostructures namely: static, [5][6][7][8][9] vibration, [10][11][12][13][14][15] bucking and postbuckling, [16][17][18][19] dynamic [20][21][22][23][24][25] and thermomechanical [26][27][28][29] behavior based on the non-classical continuum theories.On the other hand, in the proximity between material objects which are in order of a few microns down to nanometers e.g., electrodes in NEMS, a regime is governed in which intermolecular forces such as the van der Waals and Casimir forces become operative. [30][31][32] In such devices, the nanoscale surface forces are able to overcome elastic restoring reactions in the electrodes and consequently lead to the sheets' sticking during the fabrication process.…”

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confidence: 99%

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On dynamic pull‐in instability of electrostatically actuated multilayer nanoresonators: A semi‐analytical solution

Taati

2019

Z Angew Math Mech

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Based on the nonlocal Euler–Bernoulli beam theory, a theoretical approach is developed to investigate the effects of small scale and intermolecular force on the dynamic pull‐in behavior of electrostatically actuated nanoresonators. To this purpose, nanoresonators are modeled as multilayer beams with rectangular cross‐sections and fixed‐fixed and fixed‐free end conditions which are embedded in an elastic medium containing Winkler and Pasternak elastic foundations. Also, the effects of nonlocal parameter, fringing field due to the finite width of beams, Casimir or van der Waals intermolecular forces, nonlinear term induced by mid‐plane stretching and Winkler and Pasternak elastic foundations are considered in the mathematical modeling of pull‐in behavior. Finally, a hybrid semi‐analytical method is proposed to solve the nonlinear partial differential equation in two steps using the separation of variable technique. First, the Galerkin method is used to reduce a nonlinear ordinary differential equation with respect to time variable. Next, the parameter expansion method is applied to solve ensuing equation and obtain the time history response of transverse deflection. As case studies, the numerical results including curves of voltage‐normalized frequency, time history of normalized maximum deflection and phase portrait of two six‐layer cantilever and fully fixed beams are presented and discussed in detail. Findings indicate that the effect of small scale on the pull‐in voltages is more significant for both boundary conditions, in comparison with the intermolecular force. Also, it is seen that the pull‐in voltages of cantilever beams become larger by considering the nonlocal effect, contrary to the case of fully fixed beams.

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Post-buckling and vibration of post-buckled rotating pre-twisted FG microbeams in thermal environment

Cited by 37 publications

References 65 publications

Nonlinear dynamic buckling and vibration of thermally post-buckled temperature-dependent FG porous nanobeams based on the nonlocal theory

Nonlinear dynamic buckling and vibration of thermally post-buckled temperature-dependent FG porous nanobeams based on the nonlocal theory

Wave Propagation in Rotating Functionally Graded Microbeams Reinforced by Graphene Nanoplatelets

On dynamic pull‐in instability of electrostatically actuated multilayer nanoresonators: A semi‐analytical solution

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