Study of non-uniform viscoelastic nanoplates vibration based on nonlocal first-order shear deformation theory

Mohammadsalehi, M.; Zargar, Omid Ali; Baghani, Mostafa

doi:10.1007/s11012-016-0432-0

Cited by 31 publications

(9 citation statements)

References 40 publications

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“…In the Gurtin-Murdoch theory of elastic surface, Oskouie et al 31 studied, respectively, the linear and non-linear motions of fractional viscoelastic nanobeams Euler-Bernoulli and Timoshenko. In order to investigate viscoelastic micro/nanobeam bending response, the transverse vibrations of non-uniform viscoelastic nanoplates were investigated by Mohammadsalehi et al 32 in the first-order shear deformation theory, the Model Kelvin, and the DENCM. Nanoplate vibration frequencies with DQM were solved by a numeric solution.…”

Section: Introductionmentioning

confidence: 99%

Viscoelastic stressed microbeam analysis based on Moore–Gibson–Thompson heat equation and laser excitation resting on Winkler foundation

Abouelregal

Ahmad

Badr

et al. 2021

Journal of Low Frequency Noise, Vibration and Active Control

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In this work, a modified viscoelastic model of initially stressed microbeam on the base of the Winkler foundation under the effect of ultrafast laser heating and axial stress has been proposed. Viscosity effects are taken into account following the Kelvin–Voigt model. The governing equation for the thermoelastic vibration of the microbeam is obtained when the thermal field effect is defined by the non-Fourier Moore–Gibson–Thompson (MGT) heat equation. The microbeam is seen as an Euler–Bernoulli beam that is exposed to varying sinusoidal heat. An analytical solution to the problem has been presented on the basis of the Laplace transform in addition to applying a numerical method to find inverse transformations. A numerical illustration is organized in the discussion section which discusses the impact of different effective parameters both on the vibrational behavior of a microbeam system and on the field variables. The viscous damping coefficient, laser pulse duration, and axial load greatly affect the deflection and temperature responses. The results obtained are verified and compared with the literature.

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Section: Introductionmentioning

confidence: 99%

Viscoelastic stressed microbeam analysis based on Moore–Gibson–Thompson heat equation and laser excitation resting on Winkler foundation

Abouelregal

Ahmad

Badr

et al. 2021

Journal of Low Frequency Noise, Vibration and Active Control

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“…beams with a varying crosssection (abruptly or gradually) along the length of the beam, play an important role in di erent elds [26], in which they can be used architecturally and aesthetically in aspects of engineering design to optimize the strength and weight of the structure. One of the e ective applications of tapered micro beams is in the micro energy harvester, in which tailoring the structural parameters of the cantilever beam could lead to an increased harvester power [27] and can considerably in uence the natural frequency of microstructures [28]. Baghani et al [26] by considering the assumption of the inextensibility of the neutral axis, studied large amplitude free vibrations of tapered micro-bridges on a nonlinear elastic foundation.…”

Section: Introductionmentioning

confidence: 99%

Size dependent analysis of tapered FG micro-bridge based on a 3D beam theory

2019

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In the current study, an analytical solution based on a modi ed couple stress theory for a nonlinear model describing the couple 3D motion of a functionally graded tapered micro-bridge is presented. The small scale e ects and the nonlinearity arising from the mid-plane stretching are taken into consideration. Governing equations of motion are derived utilizing modi ed couple stress theory and applying the Hamilton principle. Dynamic and static analyses to determine the e ects of lateral distributed forces and mid-plane stretching are investigated. Towards this aim, analytical the Homotopy-pade technique is employed to capture the nonlinear natural frequencies in high amplitude vibrations of tapered micro-bridges with di erent types of geometry and material composition. The obtained results of frequencies propose that there is good agreement between the present analytical results and the numerical ones, as opposed to the well-known multiple-scale method. Furthermore, comparing the results in 2D and 3D analyses shows that in 2D analysis, the sti ness and natural frequency of the micro-beam is underestimated and it is observed that increasing the tapered ratio has di erent impacts on natural frequencies for micro-beams with di erent slender ratios.

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“…Rotating functionally graded disks find their application in ship propellers, aerospace structures, flywheels, and internal combustion engines. In many of these applications, the structure is under sever mechanical loading and the material can operate under such severe loadings [1][2][3][4].…”

Section: Introductionmentioning

confidence: 99%

Elastic Stress Analysis of Rotating Functionally Graded Annular Disk of Variable Thickness Using Finite Difference Method

Jalali

Shahriari

2018

Mathematical Problems in Engineering

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Elastic stress analysis of rotating variable thickness annular disk made of functionally graded material (FGM) is presented. Elasticity modulus, density, and thickness of the disk are assumed to vary radially according to a power-law function. Radial stress, circumferential stress, and radial deformation of the rotating FG annular disk of variable thickness with clamped-clamped (C-C), clamped-free (C-F), and free-free (F-F) boundary conditions are obtained using the numerical finite difference method, and the effects of the graded index, thickness variation, and rotating speed on the stresses and deformation are evaluated. It is shown that using FG material could decrease the value of radial stress and increase the radial displacement in a rotating thin disk. It is also demonstrated that increasing the rotating speed can strongly increase the stress in the FG annular disk.

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Study of non-uniform viscoelastic nanoplates vibration based on nonlocal first-order shear deformation theory

Cited by 31 publications

References 40 publications

Viscoelastic stressed microbeam analysis based on Moore–Gibson–Thompson heat equation and laser excitation resting on Winkler foundation

Viscoelastic stressed microbeam analysis based on Moore–Gibson–Thompson heat equation and laser excitation resting on Winkler foundation

Size dependent analysis of tapered FG micro-bridge based on a 3D beam theory

Elastic Stress Analysis of Rotating Functionally Graded Annular Disk of Variable Thickness Using Finite Difference Method

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