Nonlocal Vibration Analysis for Micro/Nano Beam on Winkler Foundation via DTM

Demir, Çiğdem

doi:10.24107/ijeas.281514

Cited by 6 publications

(4 citation statements)

References 52 publications

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“…Setting τ d ¼ 0 to go back to the constitutive relation for thermoelasticity without the influence of internal viscosity. Based on Hamilton's principle, the motion equation of a microbeam under an axial load σ 0 and resting on Winkler's foundation is given below (see Demir, 2016;Dinev, 2012)…”

Section: Fractional Viscoelastic Model and Problem Formulationmentioning

confidence: 99%

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Thermoelastic fractional derivative model for exciting viscoelastic microbeam resting on Winkler foundation

Abouelregal

2020

Journal of Vibration and Control

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In the current investigation, the thermoelastic vibration of a viscoelastic microbeam resting on the Winkler foundation is studied using the fractional-order theory. To describe the damping of the viscoelastic material according to experimental results, the Kelvin–Voigt model is replaced by a new form with a fractional-order derivative. The generalized thermoelasticity model and Euler–Bernoulli beam theory are used to construct the governing equation. The microbeam is subjected to axial load, ultrafast laser heating, and varying sinusoidal heat. The governing equation is then solved using the Laplace transform technique to determine the deflection and thermoelastic interaction responses of microbeams. The effects of many parameters such as the coefficient of viscosity, axial load, fractional derivative order, laser pulse duration, and foundation parameter on the microbeam response are explained and discussed in detail.

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Section: Fractional Viscoelastic Model and Problem Formulationmentioning

confidence: 99%

“…where Qðx; tÞ is the resilience of the foundation and M is the flexural moment, which is given by (Demir, 2016;Rao, 2007) Figure 1. Microbeam resting on Winkler's foundation.…”

Section: Fractional Viscoelastic Model and Problem Formulationmentioning

confidence: 99%

Thermoelastic fractional derivative model for exciting viscoelastic microbeam resting on Winkler foundation

Abouelregal

2020

Journal of Vibration and Control

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“…Due to its good compromise between model accuracy and simplicity, the Winkler foundation model is the most widely employed foundation model to account for the interactive mechanism between nanobeams and their underlying substrate media [9,38,59,63]. During the last decade, several nanobeamsubstrate medium models have been proposed in the research community to characterize the nanobeam-substrate medium system [64][65][66][67][68]. For example, Azizi et al [64] assessed the influence of the surface-free energy on the nonlinear vibration characteristics of the simply-supported nanobeam-substrate medium system; Niknam and Aghdam [65] derived the analytical solution for buckling and vibration analyses of the nonlocal functionally graded (FG) beam on the elastic foundation; Demir [66] employed the differential transform method (DTM) to compute the natural frequencies of simply supported and clamped-clamped nanobeams on elastic foundation; Ponbunyanon et al [67] extended the Winkler-Pasternak based beam-foundation of Limkatanyu et al [9] to study the flexural behaviour of the nanobeam-substrate medium system; and Jena et al [68] performed buckling analyses of single-walled carbon nanotubes on elastic substrate media under both low and high temperature environments.…”

Section: Introductionmentioning

confidence: 99%

Bending, Buckling and Free Vibration Analyses of Nanobeam-Substrate Medium Systems

et al. 2022

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This study presents a newly developed size-dependent beam-substrate medium model for bending, buckling, and free-vibration analyses of nanobeams resting on elastic substrate media. The Euler-Bernoulli beam theory describes the beam-section kinematics and the Winkler-foundation model represents interaction between the beam and its underlying substrate medium. The reformulated strain-gradient elasticity theory possessing three non-classical material constants is employed to address the beam-bulk material small-scale effect. The first and second constants is associated with the strain-gradient and couple-stress effects, respectively while the third constant is related to the velocity-gradient effect. The Gurtin-Murdoch surface elasticity theory is adopted to account for the surface-free energy. To obtain the system governing equation as well as corresponding boundary conditions, Hamilton’s principle is called for. Three numerical simulations are presented to characterize the influences of the material small-scale effect, the surface-energy effect, and the surrounding substrate medium on bending, buckling, and free vibration responses of nanobeam-substrate medium systems. The first simulation focuses on the bending response and shows the ability of the proposed model to eliminate the paradoxical characteristic inherent to nanobeam models proposed in the literature. The second and third simulations perform the sensitivity investigation of the system parameters on the buckling load and the natural frequency, respectively. All analytical results reveal that both material small-scale and surface-energy effects consistently stiffen the system response while the velocity-gradient effect weakens the system response. Furthermore, these sized-scale effects are more pronounced when the underlying substrate medium becomes softer.

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“…The relevant references provide a detailed description of the basic models. [34][35][36][37][38] Any difference in temperature in a physical system induces heat transfer from the higher to the lower temperature zone. This transportation method takes place until the temperature of the device is constant.…”

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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Nonlocal Vibration Analysis for Micro/Nano Beam on Winkler Foundation via DTM

Cited by 6 publications

References 52 publications

Thermoelastic fractional derivative model for exciting viscoelastic microbeam resting on Winkler foundation

Thermoelastic fractional derivative model for exciting viscoelastic microbeam resting on Winkler foundation

Bending, Buckling and Free Vibration Analyses of Nanobeam-Substrate Medium Systems

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

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