The vibration of a gold nanobeam under the thermoelasticity fractional-order strain theory based on Caputo–Fabrizio’s definition

Al-Lehaibi, Eman A. N.

doi:10.1177/03093247221145792

Cited by 6 publications

(4 citation statements)

References 51 publications

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“…The strain's theory of thermo-elasticity fractional-order is used to describe the vibration of a gold nano-beam in many publications, including, 8,9 within the context of Caputo-Fabrizio's. 10 Numerical results are achieved and graphically portrayed in accordance with the various values of electrical voltage and resistivity.…”

Section: Introductionmentioning

confidence: 99%

Stability and analysis of the vibrating motion of a four degrees-of-freedom dynamical system near resonance

Amer,

Ismail,

Shaker

et al. 2024

Journal of Low Frequency Noise, Vibration and Active Control

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This article investigates the impact of three harmonically external moments on the motion of a four-degrees-of-freedom (DOF) nonlinear dynamical system composed of a double rigid pendulum connected to a nonlinear spring with linear damping. In light of the system’s generalized coordinates, the governing system (GS) of motion is derived using Lagrange’s equations. With the use of the multiple-scales method (MSM), the approximate solutions (AS) of the equations of this system are obtained up to a higher order of approximation, maybe the third order. Within the framework of the absence of secular terms, the conditions of solvability are obtained. Accordingly, the different resonance cases are categorized, and three of them are investigated simultaneously. Thus, these conditions are updated in preparation for achieving the modulation equations (ME) for the examined system. The numerical solutions (NS) of the GS are achieved using the algorithms of fourth-order Runge–Kutta (4RK), which are compared with the AS, which displays their high degree of consistency and demonstrates the precision of the MSM. The motion’s time history, steady-state solutions, and resonance curves are graphed to demonstrate the influence of various system physical parameters. All relevant fixed points at steady-state situations are identified and graphed in accordance with the Routh–Hurwitz criteria (RHC). Therefore, the zones of stability/instability of are checked and analyzed. Numerous real-world applications in disciplines like engineering and physics attest to the significance of the nonlinear dynamical system under study such as in shipbuilding, automotive devices, structure vibration, developing robots, and analysis of human walking.

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Section: Introductionmentioning

confidence: 99%

Stability and analysis of the vibrating motion of a four degrees-of-freedom dynamical system near resonance

Amer,

Ismail,

Shaker

et al. 2024

Journal of Low Frequency Noise, Vibration and Active Control

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“…Abouelregal et al [ 43 ] analyzed the thermoelastic vibrations of a nonlocal isotropic solid medium subjected to a pulsed heat flux based on the Caputo-Fabrizio fractional derivative generalized thermoelasticity. AL-Lehaibi [ 44 ] solved a two-dimensions thermoelastic problem for an isotropic and homogeneous nanobeam in terms of the thermoelasticity with one relaxation time and fractional-order strain theory. Sherief and Hussein [ 45 ] solved a two-dimensional thermoporoelastic problem for infinitely porous cylinders at certain boundary conditions, using the fractional order generalized thermo-poroelasticity theory.…”

Section: Introductionmentioning

confidence: 99%

Coupling dynamic response of saturated soil with anisotropic thermal conductivity under fractional order thermoelastic theory

Guo,

Xiong,

et al. 2024

PLoS ONE

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In this paper, a two-dimensional (2D) thermo-hydro-mechanical dynamic (THMD) coupling analysis in the presence of a half-space medium is studied using Ezzat’s fractional order generalized theory of thermoelasticity. Using normal mode analysis (NMA), the influence of the anisotropy of the thermal conduction coefficient, fractional derivatives, and frequency on the THMD response of anisotropy, fully saturated, and poroelastic subgrade is then analyzed with a time-harmonic load including mechanical load and thermal source subjected to the surface. The general relationships among the dimensionless physical variables such as the vertical displacement, excess pore water pressure, vertical stress, and temperature distribution are graphically illustrated. The NMA method does not require the integration and inverse transformation, increases the decoupling speed, and eliminates the limitation of numerical inverse transformation. The obtained results can guide the geotechnical engineering construction according to different values of load frequency, fractional order coefficient, and anisotropy of thermal conduction coefficient. This improves the subgrade stability and enriches the theoretical studies on thermo-hydro-mechanical coupling.

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“…Using Caputo-Fabrizio’s, 30 a gold nanobeam’s vibration is explained by the strain theory of thermo-elasticity fractional-order in various works, for example , Refs. [31, 32].…”

Section: Introductionmentioning

confidence: 99%

Evaluation of the stability of a two degrees-of-freedom dynamical system

Amer

Ismail

Amer

2023

Journal of Low Frequency Noise, Vibration and Active Control

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This work studies a two degrees-of-freedom (DOF) dynamical system whose governing system is solved analytically using the multiple scales approach (MSA). The solvability requirements are obtained in light of the elimination of secular terms. All resonance states are classified to understand the equilibrium of the dynamical system. Two of them are examined in parallel to get the associated equations for the system’s modulation. All probable fixed points are identified at the states of stability and instability using the criteria of Routh-Hurwitz (RH). The curves of resonance and the system’s behavior during the motion are plotted and analyzed. The numerical solutions (NS) of the governing system are obtained using the method of Runge-Kutta fourth-order, and they are compared with the analytical solutions (AS). The comparison reveals high consistency between them and proves the accuracy of the MSA. To determine the positive effects of different parameters on the motion, stability zones are studied from the perspective of their graphs. The applications of such works are very important in our daily lives and were the reason for the development of several things, including protection from earthquakes, car shock absorbers, structure vibration, human walking, television towers, high buildings, and antennas.

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The vibration of a gold nanobeam under the thermoelasticity fractional-order strain theory based on Caputo–Fabrizio’s definition

Cited by 6 publications

References 51 publications

Stability and analysis of the vibrating motion of a four degrees-of-freedom dynamical system near resonance

Stability and analysis of the vibrating motion of a four degrees-of-freedom dynamical system near resonance

Coupling dynamic response of saturated soil with anisotropic thermal conductivity under fractional order thermoelastic theory

Evaluation of the stability of a two degrees-of-freedom dynamical system

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