A novel model of nonlocal thermoelasticity with time derivatives of higher order

Abouelregal, Ahmed E.

doi:10.1002/mma.6416

Cited by 72 publications

(20 citation statements)

References 52 publications

(69 reference statements)

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“…The reported findings and conclusions are consistent with those of various literature researchers [52].…”

Section: Resultssupporting

confidence: 92%

Temperature-Dependent Physical Characteristics and Varying Heat Effects on Nonlocal Rotating Nanobeams Due to Dynamic Load

Abouelregal¹,

Mohammed²,

Moustapha³

et al. 2020

Preprint

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A theoretical nonlocal thermoelastic model for studying the effects of the thermal conductivity variability on a rotating nanobeam has been described in the present article. The theory of thermal stress is employed using the Euler–Bernoulli beam model and generalized heat conduction with phase lags. It is believed that the thermal conductivity of the current model varies linearly according to temperature. Due to variable harmonic heat, the considered nanobeam excited and was subjected to a time-varying exponential decay load. Using the Laplace transform process, the analytical solutions for displacement, deflection, thermodynamic temperature and bending moment of rotating nanobeams are provided in final forms and a numerical example has been taken to address the problem. A comparison of the stated results was displayed and additionally, the influences of non-local parameters and varying load were analyzed and examined. We also investigate how the linear changes in the temperature of physical properties can influence both the static and dynamic responses to the rotating nanobeam.

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“…The reported findings and conclusions are consistent with those of various literature researchers [52].…”

Section: Resultssupporting

confidence: 92%

Temperature-Dependent Physical Characteristics and Varying Heat Effects on Nonlocal Rotating Nanobeams Due to Dynamic Load

Abouelregal¹,

Mohammed²,

Moustapha³

et al. 2020

Preprint

Self Cite

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“…Numerical results are now presented to explain the variation of displacement u, temperature θ , the strain e and the non-local thermal stress τ x x as well as discussed on the obtained results. In order to find the solutions for physical field in space-time areas, we must apply a technique of inversion approximation (40) proposed by Zakian [16,48] to equations ( 34), ( 35), ( 38) and ( 39), respectively. For all numerical calculations, Mathematica programming Language is employed.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Green and Naghdi presented a new generalized thermoelastic theory on the basis of Fourier's law [10][11][12], their theory was proposed in three separate models, the first and second theories are called GN-I and GN-II, respectively, and the third one is called GN-III. Relying on higher-order time derivatives, Abouelregal [13][14][15][16][17][18] did some investigation in order to alter the conventional Fourier's law. In recent years, many researchers have been attracted to examine the Moore-Gibson-Thompson equation (MGT) as well.…”

Section: Introductionmentioning

confidence: 99%

“…The thermal conductivity of the nanoscale beams is also supposed to depend on the temperature changes. Abouelregal [16] introduced a new differential equation system which describes the theory of non-local thermoelasticity with higher derivatives and dual-phase delays. To achieve the proposed theory, he used the Eringen's non-local elasticity and the Taylor expansion methodology of higher-order time derivatives.…”

Section: Introductionmentioning

confidence: 99%

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Computational analysis of an infinite magneto-thermoelastic solid periodically dispersed with varying heat flow based on non-local Moore–Gibson–Thompson approach

Abouelregal

Sedighi

Shirazi

et al. 2021

Continuum Mech. Thermodyn.

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In this investigation, a computational analysis is conducted to study a magneto-thermoelastic problem for an isotropic perfectly conducting half-space medium. The medium is subjected to a periodic heat flow in the presence of a continuous longitude magnetic field. Based on Moore–Gibson–Thompson equation, a new generalized model has been investigated to address the considered problem. The introduced model can be formulated by combining the Green–Naghdi Type III and Lord–Shulman models. Eringen’s non-local theory has also been applied to demonstrate the effect of thermoelastic materials which depends on small scale. Some special cases as well as previous thermoelasticity models are deduced from the presented approach. In the domain of the Laplace transform, the system of equations is expressed and the problem is solved using state space method. The converted physical expressions are numerically reversed by Zakian’s computational algorithm. The analysis indicates the significant influence on field variables of non-local modulus and magnetic field with larger values. Moreover, with the established literature, the numerical results are satisfactorily examined.

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“…Through the experimental observations of micro-/nano-scale structures, it is shown that mechanical properties depend on the size, and these properties cannot be seen when we use the classical theories of elasticity [8][9][10][11] . Hence, modified elasticity theories such as the MCS, the nonlocal continuum mechanics, the nonlocal strain gradient theory, and the strain gradient theory are widely used to analyze the dynamic and static responses of micro-/nano-scale structures [12] .…”

Section: Introductionmentioning

confidence: 99%

Size-dependent thermoelastic initially stressed micro-beam due to a varying temperature in the light of the modified couple stress theory

Abouelregal

2020

Appl. Math. Mech.-Engl. Ed.

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The bending of the Euler-Bernoulli micro-beam has been extensively modeled based on the modified couple stress (MCS) theory. Although many models have been incorporated into the literature, there is still room for introducing an improved model in this context. In this work, we investigate the thermoelastic vibration of a micro-beam exposed to a varying temperature due to the application of the initial stress employing the MCS theory and generalized thermoelasticity. The MCS theory is used to investigate the material length scale effects. Using the Laplace transform, the temperature, deflection, displacement, flexure moment, and stress field variables of the micro-beam are derived. The effects of the temperature pulse and couple stress on the field distributions of the micro-beam are obtained numerically and graphically introduced. The numerical results indicate that the temperature pulse and couple stress have a significant effect on all field variables.

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A novel model of nonlocal thermoelasticity with time derivatives of higher order

Cited by 72 publications

References 52 publications

Temperature-Dependent Physical Characteristics and Varying Heat Effects on Nonlocal Rotating Nanobeams Due to Dynamic Load

Temperature-Dependent Physical Characteristics and Varying Heat Effects on Nonlocal Rotating Nanobeams Due to Dynamic Load

Computational analysis of an infinite magneto-thermoelastic solid periodically dispersed with varying heat flow based on non-local Moore–Gibson–Thompson approach

Size-dependent thermoelastic initially stressed micro-beam due to a varying temperature in the light of the modified couple stress theory

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