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Background <p>Thermoelastic nanobeams used in NEMS/MEMS exhibit size-dependent (nonlocal) behavior and thermal relaxation eff ects that classical thermoelasticity does not fullycapture, making accurate prediction of coupled thermomechanical vibrations on elastic foundations important for reliable design and performance.</p> Purpose <p>To develop a generalized nonlocal thermoelastic vibration framework for nanobeams resting on a two-parameter Winkler–Pasternak foundation while incorporating fractionaldual-phase-lag (FDPL) heat conduction.</p> Methods <p>Coupled governing equations are formulated and nondimensionalized, solved in the transform domain using Sumudu decomposition, and then numerically inverted via aRiemann-sum approximation.</p> Results <p>Parametric studies on fractional order, nonlocal parameter, and foundation coeffi cients produce stable space–time distributions of temperature, axial displacement, transversedefl ection, and bending moment. The fractional order strongly infl uences defl ection and bending moment but has weaker eff ects on temperature and axial displacement. Nonlocalityalters the magnitude and trends of mechanical fi elds, while increasing Winkler and shear foundation parameters stiff ens the system and reduces deformation. FDPL eff ects reducepredicted fi eld amplitudes compared with non-fractional models.</p> Conclusion <p>The proposed nonlocal-fractional formulation off ers a practical framework for modeling and optimizing nanobeam resonator behavior in small-scale engineeringapplications.</p>

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Sumudu Decomposition for the Fractional Dual Phase-Lag of Thermoelastic Nano-Beams Supported by Pasternak Foundations for Nonlocal Vibrations

  • 期刊论文

  • 发表日期：

    2026年2月23日

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  • Ahmed Yahya,
  • Adam Zakria,
  • Shams A. Ahmed,
  • Abdelgabar Adam Hassan,
  • Ibrahim-Elkhalil Ahmed,
  • Ibrahim Omer Ahmed

摘要

Background

Thermoelastic nanobeams used in NEMS/MEMS exhibit size-dependent (nonlocal) behavior and thermal relaxation eff ects that classical thermoelasticity does not fullycapture, making accurate prediction of coupled thermomechanical vibrations on elastic foundations important for reliable design and performance.

Purpose

To develop a generalized nonlocal thermoelastic vibration framework for nanobeams resting on a two-parameter Winkler–Pasternak foundation while incorporating fractionaldual-phase-lag (FDPL) heat conduction.

Methods

Coupled governing equations are formulated and nondimensionalized, solved in the transform domain using Sumudu decomposition, and then numerically inverted via aRiemann-sum approximation.

Results

Parametric studies on fractional order, nonlocal parameter, and foundation coeffi cients produce stable space–time distributions of temperature, axial displacement, transversedefl ection, and bending moment. The fractional order strongly infl uences defl ection and bending moment but has weaker eff ects on temperature and axial displacement. Nonlocalityalters the magnitude and trends of mechanical fi elds, while increasing Winkler and shear foundation parameters stiff ens the system and reduces deformation. FDPL eff ects reducepredicted fi eld amplitudes compared with non-fractional models.

Conclusion

The proposed nonlocal-fractional formulation off ers a practical framework for modeling and optimizing nanobeam resonator behavior in small-scale engineeringapplications.