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<p>This study investigates the vibrational and thermal behavior of functionally graded (FG) microbeams under initial stress, employing a novel nonlocal dual-phase-lag (NDPL) thermoelasticity model combined with Euler–Bernoulli beam theory to derive governing equations. Material properties, such as density, thermal conductivity, and Young’s modulus, vary exponentially across the beam’s thickness, while Poisson’s ratio is assumed constant for simplicity. The analysis reveals that material gradation significantly influences vibrational behavior, with positive gradation enhancing flexibility and negative gradation unexpectedly increasing deflection in certain regions due to amplified thermal stresses. Initial stress amplifies deformation and thermal gradients, increasing dynamic responses, while the nonlocal thermal length-scale parameter reduces deflections by localizing thermal energy, critical for micro-scale stability. Numerical results, validated against established benchmarks, confirm the model’s accuracy. These findings provide key insights into optimizing FG microbeams for applications in MEMS, sensors, and biomedical devices, enhancing their thermomechanical performance under combined thermal and mechanical loads.</p>

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Exploring the Vibrational Characteristics of Functionally Graded Silicon Microbeams Under Initial Stress Using a Novel Nonlocal Thermoelastic Framework

  • 期刊论文

  • 发表日期：

    2026年3月4日

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  • Ahmed E. Abouelregal,
  • Salman S. Alsaeed

摘要

This study investigates the vibrational and thermal behavior of functionally graded (FG) microbeams under initial stress, employing a novel nonlocal dual-phase-lag (NDPL) thermoelasticity model combined with Euler–Bernoulli beam theory to derive governing equations. Material properties, such as density, thermal conductivity, and Young’s modulus, vary exponentially across the beam’s thickness, while Poisson’s ratio is assumed constant for simplicity. The analysis reveals that material gradation significantly influences vibrational behavior, with positive gradation enhancing flexibility and negative gradation unexpectedly increasing deflection in certain regions due to amplified thermal stresses. Initial stress amplifies deformation and thermal gradients, increasing dynamic responses, while the nonlocal thermal length-scale parameter reduces deflections by localizing thermal energy, critical for micro-scale stability. Numerical results, validated against established benchmarks, confirm the model’s accuracy. These findings provide key insights into optimizing FG microbeams for applications in MEMS, sensors, and biomedical devices, enhancing their thermomechanical performance under combined thermal and mechanical loads.