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<p>This study examines size-dependent nonlinear wave propagation in carbon nanotube (CNT) nanorods embedded in an elastic medium using the nonlocal strain gradient theory (NSGT). Classical elasticity models fail to capture nanoscale effects, making advanced formulations essential. NSGT integrates nonlocal elasticity and strain-gradient contributions, providing a robust framework for modeling dispersive and nonlinear wave phenomena. The governing equations are derived and reduced to the Korteweg–de Vries (KdV) form via the reductive perturbation method (RPM), enabling analytical solitary wave solutions. Numerical analysis reveals that size-dependent parameters significantly influence wave morphology: under SGT, increasing the length scale parameter broadens solitary waves, whereas under NSGT, the same increase narrows them, reflecting the interplay between gradient stiffening and nonlocal softening. Additionally, increasing the nonlocal parameter promotes wave spreading, consistent with recent literature, while foundation stiffness plays a secondary role. These findings provide insights into tailoring dispersion and solitary wave characteristics for nanoscale applications, offering design strategies for waveguides and signal transmission systems.</p>

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Size-Dependent Nonlinear Wave Propagation in CNT Nanorods: Role of Nonlocal Strain Gradient Effects

  • 期刊论文

  • 发表日期：

    2026年4月6日

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  • Guler Gaygusuzoglu,
  • Aydin Ozmutlu,
  • Muhammed Rasit Celik

摘要

This study examines size-dependent nonlinear wave propagation in carbon nanotube (CNT) nanorods embedded in an elastic medium using the nonlocal strain gradient theory (NSGT). Classical elasticity models fail to capture nanoscale effects, making advanced formulations essential. NSGT integrates nonlocal elasticity and strain-gradient contributions, providing a robust framework for modeling dispersive and nonlinear wave phenomena. The governing equations are derived and reduced to the Korteweg–de Vries (KdV) form via the reductive perturbation method (RPM), enabling analytical solitary wave solutions. Numerical analysis reveals that size-dependent parameters significantly influence wave morphology: under SGT, increasing the length scale parameter broadens solitary waves, whereas under NSGT, the same increase narrows them, reflecting the interplay between gradient stiffening and nonlocal softening. Additionally, increasing the nonlocal parameter promotes wave spreading, consistent with recent literature, while foundation stiffness plays a secondary role. These findings provide insights into tailoring dispersion and solitary wave characteristics for nanoscale applications, offering design strategies for waveguides and signal transmission systems.