Chaos and dynamic instabilities of FGM micro-pipes with internal fluid flow via strain gradient theory
8 affiliations
- 1Department of Physics, College of Sciences, Princess Nourah bint Abdulrahman University
- 2Advanced Technical College, University of Warith Al-Anbiyaa
- 3Faculty of Technical Education, Hourani Center for Applied Scientific Research (HCASR), Al-Ahliyya Amman University
- 4Department of Mechanical Engineering, GLA University
- 5College of Engineering, Al-Ayen University
- 6Department of Mathematics, College of Science, Jazan University
- 7Physics Department, Faculty of Science, Islamic University of Madinah
- 8Centre of Research Impact and Outcome, Chitkara University
Abstract
This study establishes a nonlinear dynamic formulation for fluid-conveying microscale pipes fabricated from functionally graded materials (FGMs), with size-dependent effects rigorously captured through the three-parameter modified strain gradient elasticity theory. The governing equations are derived via Hamilton’s principle, yielding a sixth-order nonlinear coupled system that is solved numerically using a fourth-order Runge–Kutta scheme. The dynamic response is characterized through phase portraits, Poincaré sections, bifurcation diagrams, and the largest Lyapunov exponent, revealing rich transitions between periodic and chaotic regimes. The principal novelties of the present work are threefold: (i) A strain gradient-based nonlinear dynamic model was established for fluid-conveying FGM micro-pipes that comprehensively incorporates all three independent length-scale parameters, thereby providing a theoretically complete framework that systematically unifies classical, couple-stress, and simplified gradient formulations as special limiting cases; (ii) The quantitative determination of a critical gradient index threshold was specifically provided to chaotic motion emerges at a sharp power-law index of approximately n ≈ 42 , a definitive criterion previously absent in the literature that offers a clear material-based design guideline for avoiding dynamic instability; and (iii) The discovery of a counterintuitive stabilization effect was reported to detect the chaotic vibrations are completely suppressed and periodic motion is restored when the dimensionless microscale parameter exceeds the threshold value of 0.027 ( updelta > 0.027 ), revealing a size-dependent mechanism that provides a tunable microstructural design window for actively controlling nonlinear oscillations a phenomenon entirely inaccessible to lower-order single-parameter theories. Collectively, by identifying these explicit stability thresholds and demonstrating dual controllability through both material composition (power-law index) and microstructural size (strain gradient parameter), our work advances beyond qualitative chaos characterization to establish a comprehensive, design-oriented framework for nonlinear stability control of FGM micro-systems, with direct practical implications for MEMS resonators, micro-fluidic sensors, and energy-harvesting devices.
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BibTeX
@article{alfryyan2026chaos,
title = {{Chaos and dynamic instabilities of FGM micro-pipes with internal fluid flow via strain gradient theory}},
author = {Nada Alfryyan and Ali Alkhafaji and Seif Al Bustanji and Kamal Sharma and Muthanna K. Kareem and Adel Almarashi and Mohamed Shaban and Subhav Singh},
journal = {Scientific Reports},
year = {2026},
month = aug,
doi = {10.1038/s41598-026-67181-x},
url = {https://doi.org/10.1038/s41598-026-67181-x},
note = {CC BY},
}
RIS
TY - JOUR
TI - Chaos and dynamic instabilities of FGM micro-pipes with internal fluid flow via strain gradient theory
AU - Nada Alfryyan
AU - Ali Alkhafaji
AU - Seif Al Bustanji
AU - Kamal Sharma
AU - Muthanna K. Kareem
AU - Adel Almarashi
AU - Mohamed Shaban
AU - Subhav Singh
PY - 2026
DA - 2026/08/01
JO - Scientific Reports
DO - 10.1038/s41598-026-67181-x
UR - https://doi.org/10.1038/s41598-026-67181-x
AB - This study establishes a nonlinear dynamic formulation for fluid-conveying microscale pipes fabricated from functionally graded materials (FGMs), with size-dependent effects rigorously captured through the three-parameter modified strain gradient elasticity theory. The governing equations are derived via Hamilton’s principle, yielding a sixth-order nonlinear coupled system that is solved numerically using a fourth-order Runge–Kutta scheme. The dynamic response is characterized through phase portraits, Poincaré sections, bifurcation diagrams, and the largest Lyapunov exponent, revealing rich transitions between periodic and chaotic regimes. The principal novelties of the present work are threefold: (i) A strain gradient-based nonlinear dynamic model was established for fluid-conveying FGM micro-pipes that comprehensively incorporates all three independent length-scale parameters, thereby providing a theoretically complete framework that systematically unifies classical, couple-stress, and simplified gradient formulations as special limiting cases; (ii) The quantitative determination of a critical gradient index threshold was specifically provided to chaotic motion emerges at a sharp power-law index of approximately n ≈ 42 , a definitive criterion previously absent in the literature that offers a clear material-based design guideline for avoiding dynamic instability; and (iii) The discovery of a counterintuitive stabilization effect was reported to detect the chaotic vibrations are completely suppressed and periodic motion is restored when the dimensionless microscale parameter exceeds the threshold value of 0.027 ( updelta > 0.027 ), revealing a size-dependent mechanism that provides a tunable microstructural design window for actively controlling nonlinear oscillations a phenomenon entirely inaccessible to lower-order single-parameter theories. Collectively, by identifying these explicit stability thresholds and demonstrating dual controllability through both material composition (power-law index) and microstructural size (strain gradient parameter), our work advances beyond qualitative chaos characterization to establish a comprehensive, design-oriented framework for nonlinear stability control of FGM micro-systems, with direct practical implications for MEMS resonators, micro-fluidic sensors, and energy-harvesting devices.
SN - 2045-2322
ER -