Abstract—This study concerns the nonlinear vibrations of thick porous nanobeams using nonlocal elasticity to incorporate small-scale effects. Unlike previous studies, which primarily focus on linear vibrations, uniform porosity, or neglect variations in porosity distributions, this work examines the coupled influence of nonlocal effects, geometric nonlinearity, and varying porosity distributions (including symmetric and asymmetric profiles) on the dynamic behaviour of metal foam nanobeams. This is a closed-form solution, thus offering a detailed investigation of the vibrational behaviour of the nanobeam regarding nonlocal effects accompanying the void distribution and physical parameter variations. Such results indicate that porosity distribution and void density make a considerable difference to the natural frequencies and mode shapes of a nanobeam and, hence, have something important to say in the design of lightweight, high-strength nanoscale structures. It identifies, particularly for use in advanced engineering applications, as the study that fills a research gap between linear and nonlinear analyses of porous nanobeams. This study fills a research gap by providing a comprehensive analysis bridging the divide between linear and nonlinear analyses of porous nanobeams and exploring the effects of varying porosity profiles, which were not previously addressed.

Keywords—non-linear vibration, beam theory, metal, nanobeam, elasticity

Cite: Layla M. Nassir, Nadhim M. Faleh, Raad M. Fenjan, Mustafa Qahtan Hadi Al-Ghrari , and Mamoon A. A. Al-Jaafari, "Nonlinear Vibration Analysis of Metal Foam Nanobeams with Varying Porosity," International Journal of Mechanical Engineering and Robotics Research, Vol. 14, No. 4, pp. 407-417, 2025. doi: 10.18178/ijmerr.14.4.407-417

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