This work scrutinized the vibration behavior of nanoscale beam structures with rotating motion according to the nonlocal stress-strain gradient theory (NSSGT). The surface layer energy, rotary inertia factor, and thickness-dependent scale impacts are considered in the mathematical simulation. Additionally, parametric examinations are exploited to comprehend the impressions of varying environmental fields and follower and axial forces. Adopting Hamilton’s principle, the dynamic equation of nanoscale beams with rotation is achieved. The eigenvalue analysis is accomplished with the aid of the Galerkin decomposition scheme, and dynamic characteristics are recognized. Besides, machine learning (ML)-based approaches, viz., artificial neural network (ANN) and Gaussian support vector machine (GSVM) techniques, are exploited to predict the vibration frequencies. Comparison analyses with existing scientific reports in the open technical literature are conducted to guarantee the correctness of the deduced outcomes. The performance and correctness of ANN and GSVM techniques are verified by assessing the performance parameters of ML approaches. The numerical technique outcomes are consistent with those of ML-assisted models. Furthermore, the proposed ML prediction models are perceived to have excellent performance (viz., low mean square error and high determination coefficient) and superior computational time and cost-effectiveness. It is deduced that the scale-dependency in the thickness direction improves the vibration frequency. Moreover, the vibration frequencies are decreased/increased with increasing nanobeam thickness/length by considering the surface layer energy. The current research outcomes can be valuable in designing next-generation high-speed rotating nanodevices, inspiring further innovation and development in the field.
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