Investigation of the Effect of Fluid Field on the Vibrations of a Curved Microbeam Based on Nonclassical Continuum Mechanics under Elastic Supports

Microbeams play a crucial role in mechanical processes and in the design of micro- and nanoscale structures. In many engineering applications, these structures are supported by elastic foundations, which can significantly affect their vibrational and stability characteristics. When subjected to external loading and internal fluid flow, the interaction between the microbeam and its elastic support must be accurately modeled to predict realistic dynamic behavior. The mechanical stability analysis of such structures, especially in the presence of internal fluid flow, is of great significance. In this study, the stability of a curved microbeam resting on an elastic foundation and containing an internal fluid flow is investigated. To account for the nanoscale effects, the nonlocal couple stress theory is employed for the solid domain, while the modified velocity theory is adopted for the fluid part. The internal fluid flow is analyzed using the Navier–Stokes equations, and the governi