Multiphysics modeling and numerical analysis of yawed supersonic airflow effects on vibration and stability of moving orthotropic nanoplates

This study formulates and analyzes the vibration and stability of longitudinally moving orthotropic nanoplates under yawed supersonic airflow, incorporating thickness-dependent scale effects within the nonlocal stress–strain gradient theory framework. Using a Galerkin-based reduced-order model, frequency branches, damping ratio curves, and stability maps are derived to quantify the impacts of surface energy, four-parameter foundation, rotary inertia, airflow characteristics, and varying multiphysics fields (hygro-thermo-magnetic) on instability resistance. Several comparative examinations are conducted under various operating conditions for verification purposes. Subsequently, parametric investigations are conducted to characterize the role of orthotropy ratio, follower force, geometric features, non-uniform in-plane loads, and size-dependent parameters ratio on the nanoplate response. Findings disclose that a rise in the orthotropy ratio leads to a significant enhancement in the nanoplate stability for higher airflow yaw angles. Additionally, surface energy stiffens nanoplates, especially at low thicknesses. Compressive follower forces lower critical velocities, whereas sinusoidal in-plane loads maximize stability. Moreover, divergent and flutter instability bounds widen by increasing/decreasing the length/thickness of nanoplates. The findings are crucial for optimizing the design of next-generation micro- and nanostructured sensors and robots.