Mechanical responses of nanoplates resting on viscoelastic foundations in multi-physical environments

This paper presents an analysis of the static bending, thermal buckling, free vibrations, and forced vibrations of nanoplates using analytical approaches. This study introduces analytical formulations for all three aforementioned difficulties concerning nanoplates, taking into account the simultaneous impact of elements such as magnetic effects, temperature, and viscoelastic basis. The research at hand is characterized by its intricate nature and captivating subject matter, as it explores the phenomenon of the flexomagnetic impact on a plate. Furthermore, the plate is exposed to both mechanical and magnetic stresses concurrently inside a temperature-controlled environment. The plate is supported by a viscoelastic foundation, with the drag coefficient of the foundation being explicitly specified. The mathematical methods used in this study are derived from classical plate theory. An explicit expression is derived for the natural oscillation frequency, critical load resulting from thermal buckling, as well as the static and dynamic displacements of the plate, taking into account the drag coefficient offered by the foundation. The study further conducts a quantitative analysis to investigate the impact of several parameters, including temperature, viscoelastic foundation, and natural frequency of external stimulation force, on the mechanical behaviors of nanoplates. The findings of this study provide a scientific foundation for addressing practical challenges in the design, production, and use of nanoplates.