A Novel Criterion for Predicting Stiffness Transition in Circular Aluminum Nanoplates under Axisymmetric Vibrations

The variation in modal stiffness is a key indicator for designing nanoresonators with superior resonance characteristics and stability. However, a definitive criterion for evaluating the stiffness transitions within the framework of surface elasticity theory has not yet been established. The coupling effect among multi-surface scale parameters makes conventional criteria insufficient. In this paper, a new criterion is proposed for the axisymmetric vibration of circular aluminum (Al) nanoplates, revealing that the critical multi-surface scale parameters for stiffness transition are represented as a plane rather than a conventional point or line. When the coordinates of the three surface scale parameters lie above or below the criterion plane, the surface effect exhibits a stiffening and softening mechanism for the stiffness, respectively. In addition, a predictive model for the new criterion is developed, which can accurately determine the critical multi-surface scale parameters for the stiffness transition in circular Al nanoplates with different geometric parameters. The theoretical results show excellent agreement with the molecular dynamics results. It is also found that the same set of multi-surface scale parameters may induce opposite stiffening or softening effects in different modes. The predictive model transforms the profound scale effect into practical engineering parameters, thereby avoiding complicated theoretical analysis and numerical computation and significantly improving engineering applicability. These findings provide new physical insights and practical guidance for evaluating the mechanical performance of nanodevices.