Size-dependent resonance and transient dynamics of functionally graded nanoplates via modified nonlocal strain gradient theory
摘要
Size-dependent effects play a critical role in the transient and resonance behavior of nanoplates, requiring advanced computational frameworks capable of capturing both nonlocal interactions and strain-gradient mechanisms. In this study, a simulation-based framework is developed by integrating a modified nonlocal strain gradient theory with a higher-order shear deformation theory to investigate the dynamic responses of functionally graded nanoplates under various transverse excitations. The key novelty lies in integration of the modified nonlocal strain gradient theory into a time-domain dynamic formulation, enabling the simultaneous and consistent representation of nonlocal softening and strain-gradient hardening effects in transient and resonance responses, which is not typically captured. The governing equations of motion are derived via Hamilton’s principle and solved using an analytical–numerical strategy based on the Newmark–β time integration scheme. Transient and resonance responses are examined through time histories and phase-plane representations. Parametric simulations reveal that nonlocality, strain-gradient effects, material gradation, and geometric slenderness interact in a nontrivial manner, leading to asymmetric frequency responses and sensitivity amplification rather than a simple shift in natural frequencies. The results provide physically interpretable insights into nanoscale dynamic behavior and a reliable computational tool for simulation-driven analysis of nanostructures under dynamic loading.