Size-dependent thermoelastic response of microresonator plates via nonlocal MGT framework with Pasternak support

This study introduces a novel framework that integrates three advanced mechanisms: nonlocal Moore–Gibson–Thompson (MGT) thermoelasticity, Kelvin–Voigt (KV) viscoelasticity, and Pasternak–Winkler foundation support. The framework is used to analyze circular microplate resonators. This triple integration represents a significant departure from prior work, which treated these phenomena in isolation. The key novelty lies in the synergistic combination of nonlocal heat conduction with MGT wave dynamics and viscoelastic dissipation, enabling, for the first time, the simultaneous prediction of size-dependent thermal diffusion, finite-speed transients, and energy loss under thermal shock. Our analysis reveals that nonlocal–MGT interactions counterintuitively reduce thermal stresses and dissipation while enhancing frequency stability—effects entirely absent from conventional theories. The work provides four distinct contributions: (1) the first unified nonlocal MGT–viscoelastic–foundation model for circular plates; (2) a systematic quantification of synergistic coupling effects; (3) a comprehensive field analysis under thermal shock; and (4) actionable design guidelines for MEMS resonators. These findings deliver transformative insights for aerospace, biomedical, and telecommunications applications.