Thermomechanical 3D wave propagation in biocompatible sandwich nanoplates: influence of magnetic field, foam structure, and foundation

Abstract This study presents an advanced modeling and analysis framework for three-dimensional (3D) wave dispersion in biocompatible sandwich nanoplates exposed to thermal and magnetic fields, employing higher-order plate theory and nonlocal strain gradient elasticity theory. The core innovation lies in the integration of a graphene-reinforced ceramic–metal foam core with functionally graded material (FGM) surface plates, enabling unique mechanical and thermal properties. The study investigates three distinct foam distributions with tailored uniform and symmetrical characteristics, providing unprecedented insights into wave dynamics. The motion equations, derived using Hamilton's principle and solved through the Navier technique, are adapted to a wave propagation framework, facilitating comprehensive analysis of phase velocity, frequency, and group velocity under flexural, longitudinal, and shear modes. Notably, the research examines the synergistic effects of thermal and magnetic fields, revealing transformative impacts on wave propagation, especially in high-temperature environments. Numerical simulations demonstrate that wave velocities are highly sensitive to internal architecture, with the S2-foam distribution and graphene reinforcement (V OG = 0.4) enhancing velocity components by up to 55% and 72%, respectively, while nonlocal parameters and thermal loads induce a softening effect that can reduce frequency response by a factor of 18. The findings highlight the role of core foam architecture and surface FGM attributes in enhancing wave transmission control, paving the way for breakthroughs in ultrasonic wave technology, thermal management systems, and wave cloaking applications. This study represents a significant step forward in the design of multifunctional nanostructures with tailored wave dispersion properties.