On the Wave Propagation and Dynamic Response of a Spherical Cavity in Piezoelectric Microstructures via Rabotnov Kernel-Based Moore–Gibson–Thompson Thermoelasticity Theory

This study investigates the transient dynamic response and thermomechanical stability of a transversely isotropic piezoelectric medium featuring a spherical cavity. To accurately model the small-scale effects inherent in advanced structural components, a spatiotemporal nonlocal elasticity framework of the Klein–Gordon type is employed, incorporating both internal length and intrinsic time scale parameters. The governing equations of the Moore–Gibson–Thompson (MGT) thermoelastic model are reformulated using a nonsingular Rabotnov-type fractional exponential kernel, providing a robust mathematical formulation to capture memory-dependent interactions without the paradox of infinite propagation speeds. The structural boundary of the cavity is subjected to a ramp-type thermal loading and electrical grounding, simulating realistic operational conditions for sensors and actuators. Using the Laplace transform technique and the Zakian numerical inversion method, the transient distributions of temperature, displacement, stress, and electric potential are derived. The results highlight the significant influence of the Rabotnov fractional parameter and spatiotemporal nonlocality on the structural stability and wave-front characteristics. This research provides a unique medium for understanding the latest developments in fractional-order dynamics for piezoelectric micro- and nano-structures, offering practical insights for civil, aerospace, and mechanical engineering applications.