This manuscript presents a detailed analytical study on the propagation behavior of circumferential shear horizontal (SH) waves in a tri-layered cylindrical composite structure, comprising an inner functionally graded (FG) layer, a viscoelastic (VE) middle layer, and an initially stressed piezomagnetic (PM) outer layer. Unlike prior studies that primarily focus on phase velocity analysis, this work offers a novel and in-depth exploration of stress distribution characteristics across the multilayered system. The model incorporates both mechanical and magneto-mechanical interface imperfections and examines the effects of geometric dimensions, material gradation, angular wave modes, and initial stresses on wave dynamics. A robust mathematical framework is developed using the equations of motion and constitutive relations specific to each material, leading to a dispersion relation formulated under suitable boundary conditions. Numerical simulations demonstrate that the phase velocity and surface wave responses are notably influenced by gradation parameters, layer radii, and imperfection factors. Most significantly, detailed stress profiles are constructed to reveal how material damping, gradation, and interface conditions interact to shape the internal stress landscape. This dual-phase velocity and stress analysis offers enhanced insight into wave–material interactions, providing a valuable design reference for next-generation piezomagnetic sensors, actuators, and composite structural components.
Gupta et al. (Sat,) studied this question.