Analytical and AINN-based investigation of surface wave propagation in dry long bones with initial stress, magnetic field, and rotation effects.

This study presents a comprehensive analytical and artificial intelligence neural network (AINN)-based investigation of wave propagation in dry long bones, modeled as an orthotropic hollow cylindrical structure. The proposed model incorporates the combined effects of initial stress, magnetic field, and rotational motion to capture the complex behavior of bone-like media under coupled physical influences. The governing equations are formulated within a continuum mechanics framework and solved analytically using displacement potential methods, yielding solutions in terms of Bessel functions that satisfy the cylindrical geometry and boundary conditions. Two distinct cases, corresponding to the absence and presence of rotation, are examined to assess the influence of rotational effects on wave dynamics. A detailed parametric analysis is carried out to evaluate the variation of phase velocity and frequency with respect to wave number, initial stress, magnetic parameter, density, and geometric ratios. The analytical results indicate that initial stress enhances wave propagation, while magnetic effects introduce damping and rotation significantly modifies dispersion characteristics. To improve computational efficiency and predictive capability, an AINN model is developed and trained using analytically generated data. The AINN predictions show excellent agreement with the analytical results, as confirmed through parity plots, error analysis, residual distribution, and loss convergence behavior. The novelty of the study lies in the unified analytical-AINN framework that integrates mechanical, electromagnetic, and rotational effects within a single model. The findings provide important insights for wave-based characterization of bone structures and have potential applications in non-destructive evaluation, ultrasonic diagnostics, and advanced biomedical sensing systems.