This research delves into the propagation of radial free harmonic waves in a poroelastic cylinder, conceptualized as a magnetically and rotationaly influenced hollow structure. The primary aim is to elucidate the magnetic field's and rotation impact on the vibrational behavior of such systems. The investigative method encompasses the resolution of motion equations, formulated as partial differential equations, through the application of Lame's potential theory. This analytical process is augmented by the implementation of fitting boundary conditions, culminating in the derivation of a comprehensive expression for the complex dispersion equation, predicated on the premise that the wavenumber embodies a complex entity. The precision of the model is corroborated through a comparative analysis with established literature, underpinned by an exploration of diverse scenarios. The research employed MATLAB for both numerical and graphical assessments, focusing on the dispersion and displacement attributes. Dispersion relations within the poroelastic medium were computed, considering varied magnitudes of magnetic field intensity, rotation and angular velocities. The outcomes are articulated through complex-valued dispersion relations, transcendental formulations, and numerical resolutions employing MATLAB's bisection technique. These insights hold substantial significance for the theoretical advancement in orthopedic research, particularly concerning cylindrical poroelastic media. This study deduces that the radial vibrational patterns and the corresponding frequency equation within a poroelastic medium are profoundly modified by the magnetic field's interference and rotation. This study formulate a novel governing equation for a poroelastic medium, highlighting the significance of radial vibrations and investigating the impact of magnetic field and rotation.
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