Study of Magnetic Field Influence on Vibrations of Poroelastic Hollow Cylinder

The vibration characteristics of an isotropic and homogeneous elastic hollow cylinder with porosity, emphasizing the influence of the magnetic field in the context of poroelasticity, are investigated. 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 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.