Effect of Rotation and Magnetic Field on Wave Propagation in a Cylindrical Poroelastic Bone

Abstract

This study examines the dynamic responses of wet long bones, conceptualized as transversely isotropic, hollow cylinders (crystal class 6) when subjected to rotational forces and magnetic field. The wave propagation analysis is articulated through a potential function, meeting the criteria of an eighth-order partial differential equation, from which the wave equation’s explicit solution is deduced. Mechanical boundary conditions are defined for a stress-free lateral surface, complemented by fluidic boundary conditions for stress-free fluidic surfaces. Fulfilling these boundary conditions facilitates the derivation of a dispersion relation, subsequently resolved through numerical methods. Frequency calculations for the poroelastic bone consider various rotational speeds, magnetic field and porosity levels. This research offers insights that could enhance the theoretical framework for orthopedic studies related to the behavior of cylindrical poroelastic long bones. Furthermore, a comparative analysis is conducted between the theoretical outcomes and the empirical data obtained from an innovative non-contact measurement device, thereby validating the theoretical model. This study formulate a novel governing equation for a poroelastic medium, highlighting the significance of radial vibrations and investigating the impact of magnetic field, rotation and initial stress. The numerical and graphical results underscore the significant influence of magnetic field, rotation, and initial stress on the various wave velocity and attenuation coefficient.