Analyzing radial vibrations under rotational forces in thick-walled poroelastic spherical structures

Abstract

This research delves into the radial vibrations of dissipative poroelastic spherical shells, which are embedded within an elastic foundation and subjected to rotational dynamics. The analysis identifies that the inclusion of dissipative effects gives rise to a transcendental, complex-valued frequency equation. A numerical approach, specifically the bisection method, is employed in MATLAB for solution derivation. In instances where the argument is relatively small, the study leverages the asymptotic expansions of Bessel functions, facilitating the bifurcation of the frequency equation into two distinct real-valued equations. These equations are instrumental in computing the natural frequency as a function of the shell’s thickness. Furthermore, the research rigorously examines how rotational forces influence the natural frequency. The culmination of this study is presented through a series of graphical depictions, which succinctly illustrate the impact of rotational dynamics on the radial vibrations of thick-walled hollow structures situated in various elastic media. The overall findings contribute significantly to our understanding of the behavior of poroelastic materials in rotational environments, with implications for both theoretical and practical applications in material science and engineering. The results can benefit the theoretical development of orthopedic study projects connected to spherical poroelastic medium.