Influence of rotational dynamics and initial stress on an elastic sphere with size-dependent double porosity

Abstract

The main objective of this manuscript is to conduct a comprehensive analysis of the intricate interaction between rotation and initial stress in a nonlocal elastic spherical structure characterized by dual porosity. The influence of rotation and initial stress is examined both in the presence and absence of the nonlocal elasticity effect on the elastic sphere with dual porosity. A technique based on time-harmonic variations is applied to the governing equations, simplifying them into ordinary differential equations. The analytical results, computed using MATLAB software, provide a detailed examination of the response of the nonlocal elastic sphere to rotation and initial stress. A numerical iteration method is employed for the free vibration analysis, presenting the natural frequencies in tabular form according to mode numbers. Computer simulations offer graphical representations of frequency shifts in relation to mode numbers, comparing nonlocal and local elastic spheres. The study illustrates the variations in field functions with respect to the radius, considering the effects of rotation and initial stress. Graphical presentations indicate that as the rotation factor increases, the variations exhibit more pronounced behaviors. Motivated by its relevance to engineering and geotechnical applications, this research aims to deepen our understanding of these interactions, contributing valuable insights for the optimization and design of structures across various fields.