Analysis of the Stress–Strain State of the Elastic Moment Medium When a Spherical Cavity Diffracts the Wave

• Published in: Journal of Vibration Engineering & Technologies Vol. 12; no. 3; pp. 4829 - 4844
• Main Authors: Tuan, Lai Thanh, Dung, Nguyen Van, Minh, Phung Van, Tan, Bui Dinh, Thom, Do Van, Zenkour, Ashraf M.
• Format: Journal Article
• Language: English
• Published: Singapore Springer Nature Singapore 01.03.2024
• Subjects: Acoustics; Control; Dynamical Systems; Engineering; Engineering Acoustics; Original Paper; Vibration; Legendre and Gegenbauer polynomials; Laplace transform; Asymptotic solution; Asymmetric theory; Non-stationary wave; Cosserat pseudocontinuum
• ISSN: 2523-3920; 2523-3939
• DOI: 10.1007/s42417-023-01155-5

Purpose This study aims to address the diffraction of non-stationary perturbations with axisymmetric boundaries in a moment elastic framework. Method The proposed solution utilizes the Cosserat pseudocontinuum as a model, which represents one of the asymmetric hypotheses of elasticity. The hypothesis posits that a spherical cavity inside an infinite Cosserat pseudocontinuum is subject to either a plane wave or a spherical wave for expansion–compression. The relationship between the non-zero components of the displacement vector and the rotating field is constructed inside a spheroid interrelate system. This system describes the motion of the medium with the extraction taking place at the center of the cavity. In the first stages of existence, the medium exhibits a lack of further disruptions. The initial boundary conditions are represented in terms of dimensionless quantities. Results The solution is determined using the expansion of the functions into Legendre and Gegenbauer polynomial series, as well as applying the Laplace transform at each time. The issue at hand is resolved within the domain of Laplace transforms. In the context of linear estimation, the parameters of the original series are obtained by using the Laurent series to analyze images in the vicinity of the period of origin. The findings indicate that the outcomes previously documented in the context of the classical elastic environment align with the solutions obtained via the use of limit techniques. Conclusion To facilitate the progress of modern science and technology, it is important to possess a precise comprehension of the deformative processes shown by not only conventional materials, but also those possessing complicated structures. This encompasses materials in which the deformation of the medium may be characterized not only by displacement, but also by rotation. The academic literature generally uses the name "Cosserat medium" to denote the medium characterized by the aforementioned description. Within scholarly discourse, this theory is often referred to as moment, asymmetric, and microstructural elasticity theory. Research has been conducted on the phenomena occurring in pseudo-continuum Cosserat, specifically focusing on the diffraction of waves inside a two-dimensional context, namely by a spherical cavity.