On the dispersion of bulk wave in hygrothermally affected poroelastic gymnastics beams based on refined higher-order shear deformation theory during athlete training

Poroelastic materials have gained prominence due to their beneficial characteristics, prompting the authors to investigate their behavior in wave propagation. Additionally, the balance beam used in gymnastics is a classic example of a beam structure. It is designed to support the weight of the gymnast while providing stability and strength. This paper focuses on analyzing wave dispersion behavior in a hygrothermally excited poroelastic gymnastics beam. It is considered that the beam is made of a composition of Alumina and Aluminum as ceramic and metallic phases, respectively. Initially, the basic characteristics are determined using an improved power-law homogenization scheme. Subsequently, a poroelastic beam is modeled based on a refined higher-order shear deformation theory, and based on it and Hamilton’s principle, the kinetic relations are obtained. The obtained governing equations are then solved through analytical schemes using harmonic functions, and the outcomes are presented. These results are afterward verified through comprehensive comparisons with existing literature. Furthermore, this paper findings shows that the phase velocity and wave frequency of the beam are influenced by gradient parameters, porosity, and environmental factors like temperature and humidity to gain further insights.