Nonlinear phase and group velocity analyses of hybrid nanocomposite-reinforced sports stadium roofs under aerodynamic pressures

Abstract

The nonlinear performance of a hybrid nanocomposite-stadium roof in terms of group and phase velocity under aerodynamic pressure is being studied in this paper. The composite material is an epoxy matrix that is reinforced with graphene nanoplatelets (GNP) and carbon nanotubes (CNT) in a blend, thus having improved mechanical properties overall. The study uses the sinusoidal shear deformation theory, including a nonlinear shear function, and also Von Kármán’s geometric nonlinear effects are included. Based on Hamilton’s principle, the governing equations are derived, and the aerodynamic pressure is considered to be constant using the first-order piston theory. A notable aspect of the model is the auxetic foundation made of a Haber–Schaim foundation material, and these properties will have a major impact on the overall dynamic characteristics of the system. The harmonic method of balancing the problem’s geometry is also applied to nonlinear equations. An awesome iterative method is given for precise nonlinear phase and group velocity solutions. The results imply that the combination of a hybrid nanocomposite and an auxetic base influences the dynamic response of the roof system greatly. The roof’s nonlinear phase and group velocities display this intricacy, and the strengthening of the material and foundation markedly influences them. This study brings about a new direction for the design and analysis of future stadium roofs and also offers a firm basis for dynamically optimizing the performance under wind load. The results are of particular significance for the development of structural systems with nanocomposite reinforcements that are always exposed to aerodynamic forces.