Analysis on the dynamic characteristic of a tensioned double-beam system with a semi theoretical semi numerical method

Abstract

In this study, the dynamic characteristic of an inclined and tensioned double-beam system is investigated. The double-beam system consists of two elastic beams, which are quite different in mass and stiffness, and are continuously connected by a layer of elastic springs. The beam with larger stiffness and mass is under a tensile axial loading. The oscillatory differential equations of this double-beam system are established by considering the effects of sag, flexural rigidity, boundary conditions, inclined angle of real inclined beams, and other factors simultaneously. Based on the governing equations, the element transverse dynamic stiffness matrix and global transverse dynamic stiffness matrix are derived to obtain the dynamic equilibrium equation of the system in a dynamic stiffness form. Using this, the system is simplified into a four degree-of-freedom simple oscillatory system and consequently the theoretical frequency characteristic equation is proposed for this double beam system. A numerical equation rooting approach is developed to solve the dynamical properties of the proposed equation. With the numerical case studies, the dynamic characteristics and its variation laws of a double-beam system are investigated. It shows that the proposed semi theoretical semi numerical methods can give an accurate solution for the double beam system, and rules revealed in this study are help for comprehending the dynamical behavior of double beam like engineering structures theoretically.