Wave decomposition method for the dynamic analysis of a cable-stayed beam subjected to a moving load considering structural damping

Wave analysis emerges as a compelling methodology to elucidate the phenomenon of energy propagation back and forth between junctions. To develop an efficient model for comprehending the propagation of waves in cable-stayed bridges during operation, a wave decomposition method for the dynamic analysis of viscoelastic cable-stayed beams subjected to moving loads is proposed. Initially, the cables and beams are treated as distinct subparts. The Kelvin-Voigt damping model is introduced, and the influence of moving loads is represented using the Dirac delta function. The exact frequency-domain solution of the global system is analytically derived through both the double Fourier transform approach (DFA) and the method of the reverberation-ray matrix (MRRM). Subsequently, an explicit expression for multi-wave components (EMW) is inferred from the global exact solution. These components are characterized by frequency-dependent and dispersion-dependent traits, enabling the extraction of wave components and energy flow across various waveguides. To determine an appropriate damping coefficient for the K-V model, the complex model method is employed to establish a mathematical connection between the K-V damping coefficient and the measurable damping ratio. After validating the EMW through comparison with finite element method (FEM) outcomes and model testing, we investigate the influence of moving loads and structural parameters on the energy distribution across wave frequencies and waveguide paths. This inquiry reveals the tendency of waves to select propagation pathways based on both frequency and load factors. Additionally, a wave velocity analysis is conducted to explore the mechanism underlying the augmentation of structural dynamic stiffness. This research holds promise in the realms of vibration control and the evaluation of bridge transmission efficiency.