Linear vibration analysis of multi-cable-stayed beams resting on multiple elastic supports

Cable-stayed bridges, with their captivating elegance and structural efficiency, have captivated the attention of civil and mechanical engineers, becoming a cornerstone of modern bridge engineering. This study meticulously delves into the dynamic behavior of these marvels of engineering by presenting a novel linear multi-cable beam model supported on elastic supports for in-depth transverse vibration analysis. Building upon the bedrock of Euler-Bernoulli beam theory, this work meticulously establishes general expressions for the multi-cable beam, accounting for the influence of geometric nonlinearities induced by the initial sag of the cables. To illustrate the eigenvalue problem for free in-plane vibration, a double-cable beam serves as a compelling case study. The solution involves incorporating boundary and continuity conditions using the robust Newton-Raphson algorithm. Subsequently, the analysis extends to a cable-stayed bridge with two cables resting on elastic supports. We meticulously investigate the influence of these elastic supports on the beam’s dynamic behavior, paving the way for enhancing the dynamic performance and versatility of cable-stayed structures.