Parametric Analysis Studies of the Vibrations of a Multi-Cable-Stayed Beam Resting on Elastic Suppor

Cable-stayed beams represent one of the most widely discussed topics in the current scientific world, attracting immense attention from researchers in the fields of civil and mechanical engineering. To investigate the behavior of transverse vibrations in the plane of coupled cables and beams resting on elastic supports, a linear single-beam and multi-cable mechanical model was developed. In this work, general expressions are derived for the multi-cable beam based on the fundamental principle of the Euler-Bernoulli method. By taking into account the impact of nonlinear geometric factors caused by the initial sag of the cables, the multi-cable beam model by segments is analyzed. Firstly, using the example of a double-cabled beam as a case study for the clamped-clamped, clamped-simply supported, and simply supported at both ends beam configurations, the solution of the free vibration eigenvalues in the plane is performed by combining the boundary and continuity conditions using the robust Newton-Raphson algorithm. The results obtained are compared with those of the reference articles and show good agreement. Next, the analysis is extended to a two-cable supported beam resting on elastic supports. A parametric study is conducted to evaluate the effectiveness of these supports in mitigating the structural vibrations of the cable-stayed beam. Different configurations are explored, including the variation of the stiffness, position, and number of elastic supports, ranging from a single elastic support to two and three elastic supports. The impact of these elastic supports on the dynamic behavior of the beam is examined in detail, thus promoting the improvement of the dynamic performance and flexibility of cable-stayed structures. This study demonstrates that strategic manipulation of the stiffness and configuration of elastic supports is essential for improving the dynamic performance and robustness of cable-stayed structures. This not only ensures the safety and reliability of the structure but also optimizes its performance under different loading scenarios, making this approach an effective solution for advanced applications in civil and mechanical engineering.