Multimodal linear and nonlinear vibration analysis of cable-stayed beams under free and forced excitations with elastic end supports

This paper presents an analysis of the linear and geometrically nonlinear vibrations of a cable-stayed beam equipped with elastic translational and rotational supports, based on a multimodal analytical formulation. The beam is modeled using Euler–Bernoulli beam theory, while the stay cables are considered as axially deformable elements incorporating sag effects. The governing equations are derived using Hamilton’s variational principle, accounting for geometric nonlinearities associated with large vibration amplitudes as well as beam–cable coupling. Both free and forced vibration responses are investigated. The forced vibration analysis includes different types of excitations, such as concentrated forces, uniformly distributed loads, and partially distributed loadings applied along the beam span. A parametric study is conducted to evaluate the influence of vibration amplitude, rotational stiffness of the supports, mechanical properties of the cables, and loading configuration on the nonlinear dynamic behavior. The results highlight a pronounced hardening-type nonlinear response, strongly dependent on boundary conditions and loading modes, with significant nonlinear effects observed near the cable anchorage regions. The proposed model provides accurate predictions with low computational cost and constitutes an efficient tool for the nonlinear dynamic analysis of beam–cable structures.