Wave-Based Analysis of Force Transfer in Beam–Cable-Coupled Structure Subjected to Arbitrary Impact Load

To model force transmission with time-delay effects in beam–cable coupled structures under arbitrary impact loading, a novel analysis method based on traveling wave characterization, termed WLTM, is proposed. By employing innovative shape functions to simulate impact load propagation, this method requires that degrees of freedom be defined only at structural joints, thus enabling accurate results with just a single element per member, even while fully accounting for force transmission through elements with distributed mass. To ensure broad applicability, a beam–cable coupled structure incorporating strain-rate-dependent damping is proposed, and the explicit expression for structural nodal forces is formulated as a unified formulation for arbitrary external loads. These expressions characterize the force transfer behavior of structures comprising multiple load paths as a superposition of concise local traveling wave components at each node. Four typical joint types in beam–cable coupled structures are considered, for which normalized local force vectors are constructed and assembled into a global force vector corresponding to the overall load transfer path of the structure. Furthermore, a normalized transfer path length is introduced to quantitatively evaluate the time-delay effects, incorporating the combined influence of sectional stiffness and path geometry on structural force transfer behavior. Experimental tests are conducted to validate the rationality of representing structural force transmission via a traveling waves model. Case studies demonstrate that the computational efficiency of the WLTM is significantly higher than that of the FEM, as only degrees of freedom at nodes are required. The force transfer efficiency is shown to substantially influence impact force distribution within coupled structures. The time-delay effect is inversely related to both the dynamic stiffness and the load proportion of the path. Higher vehicle speeds result in a greater proportion of the load being carried by the cables, implicating this mechanism in potential cable failure.