The vertical dynamic stiffness of long-span cable-stayed bridges under vehicle loading is a crucial concern due to their susceptibility to sustained vibrations with notable wave effects. This study investigates the dynamics stiffness perception and enhancement mechanisms of cable-stayed bridges based on fast wave analysis method, proposing wave-associated structural concepts (WSC) for designing stiffer cable-stayed bridges under traffic loading. Initially, the wave function characterizing cable-stayed bridge vibrations is introduced into the representation of the dynamic stiffness of cables and beams, and six WSC for enhancing structural dynamic stiffness are proposed. Subsequently, the fast establishment of the core module for wave function computation is achieved through modular construction of the wave propagation matrix. By employing wave decomposition to clarify the decoupling relationships among the wave components, a distributed algorithm is applied for efficient parallel solving of the wave function. Finally, the reliability and superiority of the proposed method are validated. Using wave analysis method, the stiffness enhancement mechanisms based on WSC and the criteria for implementing WSC in cable-stayed bridges are presented. The case study indicates that the structural dynamic stiffness is related to the wave characteristics which are influenced by both excitations and structural parameters. Enabling the rapid transmission of waves to the structural foundation promote uniform energy distribution and amplitude reduction of wave, thereby enhancing the dynamic stiffness. The beam section stiffness contributes to a dual-effect stiffness enhancement in cable-stayed bridges, effectively increasing the wave velocity. An alternative definition of structural dynamic stiffness is provided based on wave propagation.
