An Analytical Dynamic Model for Vibration Suppression of a Multi-Span Continuous Bridge by Tuned Mass Dampers

In this paper, an analytical dynamic model is proposed for vibration suppression of a multi-span continuous bridge by tuned mass dampers (TMDs). Firstly, the partial differential equations (PDEs) that govern the motion of the multi-span continuous bridge and the TMDs are obtained, respectively. According to the matching conditions and the boundary conditions, the mode shapes of the multi-span continuous bridge are derived, and the orthogonality relations of the mode shapes are proven. By using the mode shapes and their orthogonality relations, the PDEs that govern the motion of the bridge and the TMDs are truncated into the ordinary differential equations (ODEs) that describe the motion of the entire system. To verify the proposed model, the natural frequencies solved by the frequency equation are compared with those obtained by the finite element software ANSYS. According to the ODEs in this model, the dynamical responses of the system are worked out to study the influence of the location and the number of TMDs on the vibration suppression of the bridge.

Automated summary

In this paper, an analytical dynamic model is proposed for vibration suppression of a multi-span continuous bridge by tuned mass dampers (TMDs). The partial differential equations (PDEs) governing the motion of the bridge and TMDs are obtained, and the mode shapes and orthogonality relations are derived. The PDEs are then truncated into ordinary differential equations (ODEs) to describe the motion of the entire system. The proposed model is validated by comparing the natural frequencies with those obtained from finite element software.