Efficient design of truss footbridges with stiffness-proportional inerters

Abstract

Absract Excessive vibrations in footbridges have recently received more attention from researchers and professionals. This has resulted in a surge in popularity for passive energy dissipation systems, such as tuned mass dampers, viscous dampers, and inerters. While design methods with tuned mass dampers and viscous dampers exist, the design of footbridges using inerters is still a challenge. This paper proposes a design procedure for truss-like footbridges incorporating inerters. The concept of the approach is based upon a mathematical derivation of the eigenproblem of a multi-degree-of-freedom structural system, enhanced with stiffness-proportional inertances. This outcome enables tuning the highest natural frequency of the system to a predefined value. The proposed design procedure adjusts all natural frequencies, such that the highest natural frequency of a structural system is set lower than the frequency of the load. As implemented in the article, the procedure can be used for back-of-the-envelope estimations, or for achieving an efficient final design. The designs achieved by the suggested methodology are compared to the current traditional design, optimal design achieved through gradient-based sizing optimization, and designs with various common topologies. The methodology’s high potential and its proximity to optimal for a chosen topology are revealed.