Nonlinear vibration absorbers applied on footbridges
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Nonlinear vibration absorbers applied on footbridges Hamed Saber . Farhad S. Samani
. Francesco Pellicano
Received: 13 April 2020 / Accepted: 14 October 2020 Springer Nature B.V. 2020
Abstract This paper deals with the performance of linear and nonlinear dynamic vibration absorbers (DVAs) to suppress footbridges vertical vibrations. The walking pedestrian vertical force is modeled as a moving time-dependent force and mass. The partial differential equations govern the dynamics of the system; such equations are reduced to a set of ordinary differential equations by means of the Bubnov– Galerkin method with an accurate multimode expansion of the displacement field. The optimal vibration absorber parameters are determined using two objective functions: maximum footbridge deflection and the transferred energy from the footbridge to the DVA. The most suitable nonlinear DVA is proposed for the investigated footbridge. The results show that the DVAs with quadratic nonlinearity are the most performant DVAs. Keywords Footbridge vibrations Single pedestrian Nonlinear vibration absorber H. Saber F. S. Samani (&) Department of Mechanical Engineering, Shahid Bahonar University of Kerman, 76175-133 Kerman, Iran e-mail: [email protected] H. Saber e-mail: [email protected] F. Pellicano Department of Engineering ‘‘Enzo Ferrari’’, University of Modena and Reggio Emilia, Modena, Italy e-mail: [email protected]
1 Introduction The reduction of human-induced vibrations is a serviceability and safety issue in footbridges. Under a moving pedestrian load, in near resonance condition, the structure of the footbridge may suffer from large deflections. The resonance occurs when a natural frequency of the structure is within the range of pedestrian pacing frequencies and cause damages. There are several methods to reduce the vibrations of the footbridges including, the selection of structural material, general end conditions, and the most promising of them, dynamic vibration absorber (DVA). In Ref [1] human-structure interaction models for the vertical vibration under pedestrian excitation are considered. In the mentioned paper, the beam equation is modeled employing the modal coordinates and finite element method. Pedersen and Frier [2, 3] worked on the footbridge response under pedestrian load models and investigated the sensitivity of the footbridge vibrations to walking parameters. They represent the excessive vibrations and serviceability problems of slender footbridges under pedestrian traffic. In Ref.[2], it was shown that walking parameters such as step frequency, pedestrian mass, dynamic load factor are essentially stochastic. Pedersen and Frier [3] were focused on estimating the vertical structural response to single person loading. In Ref [4] a literature review of experimental and analytical pedestrian forces on the footbridges are brought. They investigated human-
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Meccanica
structure, dynamic interaction, and pedestrian synchronization during wa
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