Characterization of hydrodynamic properties from free vibration tests of a large-scale bridge model

https://doi.org/10.1016/j.jfluidstructs.2021.103368Get rights and content

Abstract

To accurately predict the dynamic response of a structure subjected to fluid induced loading, a thorough understanding of the dynamic properties (mass, stiffness, and damping) and associated interactions is required. Limited data are available to characterize dynamic fluid–structure interactions. Data are particularly limited for large-scale and flexible structural models. This article reports the results of the first free vibration tests of a dynamic large-scale laboratory highway bridge superstructure model. The dynamic response characteristics of the model were extracted and analyzed from free vibration tests under varying levels of water submersion and for different horizontal substructure flexibilities. The nature of the damping response was identified based on the empirically measured logarithmic decrements of the model’s free vibration displacement amplitudes, and a suitable equation of motion (EOM) was subsequently developed. Using the classical fourth-order Runge–Kutta method, the EOM was solved for the different test trials and the dynamic properties of the model were obtained through an optimization approach. The concept of added mass was introduced to explain the observed decrease in natural frequency with increasing levels of water submersion. Finally, added mass factor was computed for the case where the water level was even with the top of the bridge superstructure model. This study provides a suitable EOM needed for numerical simulations of this and similar models that study fluid–structure interaction and also provides a methodology for establishing the structural dynamic properties of generalized hydrodynamic analytical models.

Section snippets

Introduction and background

Hurricanes in 2004 (Ivan) and 2005 (Katrina) caused failure of many existing coastal highway bridges (Bradner et al., 2010, Cuomo et al., 2007). Bridge structures are the critical lifeline components of an infrastructure network, enabling disaster response and recovery. Therefore, ensuring satisfactory performance increases community resilience and minimizes both human and economic losses. The observed bridge failures spurred research to better understand wave forces on bridges and

Motivation and significance

As described in the previous section, most experimental tests and numerical models are of rigidly supported bridge structure models, that do not properly reflect realistic structural stiffness (Bradner et al., 2010, Istrati, 2017). As presented in Istrati (2017) and Schumacher et al. (2008), dynamic structural properties have an important effect on the measured forces. Except for the two large-scale experimental tests performed by Bradner et al. (2010) and Istrati (2017), substructure

Experimental test setup and description of tests

The experimental test setup used for this study is illustrated in Fig. 1. The setup was designed to study the structural response of highway bridge superstructures under hurricane wave action and is fully described in Bradner et al. (2010). In this article, we focus on the free vibration response of the model (without wave action) to characterize the dynamic properties of the model. A unique aspect of the setup is that the horizontal support flexibility was adjusted to represent different

Initial observations from free vibration tests

The bridge model in this setup can be represented as a single degree of freedom (SDF) mass–spring–damper system. In order to arrive at an equation of motion that accurately represents the physical model, the dynamic properties, including mass, stiffness, and damping, were characterized using the free vibration test results.

The time history responses of all free vibration tests (see Table 1) were visualized in the time domain and analyzed in the frequency domain by means of the discrete Fourier

Analysis

In this section, the equation of motion (EOM) that best describes the free vibration response of the bridge superstructure model under varying levels of water submersion is developed, a suitable numerical scheme to solve it is presented, and an optimization scheme to estimate the dynamic properties for the system using the empirical results are discussed. Additional details regarding the development and evaluation of the numerical scheme as well as the optimization scheme are presented in

Investigation of added mass parameters

This section investigates the added mass derived from results of the complex shaped bridge model. Added mass is represented by madd and only the full-depth submersion case, d* = 1, is considered here. Following the work presented in Chandrasekaran et al. (1972), the first quantity to be introduced is the added mass factor, α, which is the ratio between added mass, madd and dry mass (measured mass in air), mdry, it is computed as α=fa/fw21madd=mdryα where fa and fw are the natural vibration

Summary and conclusions

In this paper, the free vibration response of a large-scale highway bridge superstructure model under varying levels of water submersion was investigated. The objective of the study was to characterize the salient dynamic properties required for the numerical modeling of bridge fluid–structure interaction problems. In addition to varying water levels, the substructure flexibility in the experimental test setup was varied by employing two sets of springs having different stiffnesses. To capture

Notations and Abbreviations

c: viscous damping coefficient of the SDF system

d*: non-dimensional parameter, represents the SWL relative to the girder soffit line

EOM: equation of motion

F: friction force

fa: natural frequency of the structure in air

fn: natural vibration frequency

fw: natural frequency of the structure in water, d* = 1.

k: stiffness coefficient of the SDF system

m: mass of the SDF system

madd: added (or virtual) mass

mdry: dry mass (or mass vibrating in air) of the SDF system

mref: reference fluid mass

Phase 2a:

CRediT authorship contribution statement

Thomas Schumacher: Conception and design of study, Acquisition of data, Analysis and/or interpretation of data, Drafting the manuscript, Revising the manuscript critically for important intellectual content. Alaa W. Hameed: Conception and design of study, Analysis and/or interpretation of data, Drafting the manuscript, Revising the manuscript critically for important intellectual content. Christopher Higgins: Conception and design of study, Acquisition of data, Analysis and/or interpretation of

Declaration of Competing Interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: A financial support was provided by The Higher Committee of Education Development (HCED) of Iraq for Alaa W. Hameed’s to study at Portland State University.

Acknowledgments

The authors would especially like to thank Professor Harry Yeh of Oregon State University for his thoughtful advice and suggestions for interpretation and application of the experimental results. The second author would like to acknowledge the financial support provided by The Higher Committee of Education Development (HCED) in Iraq for her studies at Portland State University. The experimental work that produced the data set analyzed in this study was partially supported by the US Department

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