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Vibration of damped uniform beams with general end conditions under moving loads
KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges. ELU Konsult AB, Sweden.
KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges. ELU Konsult AB, Sweden.
KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges. ELU Konsult AB, Sweden.
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2016 (English)In: Engineering structures, ISSN 0141-0296, E-ISSN 1873-7323, Vol. 126, 40-52 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, an analytical solution for evaluating the dynamic behaviour of a non-proportionally damped Bernoulli–Euler beam under a moving load is derived. The novelty of this paper, when compared with other publications along this line of work is that general boundary conditions are assumed throughout the derivation. Proper orthogonality conditions are then derived and a closed form solution for the dynamical response for a given eigenmode is developed. Based on this, the dynamical response of the system to any load can be determined by mode superposition. The proposed method is particularly useful for studying various types of damping mechanisms in bridges, such as soil–structure interaction, external dampers, and material damping. Several numerical examples are presented to validate the proposed method and provide insight into the problem of non-proportionally damped systems. The numerical examples also allow for some interesting observations concerning the behaviour of modal damping for closely spaced modes (with respect to undamped natural frequencies).

Place, publisher, year, edition, pages
Elsevier, 2016. Vol. 126, 40-52 p.
Keyword [en]
Bernoulli–Euler beam, Complex mode, Moving load, Non-proportional damping, Damping, Closed form solutions, Complex modes, Euler beam, General boundary conditions, Mode superposition, Nonproportional damping, Orthogonality conditions, Numerical methods, analytical method, dynamic response, soil-structure interaction, vibration
National Category
Civil Engineering
Identifiers
URN: urn:nbn:se:kth:diva-195219DOI: 10.1016/j.engstruct.2016.07.037ISI: 000384861500004Scopus ID: 2-s2.0-84982706028OAI: oai:DiVA.org:kth-195219DiVA: diva2:1047418
Funder
Swedish Transport Administration
Note

QC 20161117

Available from: 2016-11-17 Created: 2016-11-02 Last updated: 2017-02-12Bibliographically approved
In thesis
1. Efficient Modelling Techniques for Vibration Analyses of Railway Bridges
Open this publication in new window or tab >>Efficient Modelling Techniques for Vibration Analyses of Railway Bridges
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The world-wide development of new high-speed rail lines has led to more stringent design requirements for railway bridges, mainly because high-speed trains can cause resonance in the bridge superstructure. Dynamic simulations, often utilising time-consuming finite element analysis (FEA), have become essential for avoiding such problems. Therefore, guidelines and tools to assist structural engineers in the design process are needed.

Considerable effort was spent at the beginning of the project, to develop simplified models based on two-dimensional (2D) Bernoulli-Euler beam theory. First, a closed-form solution for proportionally damped multi-span beam, subjected to moving loads was derived (Paper I). The model was later used to develop design charts (Paper II) and study bridges on existing railway lines (Paper III). The model was then extended to non-proportionally damped beams (Paper IV) in order to include the effects of soil-structure interactions. Finally, the importance of the interaction between the surrounding soil and the bridge was verified by calibrating a finite element (FE) model by means of forced vibration tests of an end-frame bridge (Paper V).

Recommendations on how to use the models in practical applications are discussed throughout the work. These recommendations include the effects of shear deformation, shear lag, train-bridge and soil-structure interactions, for which illustrative examples are provided. The recommendations are based on the assumption that the modes are well separated, so that the response at resonance is governed by a single mode.

The results of the work show that short span bridges, often referred to as `simple´ bridges, are the most problematic with respect to dynamic effects. These systems are typically, non-proportionally damped systems that require detailed analyses to capture the `true´ behaviour. Studying this class of dynamic system showed that they tend to contain non-classical modes that are important for the structure response. For example, the bending mode is found to attain maximum damping when its undamped natural frequency is similar to that of a non-classical mode.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2017. 111 p.
Series
TRITA-BKN. Bulletin, ISSN 1103-4270 ; 145
Keyword
Railway bridge, High-speed train, Closed-form solution, Non-proportional damping, Complex mode
National Category
Infrastructure Engineering
Identifiers
urn:nbn:se:kth:diva-201647 (URN)
Public defence
2017-02-24, Kol, Brinellvägen 8, Stockholm, 13:30 (English)
Opponent
Supervisors
Note

QC 20170213

Available from: 2017-02-13 Created: 2017-02-12 Last updated: 2017-02-13Bibliographically approved

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