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Živanović S - One of the best experts on this subject based on the ideXlab platform.
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Experimental validation of moving spring-mass-damper model for human-structure interaction in the presence of vertical vibration
'Elsevier BV', 2021Co-Authors: Ahmadi E, Caprani C, Živanović S, Heidarpour AAbstract:This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordThe interaction between structures and walking humans is an important factor in vibration serviceability assessment of slender, lightweight, and low-damping structures. When on bridges humans form a human-structure system and interact with the structural vibration. The conventional vertical moving force (MF) model neglects human-structure interaction (HSI) effects. In contrast, a moving spring-mass-damper (MSMD) model is shown to have the potential to incorporate HSI effects leading to more accurate vibration response prediction. The MSMD model parameters have been much studied in biomechanics. However, the literature lacks an experimental calibration of the MSMD model parameters on a vibrating surface for vibration serviceability design and assessment purposes. Consequently, an experimental-numerical methodology is developed to calibrate the MSMD model parameters in the worst-case (resonance) scenario by matching measured and simulated vibration responses. To facilitate simple implementation of HSI effects into engineering practice, results of simulation using a calibrated equivalent moving force (EMF) model are also shown. The walking force on rigid surfaces along with vibration responses of two lively full-scale laboratory Footbridges are measured for 23 test subjects by performing a total of 295 trials on the two structures. A parametric study is first performed on the MSMD model using the experimental results. The experimental results of the Monash footbridge are then used as the training dataset to extract optimal MSMD model parameters. The results from the Warwick footbridge are used to validate the model. The validation tests results show a considerable improvement in the vibration response prediction using both models. It was found that when walking in resonance with the bridge, the walker can be modelled to have natural frequency equal to the resonant frequency of the bridge, and that the damping ratio is larger for heavier walkers.Monash-Warwick Alliance Seed GrantMonash Graduate Scholarship (MGS
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A spectral pedestrian-based approach for modal identification
'Elsevier BV', 2020Co-Authors: Jesus A, Živanović S, Alani AAbstract:This is the final version. Available on open access from Elsevier via the DOI in this recordData availability: The raw and processed data required to reproduce these findings can be found at http://wrap.warwick.ac.uk/117039/ for the modal tests, and http://researchdata.uwe.ac.uk/529 for the simulated and measured vibration responses, the Matlab code and the walking forces. For any other data query, please contact the corresponding author.The dynamic behaviour of Footbridges is characterised by modal properties such as natural frequencies, mode shapes, damping ratios and modal masses. Their estimation via modal tests often requires expensive or difficult-to-operate equipment (e.g. shaker and instrumented impact hammer) or, sometimes unavailable high signal-to-noise ratios in tests relying on natural (e.g. wind, airborne noise and ground-borne vibration) excitation. In addition, the modal properties determined in modal tests do not necessarily apply to the structure under pedestrian traffic in case of amplitude-dependent frequencies and damping ratios. The current work proposes a novel approach that stands in contrast to the widely used tests, based on modal identification using an excitation induced by a single pedestrian. In order to account for estimation and observation uncertainties, the relationship between the power spectrum of the response and its modal properties is described with a likelihood function. It is shown that it is possible to reliably estimate modal properties using pedestrian walk forces measured in the laboratory, and dynamic responses measured when the same pedestrian is crossing a footbridge at timed pacing rates. The approach is validated using numerical and field data for a 16.9 m long fibre reinforced polymer footbridge. This work paves a new way for simple and low cost modal testing in structural dynamics.Engineering and Physical Sciences Research Council (EPSRC
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Vertical ground reaction forces on rigid and vibrating surfaces for vibration serviceability assessment of structures
'Elsevier BV', 2019Co-Authors: Ahmadi E, Caprani C, Živanović S, Heidarpour AAbstract:This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordLightweight structures are sensitive to dynamic force generated by human walking and consequently can exhibit excessive vibration responses. The imparted forces, known as ground reaction forces (GRFs), are a key input in the vibration serviceability assessment of Footbridges. Most GRF measurements have been conducted on rigid surfaces such as instrumented treadmills and force plates mounted on strong floors. However, it is thought that the vibrating surface of a footbridge might affect the imparted human force. This paper introduces a unique laboratory experimental setup to investigate vertical GRFs on both rigid surface (strong floor) and a higher-frequency flexible surface (footbridge). 810 walking trials were performed by 18 test subjects walking at different pacing frequencies. For each trial, test subjects travelled a circuit of a vibrating footbridge surface followed by a rigid surface. A novel data collection setup was adopted to record the vertical component of GRFs, and the footbridge vibration response during each trial. Frequency-domain analysis of both single-step and continuous GRFs was then performed. The results show that the footbridge vibration affects GRFs, and changes GRF magnitudes for harmonics in resonance with the footbridge vibration (up to around 30% reduction in the dynamic load factor of the third harmonic). This finding, and the measured GRFs, can be used for more accurate vibration serviceability assessments of existing and new Footbridges.Monash UniversityEngineering and Physical Sciences Research Council (EPSRC
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Vibration performance of a lightweight FRP footbridge under human dynamic excitation
'Springer Science and Business Media LLC', 2019Co-Authors: Živanović S, Jm RussellAbstract:This is the author accepted manuscript. The final version is available from Springer via the DOI in this recordFibre-reinforced polymer (FRP) composites are increasingly used as main load bearing materials in design of pedestrian bridges. The FRP Footbridges are typically characterised by high strength, and relatively low mass and stiffness. These properties could lead to excessive vibration response under human-induced dynamic loading. This paper studies dynamic performance of a 19.8 m long, simply supported, FRP footbridge exposed to walking and jogging. Moreover, the vibration response of this bridge is compared and critically evaluated against the response of an equivalent, in terms of natural frequency and span length, composite steel-concrete structure. The main factors that drive the vibration performance of the FRP structure are discussed and some recommendations for vibration serviceability checks are made.Engineering and Physical Sciences Research Council (EPSRC
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Measured dynamic properties for FRP Footbridges and their critical comparison against structures made of conventional construction materials
'Elsevier BV', 2019Co-Authors: Wei X, Živanović S, Russell J, Toby Mottram JAbstract:This is the final version. Available from Elsevier via the DOI in this record.This paper reports new experimental data for dynamic properties (i.e. modal mass, natural frequency and damping ratio)of eight FRP composite Footbridges in Europe, which helps to resolve the weakness in knowledge and understanding of dynamic properties of FRP Footbridges. In addition, dynamic properties are reviewed with the results of six other FRP Footbridges and 124 non-FRP Footbridges built after 1991. A comprehensive comparison of these 138 sets of dynamic properties shows that FRP Footbridges possess similar fundamental frequencies at the same span, but usually higher damping ratios (mean of 2.5% c.f. mean of
Stana živanovic - One of the best experts on this subject based on the ideXlab platform.
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Vibration Performance of a Lightweight FRP Footbridge Under Human Dynamic Excitation
Dynamics of Civil Structures Volume 2, 2020Co-Authors: Stana živanovic, Justin M. Russell, Vitomir RacicAbstract:Fibre-reinforced polymer (FRP) composites are increasingly used as main load bearing materials in design of pedestrian bridges. The FRP Footbridges are typically characterised by high strength, and relatively low mass and stiffness. These properties could lead to excessive vibration response under human-induced dynamic loading. This paper studies dynamic performance of a 19.8 m long, simply supported, FRP footbridge exposed to walking and jogging. Moreover, the vibration response of this bridge is compared and critically evaluated against the response of an equivalent, in terms of natural frequency and span length, composite steel-concrete structure. The main factors that drive the vibration performance of the FRP structure are discussed and some recommendations for vibration serviceability checks are made.
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probability based prediction of multi mode vibration response to walking excitation
Engineering Structures, 2007Co-Authors: Stana živanovic, Aleksandar Pavic, Paul ReynoldsAbstract:In vibration serviceability checks of Footbridges, a force induced by a single person walking is usually modelled as a harmonic force having a frequency that matches one of the footbridge natural frequencies. This approach assumes that, among the infinite number of harmonics a walking force is composed of, only a single harmonic is important for a vibration serviceability check. Another usual assumption is that the footbridge can be modelled as an SDOF system, implying that only vibration in a single mode is of interest. In addition, due to the deterministic nature of this approach, it cannot take into account inter- and intra-subject variabilities in the walking force that are now well documented in the literature. To account for these variabilities, a novel probabilistic approach to carry out a vibration serviceability check is developed in this paper. Factors such as the probability distribution of walking frequencies, step lengths and amplitude of walking force for its five lowest harmonics and subharmonics are taken into account. Using walking force time histories measured on a treadmill, the frequency content of the force was investigated, resulting in the formulation of a multi-harmonic force model. This model can be used to estimate the multi-mode response in Footbridges. This was verified successfully on an as-built catenary footbridge structure. Although only the vibration response of Footbridges was analysed in this paper, the force model proposed has the potential to be implemented in the estimation of floor vibration as well, where multi-mode response occurs more frequently. The model is easily programmable and as such could present a powerful tool for estimating efficiently the probability of various levels of vibration response due to single person walking. Therefore, the proposed probability-based methodology has the potential to revolutionise the philosophy of the current codes of practice dealing with vibration serviceability of structures under human-induced vibration.
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modal testing and fe model tuning of a lively footbridge structure
Engineering Structures, 2006Co-Authors: Stana živanovic, Aleksandar Pavic, Paul ReynoldsAbstract:Despite huge advances in numerical modelling of civil engineering structures in recent decades, finite element models for Footbridges should still be developed and used with caution when evaluating modal properties of these structures. This is due to some inherent modelling uncertainties related to a lack of information on the as-built structure, such as boundary conditions, material properties and the effects of non-structural elements. These are difficult to deal with at the design stage. A common method to rectify this problem is vibration testing of these structures after construction. As Footbridges are unique prototype structures, testing at this late stage does not help very much in the design of the actual structure. However, combining testing and analysis improves understanding of its vibration behaviour, helps future designs of similar structures and provides key information for the design of remedial measures, if required. This paper describes a lively full-scale footbridge, its numerical modelling and dynamic testing. This was done using state-of-the-art procedures available nowadays for finite element modelling and frequency response function based modal testing. The time efficiency of the testing and parameter estimation procedures carried out without formally closing the footbridge is demonstrated as well as good quality of results achieved. The identified vibration parameters compare well with those from an ambient vibration survey where only the bridge responses were measured. Also, it was demonstrated that properly planned testing can be performed successfully even with some limited facilities, such as only two accelerometers available. The correlation between a very detailed finite element model and experimental results is then studied. For this particular structural system, stiffnesses of girder end supports in the longitudinal direction and bending stiffness of inclined columns were identified as the modelling parameters which influenced most strongly the vertical and the horizontal modes of vibration, respectively.
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vibration serviceability of Footbridges under human induced excitation a literature review
Journal of Sound and Vibration, 2005Co-Authors: Stana živanovic, Aleksandar Pavic, Paul ReynoldsAbstract:Increasing strength of new structural materials and longer spans of new Footbridges, accompanied with aesthetic requirements for greater slenderness, are resulting in more lively footbridge structures. In the past few years this issue attracted great public attention. The excessive lateral sway motion caused by crowd walking across the infamous Millennium Bridge in London is the prime example of the vibration serviceability problem of Footbridges. In principle, consideration of footbridge vibration serviceability requires a characterisation of the vibration source, path and receiver. This paper is the most comprehensive review published to date of about 200 references which deal with these three key issues. The literature survey identified humans as the most important source of vibration for Footbridges. However, modelling of the crowd-induced dynamic force is not clearly defined yet, despite some serious attempts to tackle this issue in the last few years. The vibration path is the mass, damping and stiffness of the footbridge. Of these, damping is the most uncertain but extremely important parameter as the resonant behaviour tends to govern vibration serviceability of Footbridges. A typical receiver of footbridge vibrations is a pedestrian who is quite often the source of vibrations as well. Many scales for rating the human perception of vibrations have been found in the published literature. However, few are applicable to Footbridges because a receiver is not stationary but is actually moving across the vibrating structure. During footbridge vibration, especially under crowd load, it seems that some form of human–structure interaction occurs. The problem of influence of walking people on footbridge vibration properties, such as the natural frequency and damping is not well understood, let alone quantified. Finally, there is not a single national or international design guidance which covers all aspects of the problem comprehensively and some form of their combination with other published information is prudent when designing major footbridge structures. The overdue update of the current codes to reflect the recent research achievements is a great challenge for the next 5–10 years.
Edward Ott - One of the best experts on this subject based on the ideXlab platform.
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crowd synchrony on the millennium bridge
Nature, 2005Co-Authors: Steven H Strogatz, Daniel M Abrams, Allan Mcrobie, Bruno Eckhardt, Edward OttAbstract:Footbridges start to sway when packed with pedestrians falling into step with their vibrations.
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theoretical mechanics crowd synchrony on the millennium bridge
Nature, 2005Co-Authors: Steven H Strogatz, Daniel M Abrams, Allan Mcrobie, Bruno Eckhardt, Edward OttAbstract:Footbridges start to sway when packed with pedestrians falling into step with their vibrations.
Tubino F - One of the best experts on this subject based on the ideXlab platform.
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Serviceability Assessment of Footbridges Via Improved Interval Analysis
'ASME International', 2021Co-Authors: Santoro R, Sofi A, Tubino FAbstract:This paper studies the propagation of uncertainties on serviceability assessment of Footbridges in unrestricted traffic condition based on a nondeterministic approach. Multipedestrian loading is modeled as a stationary Gaussian random process through the equivalent spectral model which yields analytical expressions of the spectral moments of the footbridge dynamic response. The uncertain pedestrian-induced loading parameters and structural dynamic properties are modeled as interval variables. An approximate analytical procedure, based on the improved interval analysis, is introduced as an efficient alternative to classical optimization in order to propagate interval uncertainties. The presented procedure allows us to derive closed-form expressions of the bounds of the spectral moments of the response, as well as of the expected value and cumulative distribution function of the maximum footbridge acceleration. Two strategies are proposed to assess Footbridges' serviceability. The first one leads to the definition of a range of comfort classes. The second strategy enables us to estimate an interval of probability of reaching at least a suitable comfort level
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Human-induced loading and dynamic response of Footbridges in the vertical direction due to restricted pedestrian traffic
'Informa UK Limited', 2021Co-Authors: Venuti F., Tubino FAbstract:Despite extensive research in the field of human-induced vibration in the last twenty years, there is still lack of reliable load and response models to assess vibration serviceability of Footbridges under human-induced excitation, especially with reference to crowded conditions. This paper aims to provide a reliable characterization of pedestrian-induced loading on Footbridges in restricted traffic condition, and to compare the reliability of current guidelines and advanced spectral models in the serviceability assessment of Footbridges with respect to vertical vibrations. Numerical simulations of restricted pedestrian traffic are carried out through an agent-based model, considering variable pedestrian densities and deck widths. The probability distribution of the step frequency and the power spectral density function of the modal force are obtained numerically. Based on the numerical results, a Modified Generalized Equivalent Spectral Model is proposed. Finally, two numerical examples are analyzed to assess the reliability of current guidelines and of the Modified Generalized Equivalent Spectral Model in the estimate of the maximum footbridge acceleration
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Interval serviceability assessment of Footbridges
European Association for Structural Dynamics EASD, 2020Co-Authors: Santoro R, Sofi A, Tubino FAbstract:This paper studies serviceability assessment of Footbridges through a non-deterministic approach. The parameters defining pedestrian-induced loading and the structural dynamic properties are characterized through possible ranges of variation. Starting from analytical expressions for the spectral moments of the structural response, the improved interval analysis is applied together with an optimization strategy that allows us to obtain the bounds of the standard deviation of the footbridge acceleration and of the mean value and cumulative distribution function of its maximum value. Based on this approach, a possible interval of variation of the structural response is evaluated, rather than a single deterministic value. Thus, an interval level of comfort can be defined
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Pedestrian-Induced Vibrations of Footbridges: An Extended Spectral Approach
'American Society of Civil Engineers (ASCE)', 2020Co-Authors: Van Nimmen K, Van Den Broeck P, Lombaert G, Tubino FAbstract:The vibration serviceability assessment of Footbridges under pedestrian traffic requires a probabilistic approach considering the uncertainty in the dynamic behavior of the structure and the variability of multiple load parameters, such as the pedestrians' arrival time and step frequency. In view of engineering applications, a major challenge lies in the development, verification, and validation of efficient prediction models. With this challenge in mind, this paper uses a spectral approach to predict the dynamic response induced by unrestricted pedestrian traffic. A spectral load model available in the literature is extended to account for multiple harmonics of the vertical walking load and for application to arbitrary mode shapes. Furthermore, a closed-form expression is proposed to estimate the variance of the multimode structural response taking into account both resonant and nonresonant contributions. The performance of the proposed approach is evaluated for a simply supported beam as well as a real footbridge where multiple modes considerably contribute to the overall structural response. The results show that the proposed approach allows a good and mildly conservative estimate of the structural response to be obtained
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Uncertainty propagation in the serviceability assessment of Footbridges
'Informa UK Limited', 2019Co-Authors: Tubino F, Pagnini L., Piccardo G.Abstract:This paper discusses the serviceability assessment of Footbridges considering the uncertainties in definition of their structural and loading parameters. Application of the Taylor Series Expansion method to the closed-form expression of the dynamic response based on the Equivalent Spectral Model allows to obtain analytical solutions for the quantification of uncertainty propagation and to identify the parameters whose uncertainties may cause significant scatter of the results. The proposed analytical solutions are verified by Monte Carlo simulations, in the two classic scenarios of resonance and non-resonance conditions between step frequency and the bridge natural frequency. The approach provides the possibility of going beyond conventional verifications of footbridge vibration level, based on nominal values of load and structural properties. In this framework, serviceability assessment is proposed from a probabilistic point of view, associating a probability of occurrence to each comfort level
Paul Reynolds - One of the best experts on this subject based on the ideXlab platform.
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probability based prediction of multi mode vibration response to walking excitation
Engineering Structures, 2007Co-Authors: Stana živanovic, Aleksandar Pavic, Paul ReynoldsAbstract:In vibration serviceability checks of Footbridges, a force induced by a single person walking is usually modelled as a harmonic force having a frequency that matches one of the footbridge natural frequencies. This approach assumes that, among the infinite number of harmonics a walking force is composed of, only a single harmonic is important for a vibration serviceability check. Another usual assumption is that the footbridge can be modelled as an SDOF system, implying that only vibration in a single mode is of interest. In addition, due to the deterministic nature of this approach, it cannot take into account inter- and intra-subject variabilities in the walking force that are now well documented in the literature. To account for these variabilities, a novel probabilistic approach to carry out a vibration serviceability check is developed in this paper. Factors such as the probability distribution of walking frequencies, step lengths and amplitude of walking force for its five lowest harmonics and subharmonics are taken into account. Using walking force time histories measured on a treadmill, the frequency content of the force was investigated, resulting in the formulation of a multi-harmonic force model. This model can be used to estimate the multi-mode response in Footbridges. This was verified successfully on an as-built catenary footbridge structure. Although only the vibration response of Footbridges was analysed in this paper, the force model proposed has the potential to be implemented in the estimation of floor vibration as well, where multi-mode response occurs more frequently. The model is easily programmable and as such could present a powerful tool for estimating efficiently the probability of various levels of vibration response due to single person walking. Therefore, the proposed probability-based methodology has the potential to revolutionise the philosophy of the current codes of practice dealing with vibration serviceability of structures under human-induced vibration.
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modal testing and fe model tuning of a lively footbridge structure
Engineering Structures, 2006Co-Authors: Stana živanovic, Aleksandar Pavic, Paul ReynoldsAbstract:Despite huge advances in numerical modelling of civil engineering structures in recent decades, finite element models for Footbridges should still be developed and used with caution when evaluating modal properties of these structures. This is due to some inherent modelling uncertainties related to a lack of information on the as-built structure, such as boundary conditions, material properties and the effects of non-structural elements. These are difficult to deal with at the design stage. A common method to rectify this problem is vibration testing of these structures after construction. As Footbridges are unique prototype structures, testing at this late stage does not help very much in the design of the actual structure. However, combining testing and analysis improves understanding of its vibration behaviour, helps future designs of similar structures and provides key information for the design of remedial measures, if required. This paper describes a lively full-scale footbridge, its numerical modelling and dynamic testing. This was done using state-of-the-art procedures available nowadays for finite element modelling and frequency response function based modal testing. The time efficiency of the testing and parameter estimation procedures carried out without formally closing the footbridge is demonstrated as well as good quality of results achieved. The identified vibration parameters compare well with those from an ambient vibration survey where only the bridge responses were measured. Also, it was demonstrated that properly planned testing can be performed successfully even with some limited facilities, such as only two accelerometers available. The correlation between a very detailed finite element model and experimental results is then studied. For this particular structural system, stiffnesses of girder end supports in the longitudinal direction and bending stiffness of inclined columns were identified as the modelling parameters which influenced most strongly the vertical and the horizontal modes of vibration, respectively.
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vibration serviceability of Footbridges under human induced excitation a literature review
Journal of Sound and Vibration, 2005Co-Authors: Stana živanovic, Aleksandar Pavic, Paul ReynoldsAbstract:Increasing strength of new structural materials and longer spans of new Footbridges, accompanied with aesthetic requirements for greater slenderness, are resulting in more lively footbridge structures. In the past few years this issue attracted great public attention. The excessive lateral sway motion caused by crowd walking across the infamous Millennium Bridge in London is the prime example of the vibration serviceability problem of Footbridges. In principle, consideration of footbridge vibration serviceability requires a characterisation of the vibration source, path and receiver. This paper is the most comprehensive review published to date of about 200 references which deal with these three key issues. The literature survey identified humans as the most important source of vibration for Footbridges. However, modelling of the crowd-induced dynamic force is not clearly defined yet, despite some serious attempts to tackle this issue in the last few years. The vibration path is the mass, damping and stiffness of the footbridge. Of these, damping is the most uncertain but extremely important parameter as the resonant behaviour tends to govern vibration serviceability of Footbridges. A typical receiver of footbridge vibrations is a pedestrian who is quite often the source of vibrations as well. Many scales for rating the human perception of vibrations have been found in the published literature. However, few are applicable to Footbridges because a receiver is not stationary but is actually moving across the vibrating structure. During footbridge vibration, especially under crowd load, it seems that some form of human–structure interaction occurs. The problem of influence of walking people on footbridge vibration properties, such as the natural frequency and damping is not well understood, let alone quantified. Finally, there is not a single national or international design guidance which covers all aspects of the problem comprehensively and some form of their combination with other published information is prudent when designing major footbridge structures. The overdue update of the current codes to reflect the recent research achievements is a great challenge for the next 5–10 years.