dynamics of structureshomepages.ulb.ac.be/~aderaema/dynamics/7_dos... · 2. dynamics of structures...

Dynamics of Structures 2019-2020 7. Summary and Evaluation

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7. Summary and Evaluation

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Dynamics of structures

Arnaud Deraemaeker ([email protected])

Examination and how to study

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Examination

Present one of the 4 test-cases

• 30 minutes preparation• 15 minutes discussion• With lecture notes (and home preparations)

• Source of excitation• Effects• Design methodology• Remedial measures

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What you must absolutely know

• The difference between free and forced vibration• What is resonance and what do the resonant frequencies depend on ?• Read and explain a Bode diagram• Understand the role of damping• What is the Fourier transform and the difference between discr/cont• What Fourier transform is useful for• What are mode shapes and what is the advantage of projection of the

equations of motion on the modal basis• What is modal truncation and how to decide on the number of modes to

consider• What is low and high tuning• How to reduce a model to a 1dof system• Order of magnitude of damping in civil engineering structures• Working principle of a TMD• Working principle of a direct/inverse isolation device


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How you must study

- Equations- Not how to derive them- But how to use them (meaning of each term)

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- Graphs- What is on the axis ?- What is the information on the graph ?

How you must study


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What you have to pay attention to

• Units• The meaning of complex amplitudes

Case studies : summary

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A test-case based learning of vibrations in civil engineering

Case study 1 : pedestrian induced vibrations of a footbridge


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Case study 2 : Vibrations of high-rise buildings



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Case study 3 : Machinery induced vibrations in a building


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Case study 4 : Vibrations caused by traffic



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Sources of excitation

• Walking pedestrians• Machines• Traffic• Earthquake• Wind

Signal Processing(Fourier transform)

Base acceleration (Santa Cruz Earthquake)

What is the frequency content of the excitation ?

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Effects

Finite element model

For each system (bridge, tower …) how do you assess the level of vibrations ?

MDOF system-> Equivalent mass/stiffness ?


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Effects

Continuous systemFinite element model

Equivalent mass/stiffness

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Effects

MDOF systemContinuous SystemFinite element model

Projection in modal basisSet of n decoupled equations

of a 1DOF system

Mode shapes and eigenfrequencies

Based on these models, how do you compute the response to the excitation ?


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Essential to understand• Resonance• Effect of stiffness, mass and damping

Effects

Transfer function

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Effects

Time domain response


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Effects

Transfer function(Frequency response function)

Time domain response

Base acceleration

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Design methodology

Low tuning High tuning


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Remedial measures

Stiffening

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Remedial measures

Adding damping

Material damping

Tuned mass damper


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Remedial measures

Vibration isolationDirect

Inverse

Research topics in Structural Dynamics in BATir- Dynamics Group

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Vibration damping

Variability due to the environment (T°, humidity)• Effect on performance of TMD ?• Robust design of TMD ?

Other criteria for optimisation• Response spectra• Realistic input spectra (wind, earthquake)

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Structural Health Monitoring

• Aging of civil engineering infrastructure• Increasing loads

Risk of failure


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Current practice

• Manual inspections• Mostly visual

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Monitoring of civil infrastructure

• Sensor network• On-line intelligence -> Alarm triggering


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Vibration based monitoring

• Change of stiffness = change of mode shapes and eigenfrequencies

But• Also sensitive to environmental factors (T°, humidity)• Sensitive to large damage only (global method)

Monitor mode shapes and eigenfrequencies

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Wave base methods

• Will be introduced in second part of the course• Basic principle : wave travelling through material, affected by small

local changes of microstructure

Local method


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Classical ultrasonic testing

Difficulties :• coupling with the concrete• accessibility• limited wave paths• bulky and expensive transducers

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Ultrasonic testing with embedde piezoelectric transducers

Advantages :• Low cost• Flexibility in transducer configurations• Excellent coupling and linearity• Protected from environment• Inaccessible locations• Possibility of automation

Developed at ULB-BATir


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Example of application

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The Tweetcon project

Arnaud DERAEMAEKERProject Supervisor

Cédric DUMOULINResearcher‐Entrepreneur

Bryan POELMANBusiness alter‐ego

https://www.tweetcon.be


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Early age

Mid-term

Long-term

Ultrasonic testing



Current application in the Rogier tunnel (Brussels)

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Current application in the Rogier tunnel (Brussels)

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A master thesis in BATir-Dynamics Group

• Subjects published early in 2020• Numerical (finite element) and/or experimental topics

The student should• Be motivated• Show interest and skills for structural dynamics• Have a basic knowledge of Matlab

The student will• Be integrated in a very dynamic group with links to industry• Be offered a continuous supervision with regular meetings• Have access to the large testing facilities/ numerical tools of BATir

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