Research topics on ow-induced vibrations

Research topics on �ow-induced

vibrationsPEF 6000 - Special topics on dynamics of structures

Associate Professor Guilherme R. Franzini

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Outline

1 Objectives

2 Vortex-induced vibrations (VIV)

3 Passive suppression of galloping

4 Vortex-self induced vibrations (VSIV)

5 Energy harvesting

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Objectives

• To present research topics on �ow-induced vibrations;

• To highlight the contributions from EPUSP to the state-of-art.• References: MsC dissertation written by Tatiana Ueno (2019), habilitation thesis

written by Gonçalves (2013, Fujarra (2013), Rateiro (2014) and Franzini (2019)and selected papers.

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Objectives

• To present research topics on �ow-induced vibrations;• To highlight the contributions from EPUSP to the state-of-art.

• References: MsC dissertation written by Tatiana Ueno (2019), habilitation thesiswritten by Gonçalves (2013, Fujarra (2013), Rateiro (2014) and Franzini (2019)and selected papers.

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Objectives

• To present research topics on �ow-induced vibrations;• To highlight the contributions from EPUSP to the state-of-art.• References: MsC dissertation written by Tatiana Ueno (2019), habilitation thesis

written by Gonçalves (2013, Fujarra (2013), Rateiro (2014) and Franzini (2019)and selected papers.

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Some open questions

VIV still demands some investigations. Examples of open topics include:• Flow around cylinders with low aspect ratio;

• Flow around cylinders with cross-sections other than circular;• Passive control;• Flexible cylinder VIV;• Concomitant excitation.

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Some open questions

VIV still demands some investigations. Examples of open topics include:• Flow around cylinders with low aspect ratio;• Flow around cylinders with cross-sections other than circular;

• Passive control;• Flexible cylinder VIV;• Concomitant excitation.

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Some open questions

VIV still demands some investigations. Examples of open topics include:• Flow around cylinders with low aspect ratio;• Flow around cylinders with cross-sections other than circular;• Passive control;

• Flexible cylinder VIV;• Concomitant excitation.

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Some open questions

VIV still demands some investigations. Examples of open topics include:• Flow around cylinders with low aspect ratio;• Flow around cylinders with cross-sections other than circular;• Passive control;• Flexible cylinder VIV;

• Concomitant excitation.

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Some open questions

VIV still demands some investigations. Examples of open topics include:• Flow around cylinders with low aspect ratio;• Flow around cylinders with cross-sections other than circular;• Passive control;• Flexible cylinder VIV;• Concomitant excitation.

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Flow around cylinders with low aspect ratio

• Monocolumn platforms have low aspect ratio (L/D < 5);

• The �ow around these structures lead to oscillatory responses on the horizontalplane with amplitudes of order of one diameter (Vortex-Induced Motion - VIM);

• Tridimensional e�ects are of great importance (other �ow structures than thevón Kármán wake);

• Lower branch is not so well de�ned;• Examples of references: Gonçalves (2013), Fujarra (2013), Gonçalves et al

(2015)...

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• Monocolumn platforms have low aspect ratio (L/D < 5);• The �ow around these structures lead to oscillatory responses on the horizontal

plane with amplitudes of order of one diameter (Vortex-Induced Motion - VIM);

• Tridimensional e�ects are of great importance (other �ow structures than thevón Kármán wake);


(2015)...

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plane with amplitudes of order of one diameter (Vortex-Induced Motion - VIM);• Tridimensional e�ects are of great importance (other �ow structures than the

vón Kármán wake);


(2015)...

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vón Kármán wake);• Lower branch is not so well de�ned;

• Examples of references: Gonçalves (2013), Fujarra (2013), Gonçalves et al(2015)...

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vón Kármán wake);• Lower branch is not so well de�ned;• Examples of references: Gonçalves (2013), Fujarra (2013), Gonçalves et al

(2015)...

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Cylinders with di�erent cross-sections

• Floating platforms may exhibit cross-sections di�erent from the circular one;

• Examples of usual cross-sections: Square sections, with rounded corners;• Possible coexistence of galloping and VIV;• Gonçalves et al (2015): Oscillation amplitude strongly depends of the angle of

attack;• Gonçalves et al (2016): Experimental investigation on the e�ects of round

corners.

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• Floating platforms may exhibit cross-sections di�erent from the circular one;• Examples of usual cross-sections: Square sections, with rounded corners;

• Possible coexistence of galloping and VIV;• Gonçalves et al (2015): Oscillation amplitude strongly depends of the angle of


corners.

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• Floating platforms may exhibit cross-sections di�erent from the circular one;• Examples of usual cross-sections: Square sections, with rounded corners;• Possible coexistence of galloping and VIV;

• Gonçalves et al (2015): Oscillation amplitude strongly depends of the angle ofattack;

• Gonçalves et al (2016): Experimental investigation on the e�ects of roundcorners.

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• Floating platforms may exhibit cross-sections di�erent from the circular one;• Examples of usual cross-sections: Square sections, with rounded corners;• Possible coexistence of galloping and VIV;• Gonçalves et al (2015): Oscillation amplitude strongly depends of the angle of

attack;

• Gonçalves et al (2016): Experimental investigation on the e�ects of roundcorners.

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• Floating platforms may exhibit cross-sections di�erent from the circular one;• Examples of usual cross-sections: Square sections, with rounded corners;• Possible coexistence of galloping and VIV;• Gonçalves et al (2015): Oscillation amplitude strongly depends of the angle of


corners.

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Passive suppression - strakes

Figura: Extraído de Korkischko & Meneghini (2011).

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• The �ow separation occurs at �xed points located at the strakes;

• Decreases the correlation length;• Direct interference on the �ow �eld.

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• The �ow separation occurs at �xed points located at the strakes;• Decreases the correlation length;

• Direct interference on the �ow �eld.

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• The �ow separation occurs at �xed points located at the strakes;• Decreases the correlation length;• Direct interference on the �ow �eld.

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Passive suppression - NVA

• NVA (Nonlinear vibration absorber) or NES (Nonlinear Energy Sink): Masscoupled to the main structure by means of an element of null linearized naturalfrequency and a dashpot. Examples of NVA are (from Franzini (2019));

(a) VI-NES. (b) Translative NVA. (c) Rotative NVA.

• No preferential frequency for suppression;• Numerical studies based on CFD presented in Tumkur et al (2013a,b) and

Blanchard (2016): A rotative NVA is e�cient in VIV mitigation;• CFD calculations have high computational cost → Sensitivity studies with

respect to changes in the NVA parameters are practically impossible;• On the other hand, wake-oscillators appear as an interesting alternative;• The use of a rotative NVA is focus of the MsC. dissertation written by Ueno

(2019) and the paper Ueno & Franzini (2019).• At least to the best of the authors' knowledge, passive suppression of VIV-2dof

using a rotative NVA was not found in the literature.

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• No preferential frequency for suppression;

• Numerical studies based on CFD presented in Tumkur et al (2013a,b) andBlanchard (2016): A rotative NVA is e�cient in VIV mitigation;

• CFD calculations have high computational cost → Sensitivity studies withrespect to changes in the NVA parameters are practically impossible;

• On the other hand, wake-oscillators appear as an interesting alternative;• The use of a rotative NVA is focus of the MsC. dissertation written by Ueno



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Blanchard (2016): A rotative NVA is e�cient in VIV mitigation;

• CFD calculations have high computational cost → Sensitivity studies withrespect to changes in the NVA parameters are practically impossible;




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respect to changes in the NVA parameters are practically impossible;




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respect to changes in the NVA parameters are practically impossible;• On the other hand, wake-oscillators appear as an interesting alternative;

• The use of a rotative NVA is focus of the MsC. dissertation written by Ueno(2019) and the paper Ueno & Franzini (2019).

• At least to the best of the authors' knowledge, passive suppression of VIV-2dofusing a rotative NVA was not found in the literature.

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(2019) and the paper Ueno & Franzini (2019).

• At least to the best of the authors' knowledge, passive suppression of VIV-2dofusing a rotative NVA was not found in the literature.

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using a rotative NVA was not found in the literature.9/48

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Passive suppression - Rotative NVA

• Results from Ueno (2019) and Ueno & Franzini (2019).• Use of wake-oscillators allowed developing sensitivity studies with respect to the

in�uence of the NVA on the suppression;• In the following results: r = 0.50 e ζθ = 0.10. G1-Sim1: m = 0.03, G1-Sim2:

m = 0.07, G1-Sim3: m = 0.10, G1-Sim4: m = 0.12 and G1-Sim5: m = 0.15.

Ur

2 4 6 8 10 12 14

Ay

0

0.2

0.4

0.6

0.8

1

VIV Puro

Sim-0

G1-Sim1

G1-Sim2

G1-Sim3

G1-Sim4

G1-Sim5

(a) Ay (Ur ). VIV-1dof.

Ur

2 4 6 8 10 12 14

Ay

0

0.5

1

1.5

2

VIV Puro

Sim-0

G1-Sim1

G1-Sim2

G1-Sim3

G1-Sim4

G1-Sim5

(b) Ay (Ur ). VIV-2dof.

Ur

2 4 6 8 10 12 14

Ax

0

0.05

0.1

0.15

0.2

0.25

0.3

VIV Puro

Sim-0

G1-Sim1

G1-Sim2

G1-Sim3

G1-Sim4

G1-Sim5

(c) Ax (Ur ). VIV-2dof.

Extracted from Ueno (2019).

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Passive suppression - Rotative NVA

• Example of time-histories r = 0.50, ζθ = 0.10, m = 0.15 - Ur = 6. VIV-1dof.

τ

0 200 400 600 800

y(τ)

-1

0

1

Ur = 6

f = f/fn,y

0 1 2 3 4 5

A(f)

0

0.5

1

(a) y(τ) and amplitude spectrum.

τ

0 100 200 300 400 500 600 700 800

q y(τ)

-1

0

1

Ur = 6

f = f/fn,y

0 1 2 3 4 5

A(f)

0

0.5

1

(b) qy (τ) and amplitude spectrum.

τ

0 100 200 300 400 500 600 700 800

θ(τ)

-200

0

200

400

600

800

Ur = 6

(c) θ(τ).

• 1 : 1 : 1 resonance (TET mechanism).

Adapted from Ueno (2019).

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Passive suppression - Rotative NVA and VIV-1dof

• In the colorbar, the map above shows an e�ciency criterion. Values close to 1refer to high e�ciency.


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Passive suppression - Rotative NVA and VIV-1dof


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Flexible cylinders under VIV

• Already discussed: The response to VIV is intrinsically more intricate than thatobserved in rigid and elastically supported cylinders;

• Derivation of reduced-order models (ROMs): How can we choose a set ofprojection functions to be adopted in the Galerkin's method?

• Possible alternative: �Quasi-Bessel� modes.• Due to the non-linear character of the mathematical model, the system of ODEs

will be coupled How to evaluate the number of adopted modes?

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• Possible alternative: �Quasi-Bessel� modes.

• Due to the non-linear character of the mathematical model, the system of ODEswill be coupled How to evaluate the number of adopted modes?

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• Use of wake-oscillators: Forces due to the �uid-structure interaction aredistributed along the span;

• Spatial distribution: Nodal (via FEM) continuously?• What is the projection function to be adopted in the Galerkin's method for

discretizing the PDE associated with the van der Pol equation?• Use of wake-oscillators for �exible cylinder VIV: Is valid to use the empirically

calibrated parameters obtained from experiments with rigid and elasticallymounted cylinders?

• What is the gain allowed by the use of �non-standard� techniques such as theuse of invariant manifolds in VIV analysis?

• A comprehensive research project on nonlinear dynamics of risers was developedat EPUSP and LMO led the experimental activities. This class bringsexperimental results from this project.

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• Spatial distribution: Nodal (via FEM) continuously?

• What is the projection function to be adopted in the Galerkin's method fordiscretizing the PDE associated with the van der Pol equation?

• Use of wake-oscillators for �exible cylinder VIV: Is valid to use the empiricallycalibrated parameters obtained from experiments with rigid and elasticallymounted cylinders?



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discretizing the PDE associated with the van der Pol equation?

• Use of wake-oscillators for �exible cylinder VIV: Is valid to use the empiricallycalibrated parameters obtained from experiments with rigid and elasticallymounted cylinders?



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Modal-amplitude time-histories: vertical �exible cylinder

• Modal decomposition: Decompose the measured data into a set of projectionfunctions. Allows identifying the participation of di�erent modes in the response.

axn(tj ) =

∫ 10 X∗(z, tj )ψn(z)dξ∫ 1

0 (ψn(z))2dξ(1)

ayn(tj ) =

∫ 10 Y ∗(z, tj )ψn(z)dξ∫ 1

0 (ψn(z))2dξ(2)

0 2 4 6 8 10 12 14 16VR,n = U∞/fN,nD

0

0.2

0.4

0.6

0.8

1

Ay n

n = 1

n = 2

n = 3

n = 4

(a) Cross-wise characteristic modal-amplitude

oscillation Ayn .

0 2 4 6 8 10 12 14 16VR,n = U∞/fN,nD

0

0.2

0.4

0.6

0.8

1

Ax n

n = 1

n = 2

n = 3

n = 4

(b) In-line characteristic modal-amplitude os-

cillation Axn .

Extracted from Franzini et al (2016).16/48

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Example of experimental analysis - Ur ,1 = 6.99

Di�erent regimes may appear in the same nominal modal reduced velocityUr,1 = U∞/fn,1D. The �gure below is extracted from Franzini (2019).

(a) Scalogram y∗(ξ, τ). (b) Scalogram x∗(ξ, τ).

y∗(ξ, τ )-1 0 1

ξ=

z/L0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

50 < τ = tfn,1 < 55

y∗(ξ, τ )-1 0 1

ξ=

z/L0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

150 < τ = tfn,1 < 155

(c) Instantaneous deformed

cross-wise con�guration.

x∗(ξ, τ )-1 0 1 2 3

ξ=

z/L0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

50 < τ = tfn,1 < 55

x∗(ξ, τ )-1 0 1 2 3

ξ=

z/L0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

150 < τ = tfn,1 < 155

(d) Instantaneous deformed in-

line con�guration.

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Trajectories on the horizontal plane.

(a) 50 < τ < 55. (b) 150 < τ < 155.

Extracted from Franzini (2019).

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The �gure below is extracted from Franzini (2019).

(a) Scalogram y∗(ξ, τ). (b) Scalogram x∗(ξ, τ).

y∗(ξ, τ )-1 0 1

ξ=

z/L0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

15 < τ = tfn,1 < 10

y∗(ξ, τ )-1 0 1

ξ=

z/L0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1100 < τ = tfn,1 < 105

(c) Instantaneous deformed

cross-wise con�guration.

x∗(ξ, τ )-1 0 1 2 3

ξ=

z/L0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

15 < τ = tfn,1 < 10

x∗(ξ, τ )-1 0 1 2 3

ξ=

z/L0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1100 < τ = tfn,1 < 105

(d) Instantaneous deformed in-

line con�guration.

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Trajectories on the horizontal plane.

(a) 50 < τ < 55. (b) 150 < τ < 155.


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Analyses with modal-amplitude time-histories

• Modal-amplitude time-histories allow investigating the participation of eachmode in the response. They contain information of all measured points. Weillustrate two modal amplitude time-histories from di�erent tests (di�erent U∞),but at similar modal reduced velocity Ur,k = U∞/fn,kD. From free-decay tests,fn,2 = 2fn,1, fn,3 = 3fn,1

τ = tfn,1

0 50 100 150 200 250 300

ay 1(τ)

-0.5

0

0.5Ur,1 = U∞/fN,1D =4.26

f = f/fn,1

0 1 2 3 4 5 6

Sy 1

0

0.02

0.04

0.06

0.08

(a) ay1(τ) and amplitude spectrum.

τ = tfn,1

0 50 100 150 200 250 300

ay 2(τ)

-0.5

0

0.5Ur,2 = U∞/fn,2D =4.17

f/fn,2

0 1 2 3 4 5 6

Sy 2

0

0.02

0.04

0.06

0.08

(b) ay1(τ) and amplitude spectrum.

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Ur ,1 ≈ Ur ,2 ≈ 5.70. Extracted from Franzini (2019).

τ = tfn,1

0 50 100 150 200 250 300ay 1(τ)

-1

0

1

Ur,1 = U∞/fn,1D =5.63

f = f/fn,1

0 1 2 3 4 5 6

Sy 1

0

0.2

0.4

0.6

(a) ay1(τ) and amplitude spectrum.

τ = tfn,1

0 50 100 150 200 250 300

ax 2(τ)

-1

0

1

Ur,1 = U∞/fn,1D =5.63

f = f/fn,1

0 1 2 3 4 5 6

Sx 2

0

0.05

0.1

0.15

(b) ax2(τ) and amplitude spectrum.

τ = tfn,1

0 50 100 150 200 250 300

ay 2(τ)

-1

0

1

Ur,2 = U∞/fn,2D =5.78

f/fn,2

0 1 2 3 4 5 6

Sy 2

0

0.5

1

(c) ay2(τ) and amplitude spectrum.

τ = tfn,1

0 50 100 150 200 250 300ax 4(t

∗)

-1

0

1

Ur,2 = U∞/fn,2D =5.78

f/fn,2

0 1 2 3 4 5 6

Sx 4

0

0.05

0.1

0.15

(d) ax4(τ) and amplitude spectrum.

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a2kx × aky , Ur ,1 ≈ Ur ,2 ≈ 5.70.

ax2(t∗)

-1.5 -1 -0.5 0 0.5 1 1.5

ay 1(t

∗)

-1.5

-1

-0.5

0

0.5

1

1.5VR,1 = U∞/fN,1D =5.63

(a) ax2× a

y1. Ur,1 = 5.63.

ax2(tτ)-1.5 -1 -0.5 0 0.5 1 1.5

ay 1(tτ)

-1.5

-1

-0.5

0

0.5

1

1.5Ur,2 = U∞/fn,2D =5.78

(b) ax4× a

y2. Ur,2 = 5.78.


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Flexible cylinder VIV - catenary

Extracted from Rateiro et al (2016).

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• Risers and other slender structures are usually hanged in catenary con�gurationand their response to VIV are not fully understood;

• The angle of incidence between �ow and centreline varies along the structure;• Use of the independence principle: The �ow characteristics are de�ned only be

the component of the free-stream that is normal to the cylinder axis;• Near or far current incidence plays a role;• Modal decomposition: Characteristic modal-amplitude versus modal reduced

velocity exhibit good agreement in di�erent modes.

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• The angle of incidence between �ow and centreline varies along the structure;

• Use of the independence principle: The �ow characteristics are de�ned only bethe component of the free-stream that is normal to the cylinder axis;

• Near or far current incidence plays a role;• Modal decomposition: Characteristic modal-amplitude versus modal reduced


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the component of the free-stream that is normal to the cylinder axis;

• Near or far current incidence plays a role;• Modal decomposition: Characteristic modal-amplitude versus modal reduced


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the component of the free-stream that is normal to the cylinder axis;• Near or far current incidence plays a role;

• Modal decomposition: Characteristic modal-amplitude versus modal reducedvelocity exhibit good agreement in di�erent modes.

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the component of the free-stream that is normal to the cylinder axis;• Near or far current incidence plays a role;• Modal decomposition: Characteristic modal-amplitude versus modal reduced


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Combined excitation

In the o�shore engineering scenario, problems involving VIV occur under combinedexcitation. Two cases are herein highlighted:• Concomitant VIV and parametric excitation: Depending on the frequency of the

top motion ft , the response is highly increased (Franzini et al (2016, 2017,2018)). Interesting case ft : fN,1 = 2 : 1;

• Concomitant VIV and internal �ow: The dynamic behavior becomes richer(Meng et al (2017a,2017b)) Changes in the natural frequencies, decrease in theoscillation amplitudes, mode switching;

• Key-point in modeling: wake-oscillators are developed and calibrated from �PureVIV� experiments obtained with rigid and elastically supported cylinders;

• Experimental data of VIV under combined excitation are rare. For concomitantVIV and parametric excitation, LMO led a comprehensive experimentalcampaign that provided these data;

• At least to the best of the author's knowledge, experimental data concerningconcomitant VIV and internal �ow excitation are not found.

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Combined excitation







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Combined excitation







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Combined excitation







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Combined excitation







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Combined excitation

• Combined �exible cylinder VIV and parametric excitation: Experimental resultspublished in Franzini (2018);

• This class focuses on the simultaneous VIV and parametric excitation withft : fn,1 = 2 : 1 and At/L0 = 1%. Figure below, adapted from Franzini (2018),illustrates the cross-wise envelope amplitude and the cross-wise amplitudespectra;

• The simultaneous VIV and parametric excitation with ft : fn,1 = 2 : 1 (principalparametric instability in the �rst mode) signi�cantly a�ects the response of thehydroelastic system;

• A marked increase in the oscillation amplitude is observed.

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Combined excitation

Ay(ξ)0 0.5 1 1.5

ξ=

z/L0

0

0.2

0.4

0.6

0.8

1

Ur,1 =5.63

(a) Ay (ξ). �Pure VIV�. (b) Sy (ξ, f ). �Pure VIV�.

Ay(ξ)0 0.5 1 1.5

ξ=

z/L

0

0

0.2

0.4

0.6

0.8

1

Ur,1 =5.8

(c) Ay (ξ). ft : fn,1 = 2 : 1. (d) Sy (ξ, f ). ft : fn,1 = 2 : 1.

Adapted from Franzini et al (2018).

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Combined excitation

• Combined �exible cylinder VIV and excitation due to the internal �ow is also animportant and complex issue → Ongoing research topic developed at LMO;

• Usual approach: To consider wake-oscillator models with the same empiricallycalibrated parameters obtained for rigid and elastically mounted cylinders;

• Superposition of models associated with �pure VIV� and �pure� internal �owexcitation;

• Experiments on this combined excitation are quite complex → Planed to becarried out by LMO (part of the PhD research developed by Wagner Defensor).

• In Orsino et al (2018), the numerical results show that there is a range ofinternal �ow velocities associated with VIV mitigation.

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Numerical studies

• Focus on the galloping of a square prism, �tted with a rotative NVA;• Studies developed by Bianca Teixeira (former undergraduate student) and

presented in Teixeira et al (2018) and in Franzini (2019).• Use of the quasi-steady hypothesis;

Extracted from Franzini (2019).• Equations of motion

(M +m)d2Y

dt2+mr

[sin θ

d2θ

dt2+ cos θ

(dθ

dt

)2]+ cy

dY

dt+ kyY =

1

2ρU2∞DCy

(3)

mr2d2θ

dt2+mr sin θ

d2Y

dt2+ cθ

dθ

dt= 0 (4)

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Numerical studies

r = 0.40, ζθ = 0.05, ζy = 0.0009.

Ur

0 5 10 15 20

ystd

0

0.5

1

1.5

Sem supressor

m = 0.03

m = 0.05

m = 0.07

m = 0.09

m = 0.11

m = 0.13

m = 0.15

Extracted from Franzini (2019).31/48

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Numerical studies

Ur = 12, ˆm = 0.13, r = 0.40, ζθ = 0.05 and ζy = 0.0009.

τ

1500 2000 2500

θ(τ)

500

1000

1500

τ

1500 2000 2500

cosθ

-1

0

1

(a) θ(τ) and cos θ.

τ

1500 2000 2500

y(τ)

-0.2

0

0.2

f = f/fn,y

0 1 2 3 4 5A(f)

0

0.05

0.1

(b) y(τ) and amplitude spectrum.


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S(m; r)

ζθ = 0.05 e Ur = 6.5. Standard-deviation of the response without suppressor isystd,0 = 0.34. S = 1− ystd,NVA

ystd,0.


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S(m; r)

ζθ = 0.05 e Ur = 6.5. Standard-deviation of the response without suppressor isystd,0 = 0.34. S = 1− ystd,NVA

ystd,0.


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Experimental results

• Wind tunnel experiments carried out at École Polytechnique de Montréal;• Balls constrained to move along circular tracks;• Experiments carried out by Michael Selwanis (PhD candidate) and published in

Selwanis et al (2021).

Extracted from Selwanis et al (2021).35/48

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• The proposed suppressor has proved to be highly e�cient!

Extracted from Selwanis et al (2021).

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• Some features of the response numerically observed appear in the experiments

Extracted from Selwanis et al (2021).

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VSIV phenomenon

• Vortex-self induced vibrations: VIV associated with oscillatory incoming �ow;

• Applications in structures hanged in catenary: Motion prescribed to the top ofthe catenary induces, at each cross-section, oscillatory �ow;

• Structural response depends on the amplitude/frequency of the applied motion -see Pesce et al (2017).

• In the dynamics of catenary risers: Motion prescribed to the top+parametricexcitation+VIV+internal �ow e�ects=?.

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VSIV phenomenon

• Vortex-self induced vibrations: VIV associated with oscillatory incoming �ow;• Applications in structures hanged in catenary: Motion prescribed to the top of

the catenary induces, at each cross-section, oscillatory �ow;

• Structural response depends on the amplitude/frequency of the applied motion -see Pesce et al (2017).


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VSIV phenomenon


the catenary induces, at each cross-section, oscillatory �ow;• Structural response depends on the amplitude/frequency of the applied motion -

see Pesce et al (2017).


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VSIV phenomenon


the catenary induces, at each cross-section, oscillatory �ow;• Structural response depends on the amplitude/frequency of the applied motion -

see Pesce et al (2017).• In the dynamics of catenary risers: Motion prescribed to the top+parametric

excitation+VIV+internal �ow e�ects=?.

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VSIV phenomenon

Extracted from Pesce et al (2017).

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Overview

• Usually, we are interested in mitigating FIV;

• Recent research topic: energy harvesting - Conversion of part of the mechanicalenergy available in the vibrating structure into another form of energy (electricenergy, for example);

• Di�erent ways for converting energy: Gravitational potential energy,electromagnetic conversion, piezoelectric conversion;

• Focus on low-power systems (small sensors, for example).

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Overview

• Usually, we are interested in mitigating FIV;• Recent research topic: energy harvesting - Conversion of part of the mechanical

energy available in the vibrating structure into another form of energy (electricenergy, for example);



40/48PEF 6000

Overview





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Overview





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Some works - �utter and galloping

• Tang et al (2009): Flutter of a �exible plate under axial �ow and immersed in amagnetic �eld �tted with wires: Flutter-mill concept;

• Barrero-Gil et al (2010): Galloping of prismatic bodies → In�uence of thecross-section on the energy dissipated at the dashpot;

• Fernandes & Armandei (2014): Torsional galloping is employed for liftingweights;

• Franzini et al (2016,2017): Concomitant parametric excitation and gallopingincreases the harvested power in piezoelectric circuits.

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Hémon et al (2017)

Magnets are placed at the tip of the leaves-springs and can move relative to coils.

Extracted from Hémon et al (2017).

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Energy harvesting from VIV

• Bernitsas et al (2006): VIVACE (Vortex-Induced Vibrations Aquatic CleanEnergy) project → Experimental device based on VIV of a series of aligned(tandem) cylinders. Electromagnetic e�ect;

• Grouthier et al (2012,2014): Energy harvesting from VIV → wake-oscillatormodels (VIV-1dof) and energy is harvested at the dashpot;

• Mehmood et al (2013): Rigid cylinders, mounted on piezoelectric supports →Electric power is harvested from the electrical resistance. CFD is employed formodeling the hydrodynamic load;

• Bunzel & Franzini (2017), Franzini & Bunzel (2018): Piezoelectric energyharvesting from VIV → Pioneer in including in-line oscillations in the analysis.Sensitivity studies focusing on the in�uence of the piezoelectric parameters;

• Madi et al (2019): Developed by Leticia Madi (PhD candidate), this paper dealswith piezoelectric energy harvesting from �exible cylinder VIV.

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Result from Akaydin et al (2012)

Piezoelectric patches are included at the clamp.

(e) Experimental arrangement. (f) Electrical power.

Extracted from Akaydin et al (2012).

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Result from Grouthier et al (2014)

Existence of a critical structural damping ratio ξ for maximizing energy harvestinge�ciency.

Extracted from Grouthier et al (2014).

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Piezoelectric energy harvesting from VIV

• The rigid cylinder is assembled onto a piezoelectric support. The electricalcircuit is characterized by its capacitance CP,y and resistance Ry . θy is theelectromechanical coupling term.

• For the VIV-1dof condition, the solid-�uid-electric system is governed by:

(M +mpota )

d2Y

dt2+ cy

dY

dt+ kyY − θyVy =

1

2ρU2∞DLCy,v (5)

d2qy

dt2+ εyωf (q

2y − 1)

dqy

dt+ ω2f qy =

Ay

D

d2Y

dt2(6)

CP,ydVy

dt+

Vy

Ry+ θy

dY

dt= 0 (7)

Extracted from Franzini & Bunzel (2018).46/48

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• Due to energy harvesting, a small decrease in the cylinder response.

Ur

0 5 10 15

Ay

0

0.5

1

1.5

2

Piezo - VIV-1gl; VIV-1gl; Piezo - VIV-2gl; VIV=2gl

Adapted from Franzini & Bunzel (2018).

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• Energy harvesting is more e�cient if the cylinder is assembled onto a 2dofelastic support.

0 5 10 15

Ur

0

0.01

0.02

Electrictension

vy,rms - 1dof VIV; vy,rms - 2dof VIV; vx,rms - 2dof VIV

Extracted from Franzini & Bunzel (2018).

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Documents

Research topics on ow-induced vibrations