Dynamical Characteristics of External Mechanism of

2D Twin Floating Bodies for Perfect Wave Absorption

Yuki Miyazaki Munehiko Minoura

Osaka university

Contents

Characteristics of external dynamics system for perfect wave absorption

・ Derivation of characteristics ・ Considering characteristics Results of experiment ・To confirm accuracy of theory Conclusion

Introduction

Introduction(1) In order to absorb the regular wave propagating on a two-dimensional waterway perfectly by floating body with External dynamics systems. Two modes motion

To use asymmetric floating body

Realizing the perfect absorption

complex

Limit of location To place on the tank end

Limit of frequency

Using twin floating bodies allowed only the heaving motion

Introduction(2) In the future

Wave-maker

Experimental tank

Create arbitrary space in experimental tank

Characteristics of dynamics system Procedure of derivation

r1+

d1+ d1

-

r1-

x

yI

r2+

d2+ d2

-

r2-

yII

C1 N1

C2 N2

s (Incident wave)

(Diffraction wave)

(Radiation wave)

ℓ

Region I Region II Region III

Floating body 1 Floating body 2

1. Wave condition in perfect absorption External area of floating bodies (RegionⅠ,Ⅲ) Interior area of floating bodies (RegionⅡ)

2. Equation of motion of floating bodies

Derivation of characteristic

Wave condition in perfect absorption

Wave amplitude in external area

It is need to satisfy

r1+

d1+ d1

-

r1-

x

yI

r2+

d2+ d2

-

r2-

yII

C1 N1

C2 N2

s (Incident wave)

(Diffraction wave)

(Radiation wave)

ℓ

Region I Region II Region III

Floating body 1 Floating body 2

：Amplitude of diffraction wave

：Amplitude of radiation Wave

: Transfer function

External area （Region Ⅰ、Ⅲ）

for perfect absorption

：Coefficient of transmitted wave ：Coefficient of reflected wave

Wave condition in perfect absorption

Relation of the mutual interaction regarding the diffraction wave is

r1+

d1+ d1

-

r1-

x

yI

r2+

d2+ d2

-

r2-

yII

C1 N1

C2 N2

s (Incident wave)

(Diffraction wave)

(Radiation wave)

ℓ

Region I Region II Region III

Floating body 1 Floating body 2

Interior area （Region Ⅱ）

Equation of motion of floating bodies

External dynamics systems

Hydrodynamics forces

Exciting wave force by the reflect wave

Exciting wave force by incident wave

r1+

d1+ d1

-

r1- r2

+ d2

+ d2-

r2-

C1 N1

C2 N2

Floating body1

Combining this equation with wave condition

Characteristics of dynamics system

Floating body1

Floating body2

r1+

d1+ d1

-

r1-

x

yI

r2+

d2+ d2

-

r2-

yII

C1 N1

C2 N2

s (Incident wave)

(Diffraction wave)

(Radiation wave)

ℓ

Region I Region II Region III

Floating body 1 Floating body 2

No absorption Perfect reflection

Optimum characteristic

① Wedge-shaped bodies

Restoring coefficients

Dam

ping coefficients

The restoring coefficient of external dynamics system does not satisfies

At this moment, the system becomes unstable.

Considering characteristics(1)

40°

B/2

40°

B/2 s

ℓ’=ℓ/B

② Box-shaped bodies

In wider frequency, restoring coefficient of external dynamics system satisfies

Restoring coefficients

Dam

ping coefficients

s

ℓ’=ℓ/B

B/2

B/2

B/2

B/2

Considering characteristics(2)

Coefficients of floating body1 correspond with that of body2. At this moment, absorption is impossible.

③ Wedge and Box-shaped

s

ℓ’=ℓ/B

40°

αB/2 B/2

B/2

Restoring coefficients

Dam

ping coefficients

Considering characteristics(3)

Selecting optimum distance of floating bodies, it is enable to make more wider the frequency that can be absorbed.

Experiment

Floating body 1 Floating body 2

Wave maker Incident wave

Wavemeter Wavemeter

In order to confirm accuracy of theory Setting arbitrary values to the restoring and damping coefficient. Measuring the transmitted waves and reflected wave when incident

wave coming from wave-maker and calculating the absorption efficiency .

Deciding the maximum absorption efficiency point by repeating the above procedure.

Experiment

-10

-8

-6

-4

-2

0

2

4

6

8

10

0 0.2 0.4 0.6 0.8 1 1.2

C1/ρg(B/2)^2)

k B/2

Theoritical valueExperiment

00.050.1

0.150.2

0.250.3

0.350.4

0.450.5

0 0.2 0.4 0.6 0.8 1 1.2

N1/ρω

(B/2)^2

k B/2

Theoritical valueExperiment

-10

-8

-6

-4

-2

0

2

4

6

8

10

0 0.2 0.4 0.6 0.8 1 1.2

C1/ρg(B/2)^2)

k B/2

Theoritical value

Experiment

00.050.1

0.150.2

0.250.3

0.350.4

0.450.5

0 0.2 0.4 0.6 0.8 1 1.2

N1/ρω

(B/2)^2

k B/2

Theoritical valueExperiment

① Box-shaped bodies ② Wedge and Box-shaped bodies

s

ℓ’=ℓ/B

B/2

B/2

B/2

B/2

s

ℓ’=ℓ/B

40°

αB/2 B/2

B/2

Experiment No control

Experiment Under control

Conclusions

The characteristics of the external dynamics system of twin floating bodies for the perfect wave absorption are shown theoretically with the mutual interaction theory of waves. From a theoretical formula, the external dynamics system of

the floating body at the lee side (Floating body 2) of incident waves must reflect waves perfectly. From the results of experiment, the restoring coefficient of

external system provides good agreement with theoretical value. But the damping value does not.

Thank you for your attention !!