**5. Results and discussion**

#### **5.1 Orbit patterns**

From the experiment using the single cylinder, orbit patterns can be classified to six patterns such as Fig. 5. The net type is specified to *N*1 and *N*2. It can be considered that response of the type *U* and the type 8 corresponds to VIV lock-in.

Application of Wavelet Analysis for the Understanding of Vortex-Induced Vibration 603

Fig. 6. Patterns of wavelet analysis of Case 8

Fig. 5. Classifications of orbit patterns of VIV

#### **5.2 Wavelet characteristics of single cylinder**

In case of a single cylinder, wavelet patterns are made a general classification to five. These patterns are not decided due to experimental cases such as Table 1-a). Results of wavelet analysis in case of the case 8 show in Figs. 6, where "T" in subtitles stands for period of the forced oscillation. A vertical axis is the dilation parameter *a* and horizontal axis is time of VIV response. These results are the vertical bending moment which corresponds to crossflow vibration.

In Figs. 6, a) corresponds to the orbit pattern of Type *O*. In Wavelet contours from a) to c), response frequency is confirmed in wide band of *a* which is vertical axis. In case of Type *U*, there is no striped pattern from 0.0 to 1.0 in *a*.

Such this tendency can be also confirmed in case of Type 8. In the case 8, Type 8 doesn't occur so that a wavelet pattern corresponding to Type 8 is explained by using the case 3.

From Figs. 6-e) and 7-b) which results correspond to Type *U*, in range from 2.0 to 3.0 in *a*, we can confirm a clear striped pattern. However, the striped pattern is broken around *a*=1.0 when the orbit gets Type 8.


 *x/D*

Type *O* Ordinary Type Type *N*1



 *x/D*

 *x/D*


0

*y/D*

0.5

*y/D*



0

*y/D*

0.5

0

*y/D*

0.1

0.2

In case of a single cylinder, wavelet patterns are made a general classification to five. These patterns are not decided due to experimental cases such as Table 1-a). Results of wavelet analysis in case of the case 8 show in Figs. 6, where "T" in subtitles stands for period of the forced oscillation. A vertical axis is the dilation parameter *a* and horizontal axis is time of VIV response. These results are the vertical bending moment which corresponds to cross-


 *x/D*

Type *N*2 Type *U* Type 8

In Figs. 6, a) corresponds to the orbit pattern of Type *O*. In Wavelet contours from a) to c), response frequency is confirmed in wide band of *a* which is vertical axis. In case of Type *U*,

Such this tendency can be also confirmed in case of Type 8. In the case 8, Type 8 doesn't occur so that a wavelet pattern corresponding to Type 8 is explained by using the case 3.

From Figs. 6-e) and 7-b) which results correspond to Type *U*, in range from 2.0 to 3.0 in *a*, we can confirm a clear striped pattern. However, the striped pattern is broken around *a*=1.0

Fig. 5. Classifications of orbit patterns of VIV



 *x/D*

 *x/D*


0

*y/D*

0.5

0

*y/D*

0.3

0.6

flow vibration.

when the orbit gets Type 8.

**5.2 Wavelet characteristics of single cylinder** 

there is no striped pattern from 0.0 to 1.0 in *a*.

Fig. 6. Patterns of wavelet analysis of Case 8

Application of Wavelet Analysis for the Understanding of Vortex-Induced Vibration 605

0.2 0.4 0.6 0.8 1.0 [101 ]

(kgf-cm)2sec

0

a) on front cylinder

*t* **second** 

0 10.0 20.0 30.0 40.0 50.0 60.0

0.2 0.4 0.6 0.8 1.0 [102 ]

(kgf-cm)2sec

0

1.0 2.0 3.0 4.0 5.0

bending moment

1.0 2.0 3.0 4.0 5.0

bending moment

*f/f0*

*f/f0*

b) on back cylinder

*t* **second** 

*t* **second** 

Fig. 8. Comparisons of orbit, power spectrum and wavelet pattern of vertical bending

0 10.0 20.0 30.0 40.0 50.0 60.0

0 10.0 20.0 30.0 40.0 50.0 60.0

moment in case of *s*=2 and T=1.2 s

4.0 3.0 2.0 1.0

4.0 3.0 2.0 1.0

*a* 

4.0 3.0 2.0 1.0

*a* 

*a* 

Fig. 7. Patterns of wavelet analysis of Case 3
