**1.1 Marine riser**

Oceans are quite important fields for us because many resources lurk there which are oil and gas under seabed, mineral resources, water heat energy and so on. Development of submarine oil has been major in the North Sea and in the Gulf of Mexico. Today, submarine oil has been developed at ultra-deep water fields of offshore of Brazil and West Africa, which does deep over 1000m. Deepest field developed is more than 3000m in water depth of Brazilian seas. Riser system is necessary to develop and to production submarine oil. The riser is a tubing structure which is for drilling and production. Diameter of a drilling riser is greater than 50cm and that of a production riser is about 20cm. The riser is thin rope-like tube in oceans. Therefore, the tubing behaves elastically by marine currents and ocean waves and so on.

These motion behaviors are called as Vortex-Induced Vibration (VIV). VIV of the riser is a complex phenomenon, which is dominated by the natural frequency of the riser system and behavior of vortex shedding around the rider. VIV is very important for structural design of the riser system and the platform of the drilling and the production of submarine oil and so on.

There are many studies of VIV of the riser and the drilling or the production system including the riser system in the ocean engineering field with numerical approaches, theoretical approaches and model experimental approaches. Behaviors of time variation of VIV obtained from numerical calculations or model experiments using model risers in a water tank include a complicated mechanism so it is not easy to understand them, because the time variation is not steady but transient and chaos. Therefore, we need to understand VIV phenomenon in not only time characteristics but also frequency characteristics.

For understanding frequency characteristics, we often use a power spectrum with the FFT analysis or others. However, a power spectrum does not inform us time variation of VIV characteristics. Then, the wavelet analysis can be applied to the VIV analysis because we can simultaneously understand the characteristics in time domain and frequency domain.

Application of Wavelet Analysis for the Understanding of Vortex-Induced Vibration 595

Number of degrees of freedom is two in sway motion and roll motion. The sway in this experiment is horizontal displacement of center of gravity in *y* direction and rolling is rotation around *x* axis in a coordinate system of Fig. 1. Freedom of surge corresponding to *x* axis motion is allowed and decided due to forced oscillation by experimental operators.

The cylinder is suspended under a load cell through the flat spring. Most of the cylinder is submerged in still water. Side views of the experimental setup system, which corresponds to the *z*-*x* plane, are illustrated in Fig. 2. The direction of forced oscillations is right and left in

A load cell for measuring the total load in inline direction, which including the inertia force of a cylinder and hydrodynamic forces on a cylinder, is attached under the forced oscillation device. A Doppler current meter is installed at the straightly back of the cylinder, the current meter which moves together with the cylinder due to the forced oscillation. The current meter can measure fluid velocity of three directions in *x*, *y* and *z* axis. We measure the

> Transverse vibration VIV with lock-in

In the experiment, 1) inline displacement of forced oscillation with a potentiometer, 2) the total inline load with the load cell, 3) the bending moment with the flat spring and 4) fluid velocity at the back of the cylinder with the Doppler current meter are measured. The fluid velocity is measured at midship depth of the submerged cylinder. The VIV is evaluated by using the vertical bending moment and cross-flow displacement predicted from the bending

*x*

*o*

Forced oscillation in inline direction

*z*

vertical bending moment with a flat spring on which strain gages are set.

*y*

flat spring for transverse motion

Fig. 1. Idealization of VIV in experiment

moment.

**2.2 Experimental setup system** 

Fig. 2.
