**2.2 Experimental setup system**

594 Advances in Wavelet Theory and Their Applications in Engineering, Physics and Technology

The authors have investigated VIV characteristics of a circular cylinder with forced oscillation tests in still water (Ikoma & Masuda et al., 2006, 2007). As these results, VIV behaviors have been classified to the four power spectrum pattern. However an actual orbit of the model cylinder was different even if the spectrum pattern was same. Therefore detail of VIV characteristics and behaviors cannot be understood from only a power spectrum with the FFT analysis of a time history of vibrations. In addition, a vibration phenomenon of a marine riser etc. is a non-steady problem in practice so that fluid velocity in the ocean and oscillation of an upper structure such like a production platform are an unsteady phenomenon. Therefore vibration characteristics such like VIV

The Hilbert transform was applied to analysis of cylinder vibration with VIV (Khalak & Wiliamson, 1999). In there, it is described that phase deviation occurs in region entering into VIV lock-in. The Hilbert transform was useful in order to analysis of marine riser vibrations

The wavelet transform is applied to analysis of vibration problems with VIV of a rigid circular cylinder which cross-flow vibration is allowed due to vortex shedding in this study. The wavelet analysis is possible to do the time-frequency analysis as same as the Hilbert transform analysis. Objectives of this study are: 1) to examine possibility of application of the wavelet transform to VIV analysis and 2) to discuss VIV characteristics from results of the wavelet analysis. In 2010, the wavelet analysis and the Hilbert transform were also

This chapter introduces application of the wavelet analysis in the ocean engineering field using results of VIV characteristics. From the model experiment, relationship between the orbit pattern of vibration of the model cylinder and a contour pattern of the wavelet is considered. As a result, effectiveness of the wavelet analysis in order to understand VIV

Model experiments using a single circular cylinder or two arranged circular cylinders in tandem are carried out at a wave tank that has 27 m in length, 7 m in width and 1 m in water depth in the campus of Funabashi at CST of Nihon University. We cannot generate

An experimental method and concepts follow our own past model testing (Ikoma & Masuda et al., 2006, 2007). In this study, a single cylinder or double cylinders in tandem arrangement

Test models of a cylinder are made of acryl resin which is rigid. However the cylinder system is not fixed because elastic vibration is allowed in only cross-flow direction by attaching a flat spring on top of the cylinder. The flat spring does not allow inline movement of the cylinder. Inline movement is due to only forced oscillation by the oscillator. VIV

occurs such like rolling motion around *x* axis which center is the flat spring.

**1.2 Application of wavelet analysis for study of marine riser** 

and examined frequency characteristics which vary to time table.

applied to the estimation of riser behaviors (Shi et al., 2010).

current so that forced oscillation tests in still water are carried.

varies to time table.

detail is given.

**2. Model experiment 2.1 Method of experiment** 

to inline direction are used.

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 Fig. 2.

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

Fig. 1. Idealization of VIV in experiment

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 moment.

Application of Wavelet Analysis for the Understanding of Vortex-Induced Vibration 597

Detail of the cylinder models is described in the paper (Ikoma et al., 2007). Length of the flat spring is expressed as "*l*" in Table 1. Natural periods *Tn* of cross-flow vibration of a

Water depth is set to 1.0 m. The amplitude of forced oscillation is 7.2 cm, the Keulegan-

In case of double cylinders, the cylinders are straightly suspended, and then the distance *ld* between the center to center of both the cylinders is varied such as Table 2. The distance

> *D l*

*s <sup>d</sup>* . (1)

suspended cylinder were obtained with the plucked decay test in still water.

The front cylinder and the back cylinder are defined as Fig. 3.

Photo 2. Experimental models filled with sand

Carpenter (*KC*) number accordingly corresponds to 5.7 and 9.0 in the experiments.

Photo 1. Side view of experimental setup system

**2.3 Experimental conditions** 

ratio *s* is defined as follows,

b) in case of two cylinders

Fig. 2. Side views of experimental setup system

Photo 1. Side view of experimental setup system
