Y o2y o

2m da

The condition toward oscillatory instability is that the second term is negative. If Z = 0

FIGURE 13.24 Spring-mass system subjected to wind action.

becomes the condition for oscillatory instability. This is the well known Den Hartog criterion. The criterion teaches us that it is possible to estimate the occurrence of galloping from the lift forces to the angle of attack.

Figure 13.26 shows the lift force coefficient to the angle of attack of a square structure [4]. The meaning of the negative slope at zero angle of attack is as follows. When the square structure is going down, the square structure receives upward wind with the positive angle of attack and the downward force Fy is generated through the negative lift force. Therefore, Fy acts to help increase the downward displacement, that is, the force acting on the structure has the same direction as the movement of the structure, and the amplitude of vibration increases infinitely in linear vibration system. This is the mechanism of galloping. The method to estimate the dynamic behavior by using static parameters is called as the quasisteady theory. The galloping of a square structure is a representative example to which the quasisteady theory is applicable.

13.3.1.2.2 Stall Flutter

Shallow rectangular sections and shallow H-sections induce stall flutter, which is the torsional type self-excited vibration with single degree of freedom. Since this type of flutter is induced by the separation flow from the leading edge of the shallow body, it is also called "separation flow flutter.''

13.3.1.2.3 Classical Flutter

A flat plate induces classical flutter, which is the self-excited vibration with two degrees of freedom. Heaving and torsional vibrations are coupled and this is the most intense self-excited vibration.

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