Question

In: Mechanical Engineering

Vortex Excitation, Lock-In, Initial Branch, Lower Branch, Upper Branch, Added Mass and Added Damping.

Vortex Excitation, Lock-In, Initial Branch, Lower Branch, Upper Branch, Added Mass and Added Damping.

Solutions

Expert Solution

1) Vortex Excitation

It happens when wind hits a structure, causing alternating vorticies to form at a certain frequency. This in turn causes the system to excite and produce a vibrational load over the structure it is also called vortex shedding.

The frequency of the vortices is dependent on the shape of the blunt body, and the velocity of the fluid flow or wind hitting this body. The vortices create low pressure zones on the downwind side of the object on alternate sides. As the fluid flows to fill the low pressure zone, it produces a vibration at a specific calculable frequency. This vibration is only a major concern if it happens to coincide with the natural frequency of the structure. For structures that are tall and uniform in size and shape, the vibrations can be damaging and ultimately lead to fatigue failure. Masts or towers are highly susceptible to vibrations induced by vortex shedding. By completing a vortex shedding analysis of structures under realistic wind loading, engineers can evaluate whether more efficient structures can and should be developed.

2) Lock-In

The phenomenon of lock-in happens when the vortex shedding frequency becomes close to a natural frequency of vibration of the structure. When this happens large and damaging vibrations can result over the structure.

In the case of flexibly mounted rigid cylinders in uniform flow, the phenomenon of lock-in consists of self-excited, vortex-induced vibrations accompanied by the synchronization of the frequency of vortex formation with the frequency of cylinder vibration.

3) Initial Branch

The vortex formation mode in the initial branch is the same as that of a stationary cylinder, namely, the 2S mode.

the multi-frequential behavior in the initial branch dictates mass changes in the system.

4) Lower Branch

the lower branch corresponds with the 2P mode and Vorticity measurements for free vibration confirmed that the initial and lower branches correspond to the 2S and 2P vortex wake modes .

5) Upper Branch

the upper branch of the free vibrating cylinder corresponds to the 2PO mode, consistent with the conclusion drawn by Morse and Williamson based on forced vibrating cylinder.

6) Added Mass

Whenever acceleration is imposed on a fluid by acceleration of a body moving through the fluid, or acceleration of the fluid relative to the body, additional inertial forces act on the body due to the ‘added mass’ effect.

vortex added-mass coefficient is modified from the solid body case to account for entrainment of ambient fluid by the vortex. This modified coefficient for propagating vortices is shown to be equal in magnitude to the classical coefficient for a solid body of equivalent boundary geometry.

7) Added Damping

Added damping is required to reduce the amplitude of motion to prevent possible fatigue failure of the structure,when structures are vibrating with large amplitudes in the cross wind direction when the Scruton number has an insufficient value to prevent high amplitude vibrations and when the Strouhal number achieves a critical value then this phenomenon is used.


Related Solutions

Ice (mass=26.9 g) with an initial temperature of -15.8 oC is added to 181.4 g of...
Ice (mass=26.9 g) with an initial temperature of -15.8 oC is added to 181.4 g of water at 27.2oC in an isolated calorimeter. The mass of the aluminum calorimeter cup and stirrer together is 51.6 g. Using the values for specific heat and the nominal value of Lfice given in your laboratory manual, determine temperature of the system when it reaches equillibrium (Tf).
A tiny charged pellet of mass m is suspended at rest between two horizontal, charged metallic plates. The lower plate has a positive charge and the upper plate has a negative charge. Which statement in the answers here is not true?
A tiny charged pellet of mass m is suspended at rest between two horizontal, charged metallic plates. The lower plate has a positive charge and the upper plate has a negative charge. Which statement in the answers here is not true?(a) The electric field between the plates points vertically upward.(b) The pellet is negatively charged.(c) The magnitude of the electric force on the pellet is equal to mg.(d) The plates are at different potentials.  
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT