Wind induced vibration can be explained by the vortex formation that occur due to fluid-solid structure interaction. This theory attributes that the aerodynamic excitation of the structure is due to the action of periodic forces induced on it. In the case of the conductor, the wind loading imposed as a form of periodic force generated by the pressure difference, will induce a certain degree of resonance with a natural mode of vibration of the conductor. Vortices, which are formed around the trailing edge of the conductor, are shed on alternating sides, giving rise to periodic forces and the oscillations transverse perpendicularly to the direction of the wind.
The aerodynamic forces that wind imparts on a conductor depend on the wind velocity and direction, and on the size, and the shape of the conductor. Whether resonance will occur under wind forces depends on these parameters. The amplitude of oscillation that may build up depends on the strength of the wind forces, the energy damping capacity of the structure i.e. the structural damping, and the duration of the wind capable of exciting the conductor.
Wind excitation causes a transverse displacement and this transverse vibration that can be self- sustaining due to the phenomenon of lock-in effect as explained later in subsection (2.11.3). This condition occurs when the frequency of input loading by the wind coincides with one of the natural frequencies of the conductors. It becomes catastrophic if the vertical motions take place at the same coupled frequencies of the conductor over long period, generating stresses, especially in areas in which the motion is constrained.
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Several models have been developed for mathematical analysis of the wind excitation mechanism with the aim to develop a good understanding of the process of wind excitation.
The tensioning of the conductor and the tightening of the keeper of the suspension clamp induces stresses on the conductor strands at the points of support. The damage caused by wind-induced vibration to conductors seems to be noticed at the attachment position (suspension clamps, spacers, spacer-dampers, etc.) and this can be attributed to the dynamic stress resulting from wind loading being imposed on the static stress. This occurs because at this position, the motion of the conductor is constrained and the travelling waves will be reflected producing bending amplitude which will result in the bending strain and stress. The aeolian vibrations induces an alternating bending load at this area where motion is constrained, causing slip at specific contact points. This process usually results in the failure of conductors. The failures of conductors can be considered as a fretting fatigue problem [58].
2.11.2 Conductor Excitation
This concept of fluid-solid interaction (vortex induced vibration) has been used as a means of explaining wind-induced vibration on overhead lines conductor since the early 1920s when this phenomenon was first noticed. As the conductor experiences a transverse vibration caused by the wind input force, this form of oscillation is periodic in nature as shown in figure (2.18). This form of vibration usually occurs when one of the natural frequencies of the conductor is equal to the frequency of the vortex shedding of the Von Karman vortices caused by the imposed dynamic forces of the wind.
Figure 2.18: Vortex wake shedding from a conductor
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This happens due to the occurrence of resonance when the natural frequency of the cylinder coincides with the Strouhal frequency [1, 2]. The Strouhal number is a dimensionless number, defined as a function of the velocity of the airstream, the diameter of the conductor, and the frequency of vortex shedding. This vortex shedding frequency can be calculated by
D V f CS
…..………….……. (2.87) Where CS is the Strouhal number (CS ≈ 0.18 – 0.22), D is the conductor diameter, and v is the air flow velocity in the direction perpendicular to the conductor’s longitudinal axis.
2.11.3 Resonance and Lock-in Effect
As the wind flow passes the conductor, the Von Kármán vortex shedding induces an onset instability, corresponding to the wind speed. If the frequency generated by the vortex shedding approaches one of the natural frequencies of the conductor, when the Strouhal frequency generated by the wind as it flows past the conductor approaches the natural frequency of the conductor, there will be a superposition of this frequencies, initially producing beats as shown in figure (2.19)
Figure 2.19: Beating phenomenon in an oscillating conductor [1]
With a further approach, the beats frequency decreases at a value of the difference between the imposed of the excitation frequency and the natural frequency, (ω – ω0). A further decrease, the beats phenomenon will suddenly disappear and also the natural frequency, remaining the Strouhal frequency or the exciting frequency as shown in figure (2.20).
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Figure 2.20: The graph illustrating Lock-in Effects [70]
At this point the conductor is said to experience resonance or set into resonance. This produces a sensation that the natural frequency, w0 is being influenced by the external frequency w. It is assumed that there is a range of wind speeds over which the vortex shedding frequency and the conductor’s natural frequency will lock-in and this will result in large conductor vibration [70].
This occurrence indicates that the frequency of the exciting force due to the wind loading and any of the natural frequencies of the conductor are approximately equal. When this occurs, the frequency of vortex shedding envelops any of the natural frequencies of the conductor that coincide with, thus the amplitude of vibrations increases. This leads to a condition known as “Lock-in effect”.
The lock-in effect is a concept from nonlinear mechanics, it is also known as the synchronization effect. It occurs as a result of fluid-solid interaction. When the lock-in phenomenon occurs, in the case of power line conductor vibration, severe vibration can persist long enough to cause structural failure. The difficulty with lock-in phenomenon arises from finding the range of natural frequency of the structure, for each mode shape, over which lock-in can occur. To determine the frequency of wind that has the tendency of vortex shedding that can cause the vibration of conductor, with regards to lock-in effect can be computed as a range of frequencies around the shedding frequency as a comparison to modal vibration frequencies of the conductor.
The phenomenon of lock-in effect explains why during the conductor excitation by wind loading, the occurrence of lock-in means that changes in the wind speed at or near the resonant response frequency do not cause the vortex shedding frequency to change, but instead the response frequency will remain constant. After the initiation of resonance, the lock-in effect at resonance can stay for wind speed as large as 90 to 130% of the onset velocity [2]. Flow visualization as shown in figure (2.18) demonstrates the vortex-shedding as the formation of pressure fluctuation producing lifting force which equal to the Strouhal frequency, which can be sustained for a long period by the lock-in effect.