Some studies have been done modeling the oscillatory behavior of ice-covered pow

Question

Some studies have been done modeling the oscillatory behavior of ice-covered power lines in a steady wind. One model of this was proposed by Myerscough in the Journal of Sound and Vibration (28:4, 699-713). To simplify the model, the author chooses to track not the actual location of the power line, but the amplitude of the oscillation, a; in feet. This amplitude will change if the velocity of the steady wind blowing changes, and the following rst order DE demonstrates the type of behavior we can expect: a' = -0.01a^4 + 0.16a^3 - 0:73a^2 + 0.01a
v - 0.1a; where v represents the velocity of the steady wind in feet per second. (a) Explain why a steady wind would cause the power line to oscillate instead of simply blowing it sideways and holding it there in a steady way. A simple vector analysis of the component forces acting on the power line should suffice. (b) Sketch a series of phase diagrams for this DE that show all bifurcations that it undergoes as the velocity v rises from 0 through 150. WinPlot for the PC or some other software package that allows you to animate plots would be very helpful here. Be sure to record the approximate bifurcation values of v: (c) Find the values of v for which a temporary gust of wind could send the system into a permanent state of oscillation with a much larger amplitude than the velocity of the steady wind would induce. (d) At some point, the system undergoes what physicists call a hysteresis eect." That is, there is value of v at which the amplitude of oscillation will suddenly and dramatically increase. Find this value of v and also describe the value to which the velocity of the wind must return in order to reverse this effect. Hint: For this part, you will want to consider the equilibrium states of the system.

Explanation / Answer

Forms of wind-induced instability of structures are described, and two of these, typical of long bodies with bluff cross-sections, are selected for more detailed consideration. The first is vortex-induced bending oscillation, a type of resonant response to the periodic surface pressure loading caused by the discrete wake vortex street formed from the shear layers separating from the bluff cross-section. Oscillation phenomena are described, including capture of the vortex frequency by the structural response frequency over a discrete wind speed range and amplification and phase shift of the loading over this range. The second form is transverse galloping, arising from aerodynamic instability of the bluff cross-sectional shape, so that small-amplitude oscillations generate forces which increase the amplitudes to large values. Oscillation phenomena are described, including the occurrence at very nearly natural frequencies, and the relatively large amplitudes (compared to vortex-induced oscillations) increasing with wind speed beyond a critical wind speed dependent on the level of structural damping. Effects of body and wind parameters on both forms of oscillation are considered, and methods of analysis and suppression for susceptible structures are described. Some probable future requirements and prospects are considered

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