Streamwise Gate Vibration: Added Mass and Damping

Theoretical Analysis Of Push-And-Draw Pressure

In Chapter 4, Rayleigh’s wave theory was used to analyze the effect of small amplitude vertical vibrations of a vertical weir plate on the flow field. In this chapter, the same framework will be used to consider the hydrodynamic effects of small amplitude horizontal vibrations of the vertical weir plate.

The simplifications of the bounding geometry and boundary conditions that we will use for the present theoretical analysis of streamwise weir plate vibration are similar to those in the previous chapter. Figure 1 shows the simplified geometry in which the curved skinplate and the dam wall of the Tainter gate (see Figure 1 in Chapter 4) are replaced with a vertical planar weir plate oriented parallel to the Y-axis, while the inclined weir plate of the long-span gate (see Figure 2 in Chapter 4) is assumed to stand vertically along the Y-axis. The still water surface is used to define the X-axis. The analysis is done for a finite depth reservoir, which can then be extended to infinite depth reservoirs as well.