Pressure induced by vertical planar and inclined curved weir-plates undergoing streamwise rotational vibration

Added mass and wave radiation damping for flow-induced rotational vibrations of skinplates of hydraulic gates

“…(where F is the Froude number, given as F ¼ ffiffiffiffiffiffiffiffiffiffi d 0 =g p O w ), the reduced hydrodynamic pressure p b can be re-written in the following form (see Anami et al, 2000Anami et al, , 2012 for further details):…”

“…The solutions to these expressions, calculated by Newton's method, as well as the reduced pressure amplitudes are given in Anami et al (2000Anami et al ( , 2012. As a result, the functions W 0 ðiZ j Þ=i and W 0 x 0 ð Þ are given by the following expressions:…”

“…(23), is further divided yet again by another factor of the Froude number F, thus resulting in the previously noted significant decrease in wave radiation damping coefficient with increasing Froude number. In contrast, when F is moderately large, the standing pressure wave component of the hydrodynamic pressure is proportional to the square of F, as discussed in Anami et al (2000Anami et al ( , 2012. This is because the smaller the progressive pressure wave velocity becomes, the more effectively the standing pressure wave component can store the energy transferred to the fluid by the weir plate motion.…”

“…The pressure correction factor d p represents the effect of the skinplate inclination angle Y s and the effect of the circulararc of the skinplate, which are obtained by the comparison of the theoretical hydrodynamic pressure acting on a vertical, flat, rigid weir plate and the experimental hydrodynamic pressure acting on the inclined circular-arc skinplate, as detailed in Anami et al (2012). With this assumption for the pressure, the equation of motion can be derived:…”

“…The empirical value of pressure correction factor d p , which is described in Anami et al (2012) is shown in Fig. 9.…”