Resonance and corrugation
Sir - Your article ’Optimised ballastless track for HSL-Zuid’ (RG 11.99 p715) deals in particular with the influence of the so-called "pinned-pinned" resonance on formation of corrugation. It is stated (correctly) that a lighter rail section increases the receptance at high frequencies and reduces the frequency of the pinned-pinned resonance. However, I am puzzled why this should automatically result in a reduction in corrugation formation: there is a step in the logic here which the authors omit and which I at least am unable to fill in.
Stiff railpads also increase the receptance over the same frequency range (although they have no significant influence on the frequency of the pinned-pinned resonance). However, it has been demonstrated both by calculation and by field tests that resilient railpads are one of the most effective means of treating almost all types of corrugation. Unfortunately, it would appear that we shall not have the benefit of a side-by-side test of different rail sections on the same stretch of track to determine the real influence of rail section on corrugation formation.
On a slightly more academic point, there is also what I assume is a drafting error in Fig 3 which might mislead some readers. The sub-figure illustrating the deflected shape of the rail at the pinned-pinned anti-resonance suggests that there is a cusp in the rail at the point of excitation when this is over a sleeper. First year students of stress analysis will know that such a discontinuity in gradient would result in infinite bending stress in the beam. In reality, the deflected shape of the rail at the anti-resonance is essentially the same as that at the resonance shown in the other sub-figure.
However, when the rail is excited over a sleeper, these are essentially nodes of the vibration. In other words, there is very little movement, whereas at mid-span there are large deflections. A moving wheel thus experiences a support whose dynamic stiffness at the pinned-pinned resonant frequency varies enormously as the wheel runs along the track. At the second pinned-pinned frequency, there is a resonance as well as the anti-resonance shown in the figure.
Dr Stuart L GrassieBearsden, Glasgow, Great Britain