How polarization effects from cations affect H-bond strength The average hydrogen-bond strength in pure water is higher than the average H-bond strength between the first and second hydration shells around a $\ce{Al^3+}$ ion (or any cation, for that matter). This leads to a shift in the OH stretch toward the lower frequencies.

This has something to do with the induced polarization resulting from the positive charge, no doubt, but I fail get why the H-bond becomes weaker. The H-bond would get stronger if the electron density around the H-atom participating in the H-bond gets smaller (larger coulombic attraction between H and O). When $\ce{Al^3+}$ approaches the O-atom of a water molecule, electron density will be forced toward the positive charge, ultimately affecting the H-bonded H-atom, which would give stronger H-bond, at least in my head.

So what's wrong with this picture?
Okay, I realized what was wrong with my picture above.

It is not the hydrogen bond that is weakened, but the OH bond within a water molecule that is weakened, and then stretches at a lower frequency.
When the cation is introduced, and is near the oxygen atom, the electron cloud in the water molecule is moved toward the cation (polarised), leading to electron density in the OH bond being reduced => weaker bond => lower frequency vibration.

The hydrogen bond is not really of interest here, although the same effect takes place when two water molecules are H-bonded. Hence, the OH stretch of an isolated water molecule will vibrate a bit faster than the OH stretch in a H-bonded water molecule.