Why can generators be damaged by series capacitors (SSR)?
This is an interesting question, so while you understand the torque ripple, I thought I would include some context for others:
The important thing to understand about resonance is that it can occur any time energy, regardless of that energy's specific form, is circulating.
Phenomena is diverse as water (which has mass, and mass is a form of energy) sloshing around in a tank, a kid pumping their legs at just the right time to go higher and higher on a swing, an in electrical circuits like an LC tank, electron orbitals that give us chemistry, or even your own vocal chords when you speak are all forms of resonance.
And there is no requirement that resonance of one medium (such as mechanical resonance of a vibrating string) only cause things to resonant that same way (mechanically).  If there is any mechanism that can convert energy from one form to another, then resonance of one type of energy can and will excite resonance of a completely different form, as long as the resonant frequencies are close enough.
A familiar everyday example of this would be running your finger around the rim of a crystal glass, creating a tone.  You're converting tribological energy (friction) to mechanical vibration, and at the right speed, you hit the resonant frequency of the class.
This effect is even used to create musical instruments such as the Cristal Baschet that produces ethereal sounds by rubbing your fingers on glass cylinders - and inducing resonance.
In the case of subsynchronous resonance, we have a very prominent energy conversion device:  the generator.  It converts rotary motion and torque, or more generally mechanical energy to electrical energy.  This is all we need for the potential for resonances that are purely electrical in nature to induce mechanical resonance if the frequencies are conducive to it.
Generators of course experience a mechanical load on the shaft which requires a certain amount of torque to overcome.  This torque will vary with that load.  This of course results in direct variation of mechanical strain on the shaft which must turn the generator.
Specifically, it will result in torsional strain, and the generator shaft will act like an extremely rigid torsion spring.  And like any spring, it is a harmonic oscillator and has a resonant frequency.  Think of it like an unintentional balance wheel in a clock.
So where do capacitors come in?
Well, let's take a look at how the generator, power grid, and capacitors really look electrically:

The power transmission lines can have a large amount of inductance due to their shear length.  Then the capacitors, which are generally installed near the load and in series will form a resonant LC tank with the inductance of the power line.  Any time you have inductance in series (or parallel) with capacitance, you form an LC tank.
Energy oscillates between being stored in the electric field of the capacitance and then back to being stored in the magnetic field of inductance.  It sloshes back and forth at the systems resonant frequency.  This is a simplified picture of what is going on, but the true system is not any different, it just might have additional capacitances and inductances and some resistances added, but these don't change anything (except the resonant frequency).  It is still an LC tank.
This results in a slight current ripple being superimposed on the AC current ripple of the power grid itself.
These two oscillations will mix and result in a beat frequency, which is simply the frequency of the generator's rotation ± the natural resonant frequency of the LC tank formed by the load network.
In several case studies, it seems that a torsional resonant frequency for the generator shaft can often be somewhere in the 20Hz range.  The current ripple that results in slightly higher and lower armature current during each 50hz cycle will result in torque ripple at the beat frequency acting on the shaft.
And even if this ripple is relatively small (it will typically be much smaller than the ripple from the 50/60hz rotational speed it is superimposed on), if it is too close to the shaft's resonant frequency, then just like a kid on a swing pumping their legs at just the right time each time to go higher and higher, the shaft will twist to a greater and greater degree.  This will continue to build until dissipative effects equal the amount of energy the ripple is able to add to the shaft... or the twisting becomes so severe that it causes catastrophic failure of the shaft.
Resonance is everywhere and always needs to be considered, because it can cause things to fail when you least expect it.  SSR is definitely something that one should be aware of (if their job is one where they need to worry about it!).