In NUREG/CR-2859, the infamous aircraft crash evaluation performed by Argonne for NRC in 1982, it was shown that an aircraft (in those days, it as a 707) hitting a nuclear plant can produce vibrations exceeding those experienced during earthquakes.

Attached are excerpts from a later report prepared for NRC of the effects of earthquakes on electrical relays (switches) at a nuclear plant. The "relay chatter" of the vibrations causing switches to change positions can be significant if the result is turning off emergency equipment or opening up pathways for cooling water to drain away and/or radiation to leave the building.

Take a look at the paragraph numbered (6) on the 12th page of the 19-page excerpts (the bottom of this page is numbered 6-3). It says:

"The number of min cut sets is so large that, given an earthquake strong enough to cause LOSP, the probability that at least one of these cut sets will occur is close to 100% assuming that the relays chatter with the fragility function and response behavior we have assumed."

Translating this nukespeak: "min cut sets" basically refers to the number of outcomes that can result from an earthquake. An analogy might be rolling two dice. The number of "cut sets" resulting in a 7 is six: 6 & 1, 5 & 2, 4 & 3, 3 & 4, 2 & 5, and 1 & 6. The number of "cut sets" resulting in a 12 is only one: 6 & 6.

LOSP is "loss of offsite power." An event causing loss of offsite power means that equipment not powered from the onsite diesel generators is automatically disabled since no power is available for it.

There are so many combinations of relay chatter outcomes leading to disabling the equipment powered from the diesel generators (or the diesel generators themselves) that there's nearly 100% chance that the earthquake results in one of them happening.

That same paragraph goes on to say: "Therefore, in the absence of operator recovery, the value of the computed core-damage frequency, given LOSP and chattering, is approximately equal to the recurrence frequency of the earthquake strong enough to cause LOSP."

Translating this nukespeak: If an earthquake is strong enough to cause loss of offsite power and relay chattering, core damage will result.

Combining the results from NUREG/CR-2859 and NUREG/CR-4910, if an aircraft crash at a nuclear power plant causes loss of offsite power and relay chattering (or just relay chattering if offsite power is lost some other way concurrent with the crash), core damage will very likely result.

Note that the relay chattering can occur even if the aircraft doesn't penetrate through the structure it hits.