To shake, sway, or unsettle something or someone; can be used physically (to shake an object) or figuratively (to shock or disturb someone's confidence).
大きな地震が街の建物を激しく揺るがした。
A large earthquake violently shook the city's buildings.
その事件は彼の信念を揺るがす出来事だった。
That incident was something that shook his convictions.
証拠が出てきて、彼の証言は完全に揺るがされた。
With the evidence coming out, his testimony was completely undermined.