Learn Croatian: Trenje raste uslijed stalnih vibracija. - Friction grows due to constant vibrations.

They follow the preposition uslijed (due to / as a result of). This is a secondary preposition that always requires the genitive case to show the cause or consequence of an action.

Could I just use zbog instead of uslijed in this sentence?

Grammatically, yes. You could say zbog stalnih vibracija. However, uslijed is more formal and specifically emphasizes a direct physical or logical result. You will frequently see uslijed in technical, scientific, or formal writing, making it perfect for a sentence about friction.

The noun vibracija ends in -a here. Isn't that the exact same as its dictionary (nominative singular) form?

Yes, they look identical in writing! For regular feminine nouns ending in -a, the genitive plural also ends in -a, though it is pronounced with a longer vowel in spoken Croatian. You can easily tell it is plural here because the adjective modifying it, stalnih, has the standard plural genitive ending -ih.

Is raste (grows) the most natural verb to use for friction increasing?

Yes, in Croatian, rasti is widely used not just for biological growth, but for any abstract quantity, value, or intensity that goes up. You will frequently hear it used for things like prices (cijene rastu), tension, pressure, and friction.