rivet on (someone or something)
1. To attach or fasten something very securely to something else, with or as with rivets. A noun or pronoun can be used between "rivet" and "on." We'll need to rivet on a new handle before we'll be able to use this door. They riveted a makeshift ladder on the side of the house.
2. To focus one's attention or gaze on someone or something else. A noun or pronoun is used between "rivet" and "on." I riveted my gaze on the television as the final seconds of the game ticked away. I don't think I could handle celebrity. Having thousands of people rivet their attention on me every day sounds like a nightmare. As I stood atop the Empire State Building, my eyes were riveted on the tiny specks of people on the ground below.
rivet something on(to) somethingand rivet something on
to attach something to something with rivets. The pockets of these jeans are riveted onto the body of the pants. You should rivet on this part of the frame to the wall.