rütteln
to shake
To move or push something or someone back and forth forcefully and repeatedly.
Er musste kräftig an der alten Tür rütteln, um sie zu öffnen.
He had to shake the old door hard to open it.

to shake
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to shake
To move or push something or someone back and forth forcefully and repeatedly.
Er musste kräftig an der alten Tür rütteln, um sie zu öffnen.
He had to shake the old door hard to open it.

The verb 'rütteln' (to shake) is almost always used with the preposition 'an' followed by the dative. This applies to both the literal and the figurative meaning.
Der Wind rüttelte heftig an den Fensterläden.
The wind shook the shutters violently.
You can recognize the figurative meaning when something abstract is being 'gerüttelt' (shaken). If the object is a person or a physical object, the literal meaning is intended.
Der Forscher will an einem alten Dogma rütteln.
The researcher wants to shake an old dogma.
In the figurative meaning, there are fixed expressions. Common examples are 'an den Grundfesten rütteln' (to shake the foundations), 'am Thron von jemandem rütteln' (to challenge someone's throne), or 'an einem Tabu rütteln' (to challenge a taboo).
Die Opposition versucht, am Thron der Kanzlerin zu rütteln.
The opposition is trying to challenge the chancellor's throne.
to push / bump / come across
'stoßen' and 'rütteln' both describe a forceful movement against someone or something. The difference is mainly in the type of movement. 'stoßen' is usually a short, single movement in which something is pushed or hit. 'rütteln' means moving something back and forth forcefully several times. If someone pushes against a door, they can 'stoßen' it. If they move it again and again, they 'rütteln' at it.

Das Kind rüttelt an der verschlossenen Tür, weil es hineinmöchte.
The child shakes the locked door because they want to get in.
Im Bus stößt ein Mann aus Versehen gegen meine Tasche.
On the bus, a man accidentally bumps into my bag.