How are you setting your phone to silent? Are you holding down the volume button, using do not disturb, opening your volume settings and dragging the slider down? How are you setting your phone to silent?
Since we don't know how you are setting your phone to silent yet, here is something you can look for.
If you press the volume button up or down and then touch the 3 dots for the indicator it will open the control for all of your volume options.
In the second image you can see I slid the main volume control to the bottom and the phone is now silent and the wavy line indicates that it will vibrate. The wavy line indicates the vibration.
In the third image the main volume just has a speaker with a line through it and no wavy line. This means the phone will be silent and will not vibrate.
In the forth image if you open sounds and vibrations from your settings menu, you can select vibrations only or silent.
If you're using Do Not Disturb, I don't see any way to change this on a Samsung. Some devices will allow it but with Samsung it looks like you have to pick people and apps that can send you notifications or get through to you when it is enabled. It does not look like there is an option to allow vibrations when Do Not Disturb is turned on.