There used to be profiles even in Nokia 1200, not to mention Android, where the user could select different sound profiles e.g. for meeting, outdoors, silent, etc. To my surprise, I see no option in Windows Phone 8.1. Is the only solution to sound profiles in Windows Phone to manually lower down the sound volume of the smartphone (So that it becomes just vibrating and has no sound)?
You cannot create sound profiles. However, Quiet Hours may do what you want. You can find out more about it here.
If your phone is "awake" (locked or not), press a volume key and then expand the ringer status that appears at the top. From here you can mute with a tap on the icon beside the volume slider and toggle vibration separately with a tap on the vibration status at the bottom.