Shut down is a common phrase that means to close something. There are various synonyms of the word, and they can be used interchangeably. If you want to describe a situation where a device or a system ceases to function, the words turn off or power off would be appropriate. Another synonym could be lock out, which can be associated with computer programs or access to a particular system. Alternatively, when talking about a business or an establishment closing, one may use the word shut off or cease operations. Shut down may also imply termination, so words such as close, end, or finish could be used as synonyms.