retrieve .txt files from a remote machine and place them in a folder

Good Afternoon 

In my environment we have a application that write log files when ever there is an error. 

we first started with one machine which was easy to gather the logs from took only 5 seconds but now we have about 30 machines that we need to gather logs from,

I wanted to use a small script which will retrieve the logs from all the machines at once and place them in my folder called shared. THe below script will work for one machine but i will like it so that it can do all the machines at once 

copy-item -Path \\jdacto\home\logs -Destination \\server1\Shared

any help is greatly appreciated

Thank you