How to log off a single AD user from a list of servers

Question

I have a user account I need to logoff from all servers in a list.  For example domain\user2 needs to be logged off all servers in a list.  Here is what I have so far:
foreach ($_ in get-content C:/servers.txt)
{(gwmi win32_operatingsystem -ComputerName$_).Win32Shutdown(4)}
The problem is all this does is log off the first user in the session list when you are looking at task manager.  How could
I log off just a specific user?

Answer 1

This thread on stackoverflow may be useful to you if the user is connected to an RD session on your servers: Powershell Log Off Remote Session 
As a starting point:
$server = 'MyServer'
$username = "domain\usertologoff"
$session = ((quser /server:$server | ? { $_ -match $username }) -split ' +')[2]
logoff $session /server:$server
(the script listed logs the current user off, I changed it to all you to enter the username)
Jason Warren
@jaspnwarren
jasonwarren.ca
habaneroconsulting.com/Insights