List users in local admin group on all workstations

Hi, I created a script that is supposed to query workstations and list all users in the local admin group. I originally used "test-connection" for logging purposes but it caused an issues when the computer responded but dns was incorrect for that pc so i would get a false list of local admin members on that workstation. I changed to a wmi query instead and queried the system name using that so If the system name matched the workstation name being queried then write it is supposed to write to a csv. For some reason, when i use $wmi.name as the variable, it does not work. What am i missing?


    $CurrentDate = Get-Date
    $CurrentDate = $CurrentDate.ToString('MM-dd-yyyy_hh-mm-ss')

    import-module activedirectory



     $servers= get-content "C:\Scripts\AD Audits\Local Admin\workstations.txt"
     $output = "c:\temp\local admin audit $CurrentDate.csv"
     $results = @()
     $servers | ForEach-Object{
    $wmi = gwmi win32_ComputerSystem -ComputerName $_ -ErrorAction SilentlyContinue
    $connected = Test-Connection $_ -Count 1 -Quiet -ErrorAction SilentlyContinue
    $state = if($wmi.name -eq '$_') {"$_ Verified"} else {"$_ did not respond"}
    $state | Out-File -Append "c:\temp\LocalAdmin log $CurrentDate.txt"

    $group =[ADSI]"WinNT://$_/Administrators,group"
    $members = $group.Members() | ForEach-Object {$_.GetType().InvokeMember("Name", 'GetProperty', $null, $_,   $null) }

    if($wmi)
    {
       New-Object PSObject -Property @{
           DistinguishedName = (Get-ADComputer $_).DistinguishedName
           Server = $_
           Members = $members -join ";"
       }
    }

    } | Export-Csv $Output -NoTypeInformation