This script enumerates all SSAS databases and backups them using a MSOLAP linked server.
Especially usefull if your BI dudes don't allways tell the DBA they added a new SSAS database, but *do* expect that everyting is allways backed up!
Set the backup path to your desired location (line 15)
Replace the <YourServerName> stub, and run the commented part of the script once (between /* and */) , this will setup a linked server for the XMLA script
And thats it, hit F5 and see the .abf files apearing :)
After that you can tweak it to your specific situation, have datetime stamps, etc.