You are able to configure when Dynatrace sends out an alert by using alerting profiles.
Basically, for the server shutdown you would set the availability alerts to alert after the desired amount of time. Then once the problem is opened by Dynatrace and the time in the alerting profile is met an alert will be sent out.
If you are gracefully shutting down a server you might have to also enable "Alert on graceful host shutdowns" to open a problem.
Here is a link to documentation to show how to set up alerting profiles:
Also here is a link to see the different type of events (Host shutdown would be availability) :