dirksche You can enable vibration for new messages, yes. The easiest way is to press either volume button, and then tap the 'bell' symbol that appears. The top icon that appears of the three will switch to vibration mode.
Vibration settings for notifications can be customized in Settings > Sound & vibration> Vibration & haptics. You can also enable and disable vibration for each notification channel of each and every app, in the notification settings of each app, or by long pressing the notification in your notification shade, and tapping the gear icon there.