This is now possible in Windows Phone 8.1, as the Volume Bar now has an interactive slider for ringer volume and a separate toggle for vibrate:
To open the Volume Bar, press either of the volume keys as usual, then expand it by tapping the chevron. Reduce ringer volume to 0 with the volume keys or by dragging the slider, and now you can toggle between ...
You can toggle vibrate on and off in the volume bar:
Press either of the volume keys to open the volume bar, then expand it by tapping the chevron. Tap the "VIBRATE ON"/"VIBRATE OFF" icon to toggle vibrate.
Alternatively, go to Settings → ringtones+sounds, you can also toggle vibrate there.
Follow these two methods:
Turn on Notifications on Lockscreen
Go to Settings->System->Notifications & Actions.
Click on Messaging.
Turn the following options on.
Show notifications in Action center.
Turn on Background usage
Go to Settings->System->Battery->Battery usage by App.
Turn the Setting to ...
If your phone is "awake" (locked or not), press a volume key and then expand the ringer status that appears at the top. From here you can mute with a tap on the icon beside the volume slider and toggle vibration separately with a tap on the vibration status at the bottom.
I had the same symptoms and found that this setting was preventing the SMS notification sounds (and whatsapp etc):
Settings > System > Notification & Actions > Show notifications on the lock screen and play notification sounds.
This was turned off in my case. the wording of this option was slightly confusing to me, because when the screen is off i ...
It appears that this was a problem either with the Developer Preview version of Windows Phone 8.1, or its use in conjunction with the Lumia Black firmware for my Nokia Lumia 920. After doing a system restoration to Lumia Cyan with Windows 8.1 (Preview for Developers not installed), the vibrations I'm used to have been restored - single for SMS, double for e-...