Is it possible to set notifications from apps to ONLY VIBRATE on an iPhone, while simultaneously allowing all phone calls to ring and vibrate?

It's a rather simple question, but I can't figure out how to do this.

In order for all phone calls to ring and vibrate, the following settings have to be in place:

1. The "Ring/Silent" switch on the left side of the phone has to be on.
2. The "Vibrate on Ring" switch has to be on, in Settings > Sounds > "Vibrate on Ring."
3. The sounds and vibrations need to be set in Settings > Sounds > Ringtone.

Here's the problem, though: if the "Ring/Silent" switch on the left side of the phone is on, then notifications from apps can't only vibrate; they have to make an accompanying sound.

I would like my phone to vibrate when I get notifications from Messenger or Gmail, but it can get annoying when the notifications make the accompanying sounds as well.