The Star Trek Universe rarely shows Vulcan ships, and when they do, they usually don't seem to be that powerful. The Federation, Romulans, Klingons, Borg, Cardassians, Dominion, etc. all seem to have ships that are designed for battle. They had to have had their own fleet before they became a member of the Federation. We usually see Vulcan ships as science and exploration ships, and they didn't seem to be heavily armed. Why do Vulcans, as an advanced species, have such a small fleet onscreen, and why didn't see see them in the TNG era after they joined the Federation?
The Vulcans have at least one canonically seen combat vessel: the D'kyr class "combat cruiser". It's both well-shielded and well-armed as well as being quite nippy.
ARCHER: Take a look at your long-range sensors. There's a Vulcan combat cruiser a few million kilometres from here. Unless you want to upset them, I suggest you turn around.
This class of vessel is referred to in the scripts as being a
powerful-looking Vulcan ship[s]
In the Extended Universe, we encounter an even more formidable Vulcan ship, the ShRaan-class, described as being even more powerful than their combat cruisers.
Dropping out of warp were two more DKyr-type combat cruisers, and one of the larger, better-armed ShRaan-class ships, which looked like a spear jammed through a hoop. The weaponry the newcomers carried between them would be more than enough to blow both Columbia and the remnants of the cargo fleet to little more than drifting trails of vapor in a few seconds, polarized hull plating notwithstanding.
Assuming you are asking about the TOS/TNG era, the Vulcans are a Federation member and don't have their own warships just like Earth doesn't have its own warships.
The Vulcan ships that we do encounter are generally civilian or science vessels. While it may appear that most Federation ships are human-dominated, we do sometimes encounter Federation ships that are primilary manned by Vulcans, such as TOS era Intrepid.
In short, this is sort of like asking why California doesn't have battleships.