Timpani, when played in the standard playing position, are extremely resonant instruments. In some cases, this is a desired and effective sound. In others, it can disrupt an intentional silence or throw a wedge into a piece’s harmony.
In most cases, the drums are muted with the hands pressing lightly on the head to stop vibration. Usually the decision on when to mute is left to the performer, but it is possible to notate specific moments on which to do so. This (and many other timpani techniques) is notated wonderfully in Elliot Carter’s Eight Pieces for Four Timpani.
In this piece, Carter uses small x note heads to indicate when a certain drum should be dampened, notated rhythmically to maximize clarity.
If continuous muted sounds are desired, one solution is to lay pieces of felt on the drum’s head to take away any resonance. Keep in mind that removing a mute is an action just like striking a drum, and changing the status of the mute while playing can be demanding, and in some cases, physically impossible.
A note on staccato: Staccato markings on timpani do not automatically imply anything. For many, this might just change the way a player strikes the head. Muting techniques of any kind should be specified beyond this.