People familiar with music terms use timpanum for a single kettledrum, and timpani (the Latin plural of timpanum) for multiple drums. For all senses of the word unrelated to music (mainly in biology, zoology, and architecture), tympanum and tympani are the preferred spellings.
Anyone not comfortable with these Latin-derived terms might understandably use English plural forms instead of the traditional Latin ones. Timpani, for instance, often appears in reference to a single drum, but musically inclined readers might see it as incorrect.