Press your lips together to stop the air, then release. No vocal cord vibration.

Americans pronounce periodic as peer-ee-AH-duhk (/ˌpɪriˈɑdək/). In "periodic", the "t" between vowels sounds like a quick "d" — the tongue briefly taps the ridge behind the upper teeth. This is called the Flap T, a small move that separates 'classroom' from 'native'. So instead of peer·ee·AH·tuhk, you get PEER·ee·AH·duhk. Stress falls on the third syllable — keep everything else short and quick. You'll hear it in sentences like "The periodic table lists all known chemical elements".
Record yourself saying "periodic" and play it back. The mic stays on your device — nothing's uploaded.
4 syllables, 7 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Quickly bounce the front of your tongue against the roof of your mouth. Same as Flap T — a quick tap without stopping airflow.

Relax your lips, jaw, and tongue completely. Drop your jaw slightly and keep the tongue neutral.
Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "periodic", the "t" between vowels sounds like a quick "d" — the tongue briefly taps the ridge behind the upper teeth. /t/ or /d/ becomes a quick tap [ɾ] — sounds like a soft D. The tongue briefly taps the ridge behind the upper teeth.
In "periodic", the "k" is not released — the articulators get into position but hold without the burst of air. Air stops but there's no release burst — the articulators hold position.
Stress falls on the third syllable, not the others. Stretch AH — keep everything else short and quick.
Don't pronounce the third syllable too fully. The unstressed syllable reduces to a schwa — the lazy "uh" sound — in casual speech.