"to break in or into pieces," c.1200, from the source of shiver (n.). Chiefly in phrase shiver me timbers (1835), "a mock oath attributed in comic fiction to sailors" [OED]. My timbers! as a nautical oath is attested from 1789 (see timber (n.)). Related: Shivered; shivering.
"shake," c.1400, alteration of chiveren (c.1200), of uncertain origin, perhaps from Old English ceafl "jaw," on notion of chattering teeth. Spelling change of ch- to sh- is probably from influence of shake. Related: Shivered; shivering.
"small piece," c.1200, probably related to Middle Low German schever, schiver "splinter," from Proto-Germanic *skif- "split" (cf. Old High German skivaro, German Schiefer "splinter, slate"). Commonly in phrases to shivers. Also, shiver is still dialectal for "a splinter" in Norfolk and Lincolnshire.