What type of clear adhesive would you use?
You don't use adhesives. Plexiglass moves. A piece 12" long might expand 1/2" with change in temperature. Lexan doesn't expand that much, but it still needs room to move. Also Plexiglass will break and Lexan won't. Go to an art store that has custom frames, or ask the dealer at the plastic store what is recommended.
You said wood frame. Can you cut grooves in the wood to hold the plastic?