I've got several large metal and plastic sheets and they make a peculiar sound when I hold them up from one end and shake them.

The sound can be described as "warbling or wowbling" effect. I've heard the same sound from a wood saw by flexing it. My interpretation is that the sheets are are slightly concave (rather than simply flat) and flexing them applies stresses that are suddenly released and that generates an acoustical shock wave.

The process may be like the snap that's heard from the clicker in a computer mouse, except the frequency is much lower in sheets.

 

You have rediscovered an old musical instrument called a "wobble board". Now learn to play some tunes and you may win a part on American Idol!

 

A long time ago there was a musical saw that you played by flexing it.

 

Believe it or don't you can still play music on a modern saw (I have). You just need a bow with rosin coated strings or a small mallet to pint the saw you can play music.

This reminds me of Frank Zappa playing a bicycle on the Steve Allen Show (no, I'm not dating my self, am I?)

 

Rolf Harris and his wobble board

 

Stage "thunder" is done that way - shaking a big metal sheet.

 

Stage "thunder" is done that way - shaking a big metal sheet.

That's what I did for a high school play that had a thunder and lightning scene. The lightning was a strobe light from a camera.