Question

How to calculate the energy in thermoelastic damping?

Answer 1

If a force is applied to an elastic rod such that it elastically bends the rod, there is some amount of heat energy created in the rod due to this bending. If the rod is released from it's displaced state it would swing back to it's original state and then over swing by some value, this oscillation would quickly damp to 0 and there would be a static rod remaining.

Now the #1 rule when it comes to energy lost is it's always heat - so clearly the energy from this rod is lost through heating (in fact if I repeatedly stretch an elastic band it heats - this is probably related). 

Answer 2

As a result, the developed thermal-energy method can calculate thermoelastic damping in micromechanical resonators ...