A mathematical model for linear elastic systems with structural damping

Source abstract

We present a mathematical model exhibiting the empirically observed damping rates in elastic systems. The models studied are of the form ( A A the relevant elasticity operator) $$x ¨ + B x ˙ + A x = 0 \ddot x + B\dot x + Ax = 0$$ with B B related in various ways to the positive square root, A 1 / 2 {A^{1/2}} , of A A . Comparison with existing “ad hoc” models is made.