Damping Operators in Continuum Models of Flexible Structures: Explicit Models for Proportional Damping in Beam Torsion.

摘要

A new, explicit representation of damping operators for strictly proportional damping for the torsion mode of a finite beam is presented. The damping operator is the square root of the stiffness operator (enhanced to include the boundary) and is calculated using the Balakrishnan formula. It is nonlocal, and for the clamped (or fixed ) end case, turns out to be a finite-limit version of the Hilbert transform; with end mass (or boundary control), the square-root operator introduces nonlocal terms on the boundary as well. Keywords: Damping; Flexible structures; Torsion; Beams(Structural); AMS Subject classifications: 35MO5, 76A10; Reprints; Structural engineering; Americal mathematical society. (JG)