On the transfer function modeling of flexible structures with distributed damping

Abstract

The authors have suggested the use of distributed passive damping via constrained viscoelastic layer surface treatments, as a means of augmenting active controllers for flexible structures. This enhances system stability and provides justification for the use of low order dynamic models and controllers. In previous work a co located transfer. function based upon experimental measurements was employed in root locus analysis of a system with passive damping. Here we present a method of deriving co located and non-colocated transfer functions for flexible systems with distributed damping. The (sandwich) flexible structure is modeled as though it was constructed of an equivalent homogeneous material exhibiting linear viscoelastic behavior. Transfer functions are obtained through solution of a modified form of the Bernoulli-Euler equation which is derived using the standard constitutive relationship between stress and strain for viscoelastic materials in place of Hook's law. General observations are made with regard to open loop pole and zero locations for colocated and non-colocated transfer functions. The effect of joint damping is also considered.