Viscoelastic and structural damping analysis with designer materials

The interrelationships between viscoelastic, Newtonian viscous and structural (Coulomb friction) damping are analyzed in terms of Fourier transforms and complex moduli in the frequency domain and are also interpreted in terms of behavioral responses associated with real material compliances or moduli in the real time space. It is shown that the correspondence between viscous and elastic structural damping is spurious, severely limited to only harmonic motion and that it does not extend to more complicated viscoelastic materials beyond Newtonian viscous flow dissipation. The dissipation energy generated by viscoelastic and structural damping is also examined. The effects of structural damping on elastic and viscoelastic bending-torsion flutter are evaluated with the help of numerical examples. The material considered is aluminum, but the analysis is general and can be applied to any viscoelastic material such as high polymer composites. It is shown that the presence of increased structural damping does not necessarily have stabilizing effects by decreasing the viscoelastic or elastic flutter speed nor are the viscoelastic flutter speeds necessarily lower than the corresponding elastic ones. An analysis is developed for analytically designing material properties and geometric sizing to tailor elastic and viscoelastic damping responses in order to control prescribed events subject to pre-selected constrains, such as cost, weight, geometry, maximum deflections, minimum flutter velocity, life times, dissipation energy, composite fiber orientation, volume fractions, etc. A simple illustrative example and future research directions are presented.