ASYMPTOTIC APPROXIMATIONS FOR SYSTEMS INCORPORATING FRACTIONAL DERIVATIVE DAMPING

Viscoelastic constitutive relationships incorporating fractional deriv atives have been previously shown to be extremely useful in describing the frequency dependent behavior of common damping materials. However , the implementation of such models in the analysis of damped mechanic al systems is some,what complicated by the fact that polynomial equati ons with noninteger order exponents must be solved. This paper develop s accurate approximations from which the damping factor and damped nat ural frequency of such systems may be obtained by evaluating relativel y simple algebraic expressions.