Frequency-Dependent Material Damping Using Augmenting Thermodynamic Fields (ATF) with Fractional Time Derivatives
Abstract
This study developed a material damping model using the concept of augmenting thermodynamic fields ATF wherein the equations of thermodynamic equilibrium are allowed to have derivatives of fractional order. Current models of material damping cannot predict well the dependency of damping on frequency. Two newer models are discussed. They include the ATF model, and Bagley and Torvik's, AFIT, 4-parameter model, which allows fractional derivatives in the description of viscoelastic materials. This research effort applies fractional order derivatives to the ATF model. Coupled material constitute relations are developed using the concept of augmenting thermodynamic fields, with non integer differentials allowed in the resulting partial differential equations. The complex modulus that results from solution of these partial differential equations is compared to the complex moduli of thermoelasticity, integer order viscoelasticity, and viscoelasticity with fractional derivatives (the 4 parameter model) for the case of a uniaxial rod. In each case, the fractional order ATF model reduced to the respective model, and accurately describes the damping mechanism resulting from each of these models.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1990
- Accession Number
- ADA227053
Entities
People
- David S. Hansen
Organizations
- Air Force Institute of Technology