Fractional Calculus Formulation of the Quasi-Static Viscoelastic Problem

Abstract

The purpose of this study was to demonstrate the use of fractional derivatives to capture the frequency and temperature dependency of viscoelastic material behavior. To model the frequency dependency of viscoelastic material, fractional derivatives were included in the complex modulus. Solution techniques were performed in the Laplace domain to allow for easy manipulation of the fractional derivative terms. To incorporate the temperature dependency of viscoelastic material in the complex modulus model, the method of reduced variables was employed with the use of the WLF equation. With the frequency and temperature dependency built into complex modulus, a finite element formulation was devised that incorporated elastic and viscoelastic response of a truss structure. The formulation was limited to the use of the complex modulus in the transition region, the region where the damping ability of viscoelastic material is maximized. Quasi-static motion was also assumed, which limited the response to low frequencies. Theses.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1989
Accession Number
ADA206136

Entities

People

  • Joseph B. Mccullough Iii

Organizations

  • Air Force Institute of Technology

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Aluminum
  • Calculus
  • Climate Change
  • Differential Equations
  • Eigenvalues
  • Elements
  • Engineering
  • Equations
  • Equations Of Motion
  • Frequency
  • Materials
  • Modulus Of Elasticity
  • Neoprene
  • Rubber
  • Temperature Gradients
  • Transitions

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Polymer Science and Engineering.