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Constitutive Equations for Steady-State Oscillations

  • Danton Gutierrez-LeminiEmail author
Chapter

Abstract

Although the viscoelastic constitutive equations in either integral or differential form apply in general, irrespective of the type of loading, or the point in time at which the response is sought, it is possible to derive from them constitutive equations of a form especially well suited to steady-state oscillations. This chapter uses complex algebra to transform the integral and differential constitutive equations of viscoelasticity, defined in the time domain, into algebraic expressions in the complex plane. The chapter also examines the relationships between the material property functions defined in the time domain, and their complex-variable counterparts, and examines the problem of energy dissipation during steady-state oscillations, important in the design of mounts for vibratory equipment, among others.

Keywords

Steady state Complex Real Imaginary Harmonic Excitation Frequency Storage Loss Constitutive Euler Fourier Argand Dirichlet Laplace Newton Transform Modulus Compliance Amplitude Integral Differential Energy 

References

  1. 1.
    J.D. Ferry, Viscoelastic Properties of Polymers (Wiley, New York, 1980), pp. 11–14Google Scholar
  2. 2.
    W. Flügge, Viscoelasticity, 2nd edn (Springer, New York, 1975), pp. 95–120Google Scholar
  3. 3.
    A.S. Wineman, K.R. Rajagopal, Mechanical Response of Polymers, an Introduction (Cambridge University Press, Cambridge, 2000), pp. 115–147Google Scholar
  4. 4.
    R. M. Christensen, Theory of viscoelasticity,2nd edn (Dover, New York, 1982), pp. 21–26Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Special Products DivisionOil States Industries, Inc.ArlingtonUSA

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