Viscoelastic Timoshenko beam theory

Harry H. Hilton

Research output: Contribution to journalArticlepeer-review


The concept of elastic Timoshenko shear coefficients is used as a guide for linear viscoelastic Euler-Bernoulli beams subjected to simultaneous bending and twisting. It is shown that the corresponding Timoshenko viscoelastic functions now depend not only on material properties and geometry as they do in elasticity, but also additionally on stresses and their time histories. Possible viscoelastic definitions are formulated and evaluated. In general, the viscoelastic relations are sufficiently complicated so that the elastic-viscoelastic correspondence principle (analogy) cannot be applied. This is particularly true for, but not limited to, elastic shear coefficients which are Poisson ratio dependent. Expressions for equivalent viscoelastic Timoshenko shear functions must, therefore, be derived de novo on a case by case basis, taking in to account specific relaxation moduli, stresses, temperatures and their time histories. Thus the elastic simplicity and generality is lost and hence rendering the use of viscoelastic Timoshenko shear functions as highly impractical. Consequently, it is necessary to directly solve the coupled viscoelastic beam governing relations for bending and twisting deflections by using appropriate solution protocols as discussed herein.

Original languageEnglish (US)
Pages (from-to)1-10
Number of pages10
JournalMechanics of Time-Dependent Materials
Issue number1
StatePublished - 2009


  • Timoshenko beams
  • Timoshenko shear coefficients and functions
  • Viscoelasticity

ASJC Scopus subject areas

  • General Chemical Engineering
  • General Materials Science
  • Aerospace Engineering
  • Mechanical Engineering


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