Viscoelastic Timoshenko beam solutions from Euler-Bernoulli solutions

Abstract

This study presents exact relationships between the bending solutions of linear viscoelastic Timoshenko beams and linear viscoelastic Euler-Bernoulli beams under quasi-static loadings. The relationships provide a direct conversion of well-known Euler-Bernoulli solutions to that of Timoshenko solutions without further need for a more complicated shear deformable analysis. They should be useful to engineers designing shear deformable beam constructed from viscoelastic materials or exhibiting viscoelastic behavior. Further, they provide valuable exact solutions for checking the validity, convergence, and accuracy of numerical results and software for the bending analysis of linear viscoelastic Timoshenko beams.