Numerical analysis of viscoelastic Timoshenko beams reveals dynamic response patterns, suggesting effective modeling techniques.
Summary: The quasi-static and dynamic responses of a linear viscoelastic Timoshenko beam on Winkler foundation are studied numerically by using the hybrid Laplace-Carson and finite element method. In this analysis we use the field equation for viscoelastic material. In the transformed Laplace-Carson space, two new functionals have been constructed for viscoelastic Timoshenko beams through a systematic procedure based on the Gâteaux differential. These functionals have six and two independent variables, respectively. We obtain two mixed finite element formulations: TB12 and TB4. For the inverse transform, Schapery and Fourier methods are used. Numerical results for quasi-static and dynamic responses of several viscoelastic models illustrate the approach.
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Yalçin et al. (1999) studied this question.
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