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Structural Engineering and Mechanics
  Volume 38, Number 5, June10 2011 , pages 593-618

Analytic solution for the interaction between a viscoelastic Bernoulli-Navier beam and a winkler medium
Claudio Floris and Francesco Paolo Lamacchi

    This paper deals with the problem of the determination of the response of a viscoelastic Bernoulli-Navier beam, which is resting on an elastic medium. Assuming uniaxial bending, the displacement of the beam axis is governed by an integro-differential equation. The compatibility of the displacements between the beam and the elastic medium is imposed through an integral equation. In general and in particular in the case of a Boussinesq medium, the solution has to be pursued numerically. On the contrary, in the case of a Winkler\'s medium the compatibility equation becomes a linear finite relationship, which allows finding an original analytical solution of the problem for both hereditary and aging behavior of the beam. Some numerical examples complete the paper, in which a comparison is made between the hereditary and the aging model for the creep of the beam.
Key Words
    beams; creep; analytical solution; contact problem; Winkler
Claudio Floris and Francesco Paolo Lamacchi: Department of Structural Engineering, Politecnico di Milano, I-20133 Milano, Italy

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