Fractional Viscoelastic Transversally Isotropic Timoshenko Beam

In this paper the viscoelastic behavior of pultruded beams has been examined. Pultruded beams are constituted by a polymer infilled with reinforcement in longitudinal direction, while in the orthogonal direction no fiber are present for technological reasons. As a consequence the material has two different behaviors in longitudinal and in orthogonal directions. It follows that pultruded beams are transversally isotropic, and the shear deformation may not be neglected. Based upon the previous observations and assuming for Creep and/or Relaxation test the power law, the constitutive equations are ruled by fractional operators. From constitutive laws, and assuming the Timoshenko beam theory to account for the shear, the equations of the beam are derived. Experimental test performed on the specimen of the pultruded beam have been carried out confirming the validity of the fractional differential equations here derived.