Speaker
Description
The paper is devoted to ambient temperature influence on dynamic characteristics of viscoelastic layered plates i.e. structures applied in many fields of engineering under various physical conditions. Damping properties of common viscoelastic materials depend on thermal conditions, as is frequently reported [1], thus the problem has significant practical importance.
The Zener fractional material model with separation of deviatoric and volumetric deformation is chosen to describe viscoelasticity of the plate layers. Plate kinematics is described using the refined zig-zag theory [2].
It is assumed that viscoelastic material is rheologically simple, thus the temperature influence obeys the time-temperature superposition principle. The vertical shift of characteristic curves is neglected and the horizontal shift factor is computed. In the analyses the results obtained using the most frequently used Williams-Landel-Ferry formula [1] and those from less frequently applied methods including the Arrhenius, Kaelble and Drake-Soovere formulae [3,4] will be compared and discussed. Two latter approaches can also be used in the thermal conditions corresponding to the glassy phase, as they remain valid on both sides of the deflection point of the characteristic curve.
The principle of virtual work and the Laplace transform are used to formulate the problem of the plate free vibrations. The resulting non-linear eigenvalue problem is solved iteratively using the homotopy method. The results in the form of complex eigen-values and eigen-vectors allow to find the natural frequency, the damping ratio, and the vibration modes.
The results of several analyses of layered plates with various viscoelastic materials with the material data available in the literature [3], will be presented in the conference. In particular, the analyses will focus on the comparison of the dynamic characteristics obtained for various methods for the shift factor determination.
Acknowledgments
The research presented in this paper was funded by the university grant 0411/SBAD/0010.
REFERENCES
[1] H.F. Brinson, L.C. Brinson, Polymer Engineering Science and Viscoelasticity. an introduction, Springer, New York (2008)
[2] A. Tessler, M. Di Sciuva, M. Gherlone, A consistent refinement of first-order shear deformation theory for laminated composite and sandwich plates using improved zigzag kinematics, J. Mech. Mater. Struct. 5(2), 341–367 (2010)
[3] A. Arikoglu, A new fractional derivative model for linearly viscoelastic materials and parameter identification via genetic algorithms, Rheol. Acta 53, 219–233 (2014)
[4] G.M. Rowe, M.J. Sharrock, Alternate shift factor relationship for describing temperature dependency of viscoelastic behaviour of asphalt materials, Transport Res. Rec. 2207, 125–135 (2011)
