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Dispersion of Axisymmetric Longitudinal Waves in A Bi-Material Compound Solid Cylinder Made of Viscoelastic Materials

S.D. Akbarov1,2, T. Kocal3, T. Kepceler1
Department of Mechanical Engineering, Yildiz Technical University, Yildiz Campus, 34349, Be-siktas, Istanbul, Turkey; E-mail: (S.D. Akbarov); Kepceler)
Institute of Mathematics and Mechanics of the National Academy of Sciences of Azerbaijan, 37041, Baku, Azerbaijan
Department of Marine Engineering Operations, Yildiz Campus, 34349 Besiktas, Istanbul, Turkey,E-mail:

Computers, Materials & Continua 2016, 51(2), 105-143.


The paper studies the dispersion of axisymmetric longitudinal waves in the bi-material compound circular cylinder made of linear viscoelastic materials. The investigations are carried out within the scope of the piecewise homogeneous body model by utilizing the exact equations of linear viscoelasto-dynamics. The corresponding dispersion equation is derived for an arbitrary type of hereditary operator and the algorithm is developed for its numerical solution. Concrete numerical results are obtained for the case where the relations of the constituents of the cylinder are described through fractional exponential operators. The influence of the viscosity of the materials of the compound cylinder on the wave dispersion is studied through the rheological parameters which indicate the characteristic creep time and long-term values of the elastic constants of these materials. Dispersion curves are presented for certain selected dispersive and non-dispersive attenuation cases under various values of the problem parameters and the influence of the aforementioned rheological parameters on these curves is discussed. As a result of the numerical investigations, in particular, it is established that in the case where the rheological parameters of the components of the compound cylinder are the same, the viscosity of the layers' materials causes the axisymmetric wave propagation velocity to decrease.


Characteristic creep time, Viscoelastic material, Wave dispersion, Bi-material compound solid cylinder, Wave attenuation.

Cite This Article

S. . Akbarov, T. . Kocal and T. . Kepceler, "Dispersion of axisymmetric longitudinal waves in a bi-material compound solid cylinder made of viscoelastic materials," Computers, Materials & Continua, vol. 51, no.2, pp. 105–143, 2016.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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