• Structural Engineering and Mechanics
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• v.71 no.5
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• pp.577-601
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• 2019

The paper investigates the influence of the rheological parameters which characterize the creep time, the long-term values of the mechanical properties of viscoelastic materials and a form of the creep function around the initial state of a deformation of the materials of the hollow bi-layered cylinder on the dispersion of the flexural waves propagated in this cylinder. Constitutive relations for the cylinder's materials are given through the fractional exponential operators by Rabotnov. The dispersive attenuation case is considered and numerical results related to the dispersion curves are presented and discussed for the first and second modes under the first harmonic in the circumferential direction. According to these results, it is established that the viscosity of the materials of the constituents causes a decrease in the flexural wave propagation velocity in the bi-layered cylinder under consideration. At the same time, the character of the influence of the rheological parameters, as well as other problem parameters such as the thickness-radius ratio and the elastic modulus ratio of the layers' materials on the dispersion curves, are established.

• Structural Engineering and Mechanics
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• v.77 no.5
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• pp.571-586
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• 2021

The present paper studies the influence of the inhomogeneous initial stresses in the bi-layered hollow cylinder and it is assumed that these stresses are caused by the hydrostatic pressures acting on the interior and outer free surfaces of the cylinder. The study is made by utilizing the version of the three-dimensional linearized theory of elastic waves in bodies with initial stresses for which the initial stress-strain state in bodies is determined within the scope of the classical linear theory of elasticity. For the solution to the corresponding eigenvalue problem, the discrete-analytical method is employed. Numerical results are presented and analyzed for concrete selected pairs of materials. According to these results and their analyses, it is established that, unlike homogeneous initial stresses, the influence of the inhomogeneous initial stresses on the torsional wave dispersion has not only quantitative but also qualitative character. For instance, in particular, it is established that as a result of the initial stresses caused by the hydrostatic pressure acting in the interior free surface of the cylinder, the cut-off frequency appears for the fundamental dispersive mode and the values of this frequency increase with the intensity of this pressure.

• Structural Engineering and Mechanics
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• v.61 no.1
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• pp.143-160
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• 2017

The paper studies the attenuation of the axisymmetric longitudinal waves propagating in the bi-layered hollow cylinder made of linear viscoelastic materials. Investigations are made by utilizing the exact equations of motion of the theory of viscoelasticity. The dispersion equation is obtained for an arbitrary type of hereditary operator of the materials of the constituents and a solution algorithm is developed for obtaining numerical results on the attenuation of the waves under consideration. Specific numerical results are presented and discussed for the case where the viscoelasticity of the materials is described through fractional-exponential operators by Rabotnov. In particular, how the rheological parameters influence the attenuation of the axisymmetric longitudinal waves propagating in the cylinder under consideration, is established.