Investigation of the distribution of elastic waves in the composite cylinder with the initial torch

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Abstract


The aim of work. The work is devoted to the study of the propagation of axisymmetric longitudinal waves in a compound cylinder with initial torsion. Solution technique. The initial stresses in the cylinder are determined using the classical linear theory of elasticity. Methods for solving corresponding problems of intrinsic significance are proposed. Numerical results are given and their analysis is carried out. Results. It was found that the presence of initial torsion in cylinders does not exclude the appearance of an axisymmetric longitudinal and axisymmetric waves in a compound cylinder separately. It is found that, in the absence of initial torsion in the compound cylinder, there are intersection points between the dispersion curves corresponding to the modes of axially symmetric longitudinal and torsional waves. It is shown that in the case when initial torsion takes place on at least one cylinder, the axisymmetric longitudinal and torsional waves can not propagate separately, i.e. there is an interference between these two types of axisymmetric waves in a composite cylinder. Methods for solving the problem are developed and corresponding dispersion equations for a compound cylinder are obtained. Dispersion equations are solved and dispersion curves are obtained, an algorithm is developed for constructing these curves.


About the authors

Mugan S Guliyev

Ganja State University

Author for correspondence.
Email: a.seyfullayev@yahoo.com
187 Sh.I. Xatai Avenue, Ganja, AZ2000, Republic of Azerbaijan

Dr Sci. (Phys.-Math.), Professor, Faculty of General Technical Disciplines, Department of Physics

Alizade I Seyfullayev

Institute of Mathematics and Mechanics of the Azerbaijan National Academy of Sciences

Email: a.seyfullayev@yahoo.com
9 B. Vahabzade, Baku, AZ1143, Republic of Azerbaijan

Cand. Sci. (Phys.Math.), Chief Research Fellow, Professor Assistant, Department of Wave Dynamics, Institute of Mathematics and Mechanics

Jamile N Abdullayeva

Azerbaijan State Pedagogical University

Email: a.seyfullayev@yahoo.com
68 Uzeyir Hacibeyli, Baku, AZ1000, Republic of Azerbaijan

Lecturer, Department of Methodology for Mathematics

References

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  4. Akbarov S.D., Guliev M.S. (2008). Propagation of axisymmetric longitudinal waves in afinitely pre-strained circular cylinder embedded in a finitely pre-strained infinite elastic body. Mechanics of Composite Materials, 44(5), 465–478, doi.org/10.1007/s11029-008-9045-6.
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  6. Ozturk A., Akbarov S.D. (2009). Torsional wave propagation in a pre-stressed circular cylinder embedde in a pre-stressed elastic medium. Applied Mathematical Modelling, 33, 3636–3649.
  7. Seyfullayev A.I., Guliyev M.S. (2010). On the axisymmetric wave propagation in a finite restrained compound circular cylinder made from compressible materials. International Journal of Nanosystems, 2(2), 33–42.

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Copyright (c) 2018 Guliyev M.S., Seyfullayev A.I., Abdullayeva J.N.

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