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Structural Engineering and Mechanics Volume 72, Number 5, December10 2019 , pages 597-615 DOI: https://doi.org/10.12989/sem.2019.72.5.597 |
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Dispersion of axisymmetric longitudinal waves in a \"hollow cylinder + surrounding medium\" system with inhomogeneous initial stresses |
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Surkay D. Akbarov and Emin T. Bagirov
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| Abstract | ||
| The paper studies the dispersion of the axisymmetric longitudinal wave propagating in the \"hollow cylinder + surrounding medium\" system with inhomogeneous initial stresses caused by the uniformly distributed radial compressional forces acting at infinity. Up to now in the world literature, there exist only a few investigations related to the wave dispersion in a hollow cylinder with inhomogeneous initial stresses. Therefore, this paper is one of the first attempts in this field in the sense of the development of investigations for the case where the cylinder is surrounded with an infinite medium. The three-dimensional linearized theory of elastic waves is used for describing the considered wave propagation problem and, for a solution to the corresponding mathematical problem, the discrete-analytical solution method is developed and employed. The corresponding dispersion equation is obtained and this equation is solved numerically and, as a result of this solution, the dispersion curves are constructed for the first and second modes. By analyzing these curves, the character of the influence of the inhomogeneous initial stresses on the dispersion curves is established. In particular, it is established that as a result of the inhomogeneity of the initial stresses both new dispersion curves and the \"band gap\" for the wave frequencies can appear. | ||
| Key Words | ||
| inhomogeneous initial stresses; \"hollow cylinder + surrounding medium\" system; discrete-analytical method; wave dispersion; dispersion curves; band gap | ||
| Address | ||
| Surkay D. Akbarov and Emin T. Bagirov: Yildiz Technical University, Faculty of Mechanical Engineering, Department of Mechanical Engineering, Yildiz Campus, 3349, Besiktas, Istanbul-Turkey Emin T. Bagirov: Institute of Mathematics and Mechanics of National Academy of Sciences of Azerbaijan, Az141, Baku, Azerbaijan | ||