Axisymmetric longitudinal wave dispersion in a bi-layered circular cylinder with inhomogeneous initial stresses

Forced Vibration of the Non-Homogeneously Pre-Stressed System Consisting of the Hollow Cylinder and Surrounding Medium

“…Finally, note that the discrete-analytical solution method which is employed in the present paper was also used in the papers [Akbarov (2006); Akbarov and Panachli (2015); Akbarov, Guliyev and Yahnioglu (2017); Akbarov, Guliyev, Sevdimaliyev et al (2018)], and is also detailed in the monograph by Akbarov [Akbarov (2015)]. Moreover, note that this method was used in the works [Akbarov and Bagirov (2019); Bagirov, Akbarov and Seyfullayev (2018)] in which an attempt is made for consideration of the corresponding wave dispersion and moving load problem acting in the cylindrical cavity containing the infinite elastic medium with non-homogeneous pre-stresses.…”

“…In the principal sense, the discrete analytical method employed in the present paper is the same as that employed in the papers [Akbarov, Guliyev, Sevdimaliyev et al (2018); Akbarov and Bagirov (2019)]. However, in the present paper, this method is developed and employed for the problem under consideration, wherein the solution procedure differs significantly from those considered in the previous papers.…”

“…Despite the significance of the related investigations, up to now such investigations, i.e. investigations regarding the dynamics of the structural elements with non-homogeneous pre-stresses are almost completely absent (except for a few works carried out in the investigations [Engin and Suhubi (1978); Shearer, Abrahams, Parnel et al (2013); Wu, Su, Liu et al (2018); Akbarov and Bagirov (2019); Bagirov, Akbarov and Seyfullayev (2018)]. Notwithstanding this, the corresponding problems related to the stability loss of mine workings with inhomogeneous initial stresses have been studied by Guz and his students, the results of which are detailed in the monograph by Guz [Guz (1977)] and a review of which is given in the paper by Guz [Guz (2003)].…”

“…At the same time, it should be noted that in these investigations, the mine workings are modelled as an infinite homogeneous elastic or elastoplastic medium containing a cylindrical cavity and having initial nonhomogeneous axisymmetric stresses and the variational method is developed for the solution to the corresponding eigenvalue problems. Now we attempt to detail the investigations made in the aforementioned works [Engin and Suhubi (1978); Shearer, Abrahams, Parnell et al (2013); Wu, Su, Liu et al (2018); Akbarov and Bagirov (2019); Bagirov, Akbarov and Seyfullayev (2018)]. Note that in the papers [Engin and Suhubi (1978); Shearer, Abrahams, Parnell et al (2013)], torsional waves in the hollow cylinder made of incompressible highly elastic materials are studied and it is assumed that the non-homogeneous pre-stresses therein are caused by static internal and external uniformly distributed compressional radial forces.…”

“…Consequently using the results obtained in these works, the paper by Wu et al [Wu, Su, Liu et al (2018)] solves the wave propagation equations by utilizing the state-space formalism for these equations with the approximate laminate or multi-layer technique. The paper by Akbarov et al [Akbarov and Bagirov (2019)] studies the longitudinal axisymmetric wave dispersion in a bi-layered (bi-material) hollow cylinder with nonhomogeneous pre-stresses caused by the hydrostatic pressures acting on the faces of that. For the solution to the corresponding field equations, the discrete analytical method is employed and numerical results on the influence of the mentioned non-homogeneous pre-stresses on the dispersion of the longitudinal axisymmetric waves are presented and discussed.…”