Lateral oscillations of a straight section of a two constant based heterogeneous pipeline




heterogeneity, pipe, continuity, base, frequency, elasticity module, density


The study focuses on the natural oscillation of a straight section of an invariably heterogeneous elastic pipeline lying on a twoconstant base devised by P. L. Pasternak. The elasticity module and the specific density are regarded as a continuous function of the pipeline length coordinate, whereas the continuous function is a function that characterizes heterogeneity of the elasticity module together with its first and second derivatives. Hereby, the equation on the motion-relative deflection is a linear equation with variable coefficients of the fourth order. The problem is solved in a combined way: the first stage involves a variables separation method, whereas the second stage is carried out by the Bubnov-Galerkin orthogonality method. Specific values are calculated in the first approximation; the findings are presented in tables and graphs that illustrate dependencies between the circular frequency and heterogeneity-specifying parameters. The calculation results show a significant impact of heterogeneity upon the value of circular frequency and depend on the law of heterogeneity distribution.

Author Biographies

Вагиф Джамал оглы Гаджиев, National Academy of Sciences of Azerbaijan Str. B. Vahabzadeh 9, Baku, Azerbaijan, AZ 1143

Professor, Doctor of Physical and Mathematical sciences

Head of the Department of ''Theory of Elasticity and Plasticity''

Institute of Mathematics and Mechanics

Хагани Гияс оглы Джафаров, Azerbaijan Architecture and Construction University Str. A. Sultanova, 5, Baku, Azerbaijan, AZ 1073

graduate student


  1. Tartakovskii, S. A. (1967). Structural mechanics of pipelines. Moscow: Nedra, 312.
  2. Zavoychinskii, B. I. (1992). Durability of the main and technological pipelines. Theory, methods for calculation design. Moscow: Nedra, 271.
  3. Kravchuk, A. I., Maiboroda, V. P., Urzhumtsev, Yu. S. (1985). Mechanics of polymers and composites. Moscow: Nauka, 303.
  4. Matkarimov, A. (1986). Investigation of oscillation of viscoelastic underground pipelines under seismological influences. IZV. AN Usb.SSR, ser. tech. science, 3, 40‑44.
  5. Gadjiev, V. D., Jafarov, Kh. G. (2013). On non-homogeneous underground pipelines stability. Transactions issue mathematics and mechanics. series of physical-technical and mathematical science, XXXIII (1), 85‑89.
  6. Sofiyev, A. H., Schack, E., Haciyev, V. C., Kuruoglu, N. (2012). Effect of the two-parameter elastic foundation on the critical parameters of non-homogeneous orthotropic shells. International Journal of Structural stability and Dinamics, 12 (5), 120048‑120065. doi: 10.1142/s0219455412500411
  7. Shamrovskii, A. D., Kolesnik, D. N., Mikhailutsa, E. N. (2013). Influence of heterogeneities on rigidity of a cantilever beam. Eastern-European Journal of Enterprise Technologies, 6/7(66), 4‑7. Available at:
  8. Pasternak, P. L. (1954). Bases of a new method for calculation of bases on elastic foundation by means of two bed coefficients. Moscow: Stroyizdat, 56.
  9. Carnet, H., Lieyy, L. (1969). Free vibrations of Reinforced elastic shells. Conference of ASME, 16‑20.
  10. Babakov, I. M. (1968). Theory of oscillations. Moscow: Nauka, 559.



How to Cite

Гаджиев, В. Д. о., & Джафаров, Х. Г. о. (2014). Lateral oscillations of a straight section of a two constant based heterogeneous pipeline. Eastern-European Journal of Enterprise Technologies, 6(7(72), 4–7.



Applied mechanics