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Construction of the approximate stability equations of motion for an elastic cylindrical body under axial compressive load

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Abstrakty
EN
A method of constructing nonlinear motion stability equations for isotropic elastic bodies is developed for cylindrical bodies of standard material of the 2nd order subjected to the action of “dead” axial compressive forces. The perturbation of the displacement vector is given by its approximate decomposition with respect to the base of tensor functions of the 1st, 2nd and 3d valences. The time-dependent tensor coefficients of the decomposition satisfy the system of ordinary differential equations. Based on the obtained equations one can investigate the balance stability of cylindrical bodies under various fixing conditions.
Twórcy
autor
  • Institute for Applied Problems of Mechanics and Mathematics, Ukraine
autor
  • Lviv National Ivan Franko University, Ukraine
Bibliografia
  • 1. Azhermachev G. 2013. Technique of analysis of reinforced concrete columns operating at a cyclic load [in Russian]/ G. Azhermachev, E. Mennakov, N. Shevchenko // MOTROL. MOTORYZACJA I ENERGETYKA ROLNICTWA. – Tom 15. № 5, Lublin, 77-81. (in Poland).
  • 2. Banakh I. 2004. Approximate equations of motion stability for elastic bodies under complex load/ I.Banakh and M. Kolinko // Visn. Lviv. Derzh. Ah-rar. Univ., Ser. Arkhitekt. Sil’s’ko-Hospod. Budivn., No. 5, 105–116. (in Ukraine).
  • 3. Banakh I. 2003. On a variant of equations of motion stability of elastic bodies/ I.Banakh and M. Kolinko// Visn. Lviv. Derzh. Ahrar. Univ., Ser. Arkhitekt. Sil’s’ko-Hospod. Budivn., No. 4, 52–58. (in Ukraine).
  • 4. Banakh I.Ya. 1997. The construction of a solution of the problem of the stress-strain state of a cylinder under complex load by the method of expansion in tensor functions / I.Ya Banakh// Visn. Lviv. Univ., Ser. Mekh.-Matem., No. 48, 114–123. (in Ukraine).
  • 5. Bolotin V.V. 1961. Nonconservative Problems of the Theory of Elastic Stability [in Russian] / V.V. Bolotin // Moscow, 1961. (in Russia).
  • 6. Bolotin V.V. 1956. The Dynamic Stability of Elastic Systems [in Russian]/ V.V. Bolotin // Moscow. (in Russia).
  • 7. Chernykh K. F. 1986. The Nonlinear Theory of Elasticity in Engineering Calculations [in Russian]/K.F.Chernykh// Mashinostroenie, Leningrad. (in Russia).
  • 8. Domanskii P. P. 1997. Method of expansion in tensor functions in constructing the equations of motion stability for elastic cylindrical bodies/ P. P. Domanskii// Dopovidi Akad. Nauk Ukrainy, No. 6, 53–59. (in Ukraine).
  • 9. Grinchenko V. T. 1978. Equilibrium and Steady- State Vibrations of Elastic Bodies of Finite Dimensions [in Russian]/ V. T. Grinchenko// Naukova Dumka, Kiev. (in Ukraine).
  • 10. Guz' N. 1986. Fundamentals of the Three- Dimensional Theory of Stability of Deformable Bodies [in Russian]/ N. Guz'// Vyshcha Shkola, Kiev. (in Ukraine).
  • 11. Lakshmikantham V. 1991. The Stability of Motion: A Comparison Method [in Russian]/ V. Lakshmikantham, S. Leela, and A. A. Martynyuk// Naukova Dumka, Kiev. (in Ukraine).
  • 12. Lurie A.I. 1980. Nonlinear theory of elasticity [in Russian]/ A.I. Lurie// Nauka, Moscow. (in Russia).
  • 13. Sintsov V. 2014 The stress-strain state of the elements of a supporting column of a marine steel stationary structure of a platform in zone of contact with ice [in Russian]/ Sintsov, A. Fursov// MOTROL. MOTORYZACJA I ENERGETYKA ROLNICTWA. – Tom 15. № 5, Lublin, 157-163. (in Poland).
  • 14. Timoshenko S.P. 1970. Theory of Elasticity S.P./ Timoshenko, J.N. Goodier// McGraw-Hill. (in Ukraine).
  • 15. Ulitko F. 1979. The Method of Eigen Vector Functions in the Spatial Problems of Elasticity Theory [in Russian]/ F. Ulitko //Nauk. Dumka, Kiev. (in Ukraine).
  • 16. Vol'mir S. 1967. The Stability of Deformable Systems [in Russian]/ S. Vol'mir// Nauka, Moscow. (in Russia).
  • 17. Vus I.Ya. 1996. The mathematical model of a spatial motion of elastic bodies/ I.Ya. Vus and P.P. Domanskii// Visn. Lviv. Univ., Ser. Mekh.- Matem., No. 45, 154–161. (in Ukraine).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-08005ed5-803f-4d9a-830e-81a4f8748f61
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