DOI: https://doi.org/10.32347/2410-2547.2019.103.235-242

Influence of conical shells geometric characteristics on their dynamic stability

Oksana Paliy, Olga Lukianchenko

Abstract


The influence of geometrical characteristics on the stability of established oscillations conical shells under the action of uniformly distributed longitudinal loads periodic in time is studied. The stability problem of nonlinear forced vibrations shells is formed on the basis of a modified finite-difference method of curvilinear grids, which allowed the transition from vector ordinary differential relations to a nonlinear system of equations. The solution of the system is constructed using the method of continuation the solution by parameter in combination with the Newton-Kantorovich method. At each step the implementation of the computational algorithm, the values of the determinants the matrix of linearized equations corresponding to symmetric or cyclically symmetric vibration modes are analyzed. The criterion for the conical shells loss of the dynamic stability was a change in the sign of the corresponding determinant or a change in the number of positive and negative diagonal elements of the matrix of linearized equations. The critical value of the dynamic load characterized the level of its intensity with the loss of stability of the shells.

The features of the oscillatory motion and loss forms of conical shells  stability are revealed. The critical values of the longitudinal loads are determined. The dependence of the critical values of the load intensity on the frequency of steady oscillations with varying geometric parameters of the conical shell is investigated.


Keywords


natural frequencies; forced oscillations; dynamic stability; conical shell; curvilinear grids method; parameter continuation method; Newton-Kantorovich method

References


Volmir A.S. Ustoychivost deformiruemyih sistem [Stability of deformable systems]. – M.: Nauka, 1967. – 984 s.(rus).

Grigolyuk E.I., Kabanov V.V. Ustoychivost obolochek [Shell stability]. – M.: Nauka, 1978. – 359 s.(rus).

Gotsulyak E.A., Gulyaev V.I., Dehtyaryuk E.S., Kirichuk A.A. Ustoychivost nelineynyih kolebaniy obolochek vrascheniya [Stability of nonlinear vibrations of revolution shells]// Prikladnaya mehanika. – Kiev, 1982. – T. 18, #6. – S. 50- 56. (rus).

Kirichuk A.A., Paliy O.N. Chislenno-analiticheskiy metod issledovaniya ustanovivshihsya kolebaniy obolochechnyih konstruktsiy [A numerical-analytical method for studying the steady-state vibrations of shell structures]// Matematicheskie modeli v obrazovanii, nauke i promyishlennosti: Sbornik nauchnyih trudov. – Sankt-Peterburgskoe otdelenie MAN VSh, 2003. – S. 55-58. (rus).

Kyrychuk O.A., Palii O.M. Matematychna model parametrychnykh neliniinykh kolyvan tonkykh obolonok [Mathematical model of parametric nonlinear oscillations of thin shells] // Vistnyk KhNTU. – Kherson: KhNTU, 2008. – Vyp. 2(31). – S. 230-234.(ukr)

Palii O.M., Lukianchenko O.O. Chastotnyi analiz vidhuku odnopoloho hiperboloida na periodychne povzdovzhnie navantazhennia [Frequency analysis of response of same-sex hyperboloid to periodic longitudinal loading]// Opir materialiv i teoriia sporud: nauk.-tekh. zbirn. – K.: KNUBA, 2019. – Vyp. 102. – S. 199-206.


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