caa a22 4500 467954496 CHVBK 20180405193745.0 cr unu---uuuuu 170328e20050301xx s 000 0 eng 10.1007/BF02637035 doi (NATIONALLICENCE)springer-10.1007/BF02637035 (NATIONALLICENCE)springer-10.1007/s00419-004-0356-3 Chaotic vibrations of spherical and conical axially symmetric shells [Elektronische Daten] [V. Krysko, J. Awrejcewicz, T. Shchekaturova] Summary: Chaotic vibrations of deterministic, geometrically nonlinear, elastic, spherical and conical axially summetric shells, subject to sign-changing transversal load using the variational principle, are analysed. The paper is motivated by an observation that variational equations of the hybrid type are suitableto solve many dynamical problems of the shells theory. It is assumed that the shell material is isotropic, and the Hook's principle holds. Intertial forces in directions tangent to mean shell surface and rotation inertia of a normal shell cross section are neglected. A transition form PDEs to ODEs (the Cauchy problem) is realized through the Ritz procedure. Next, the Cauchy problem is solved using the fourth-order Runge-Kutta method. Qualitative and quantitative analysis is carried out in the frame of both nonlinear dynamics and quantitative theory of differential equations. New scenarios from harmonic to chaotic dynamics are detected. Various vibration forms development versus control parameters (rise of arc; amplitude and frequency of the exciting force and number of vibrational modes accounted) are illustrated and discussed. Springer-Verlag, 2005 Chaos nationallicence Shells nationallicence Cauchy problem nationallicence Ritz procedure nationallicence Krysko V. Department of Mathematics, Saratov State University, 410054, B. Sadovaya, 96a, fl. 77, Saratov, Russia aut Awrejcewicz J. Department of Automatics and Biomechanics, Technical University of Lodz, 1/15 Stefanowskiego St., 90-924, Lodz, Poland aut Shchekaturova T. Department of Mathematics, Saratov State University, 410054, B. Sadovaya, 96a, fl. 77, Saratov, Russia aut Archive of Applied Mechanics Springer-Verlag 74/5-6(2005-03-01), 338-358 0939-1533 74:5-6<338 2005 74 419 https://doi.org/10.1007/BF02637035 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02637035 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Krysko V. Department of Mathematics, Saratov State University, 410054, B. Sadovaya, 96a, fl. 77, Saratov, Russia aut NATIONALLICENCE 700 1- Shchekaturova T. Department of Mathematics, Saratov State University, 410054, B. Sadovaya, 96a, fl. 77, Saratov, Russia aut NATIONALLICENCE 700 1- Awrejcewicz J. Department of Automatics and Biomechanics, Technical University of Lodz, 1/15 Stefanowskiego St., 90-924, Lodz, Poland aut NATIONALLICENCE 773 0- Archive of Applied Mechanics Springer-Verlag 74/5-6(2005-03-01), 338-358 0939-1533 74:5-6<338 2005 74 419 NATIONALLICENCE 856 40 https://doi.org/10.1007/s00419-004-0356-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Shchekaturova T.V. Department of Mathematics, Saratov State University, B. Sadovaya, 96 a, fl. 77, 410054, Saratov, Russia aut NATIONALLICENCE 700 1- Krysko V.A. Department of Mathematics, Saratov State University, B. Sadovaya, 96 a, fl. 77, 410054, Saratov, Russia aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE NATIONALLICENCE NL-springer