Periodic, quasi-periodic, and chaotic geometrically nonlinear forced vibrations of a shallow cantilever shell

被引：0
作者：
K. V. Avramov
S. E. Malyshev
机构：
[1] National Academy of Science of Ukraine,Department of Vibrations, Podgorny Institute for Mechanical Engineering
[2] National Technical University “KhPI”,Department of Continuum Mechanics
来源：
Acta Mechanica | 2018年 / 229卷
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摘要：
Geometrically nonlinear forced vibrations of a cantilever shallow shell are analyzed. A finite degree of freedom nonlinear dynamical system is derived using the assumed mode method. The Neimark–Sacker bifurcations are detected close to the first principal resonance. The quasi-periodic vibrations, which originate from these bifurcations, are investigated numerically. These vibrations are transformed into chaotic motions as a result of the forcing frequency variation. Sub-harmonic vibrations with large amplitudes are analyzed in a wide forcing frequency range close to the second principal resonance.
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页码：1579 / 1595
页数：16
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  • [31] Thomas O(2017)Analysis of nonlinear free vibration of circular plates with cut-outs using J. Sound Vib. 394 593-611
  • [32] Touze C(2015)-function method Int. J. Non-Linear Mech. 69 109-128
  • [33] Chaigne A(2003)Vibrations of shallow shells rectangular in the horizontal projection with two freely supported opposite edges Appl. Mech. Rev. 56 349-381
  • [34] Amabili M(2014)Dynamic instability of shallow shells in three-dimensional incompressible inviscid potential flow Int. J. Non-Linear Mech. 58 233-257
  • [35] Nagai K(2001)Non-linearities in rotation and thickness deformation in a new third-order thickness deformation theory for static and dynamic analysis of isotropic and laminated doubly curved shells ZAMM J Appl. Math. Mech. 96 458-467
  • [36] Maruyama S(2001)Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid structure interaction SIAM J. Numer. Anal. 39 442-462
  • [37] Murata T(1991)Non-linear vibrations of shells: a literature review from 2003 to 2013 Int. J. Bifurc. Chaos 1 3-11
  • [38] Yamaguchi T(1997)Investigation of the stress-strain state of the laminated shallow shells by R-functions method combined with spline-approximation Int. J. Bifurc. Chaos 7 2105-2126
  • [39] Kurpa L(2016)Weighted extended B-spline approximation of Dirichlet problems J. Vib. Control 25 1198-1216
  • [40] Pilgun G(undefined)Tutorial on continuation undefined undefined undefined-undefined
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