Analysis of complex parametric vibrations of plates and shells using Bubnov-Galerkin approach

Abstract

The Bubnov-Galerkin method is applied to reduce partial differential equations governing the dynamics of flexible plates and shells to a discrete system with finite degrees of freedom. Chaotic behaviour of systems with various degrees of freedom is analysed. It is shown that the attractor dimension of a system has no relationship with the attractor dimension of any of its subsystems.

Original language	English
Pages (from-to)	495-504
Number of pages	10
Journal	Archive of Applied Mechanics
Volume	73
Issue number	7
DOIs	https://doi.org/10.1007/s00419-003-0303-8
Publication status	Published - 1 Dec 2003
Externally published	Yes

Keywords

Bubnov-Galerkin method
Chaotic vibration
Lyapunov exponent
Poincaré section
Runge-Kutta method
Shell

ASJC Scopus subject areas

Mechanics of Materials
Computational Mechanics

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10.1007/s00419-003-0303-8

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abstract = "The Bubnov-Galerkin method is applied to reduce partial differential equations governing the dynamics of flexible plates and shells to a discrete system with finite degrees of freedom. Chaotic behaviour of systems with various degrees of freedom is analysed. It is shown that the attractor dimension of a system has no relationship with the attractor dimension of any of its subsystems.",

keywords = "Bubnov-Galerkin method, Chaotic vibration, Lyapunov exponent, Poincar{\'e} section, Runge-Kutta method, Shell",

author = "J. Awrejcewicz and Krys'ko, {A. V.}",

year = "2003",

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AB - The Bubnov-Galerkin method is applied to reduce partial differential equations governing the dynamics of flexible plates and shells to a discrete system with finite degrees of freedom. Chaotic behaviour of systems with various degrees of freedom is analysed. It is shown that the attractor dimension of a system has no relationship with the attractor dimension of any of its subsystems.

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KW - Poincaré section

KW - Runge-Kutta method

KW - Shell

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