Titlebook: Chaos in Structural Mechanics; Jan Awrejcewicz,Vadim Anatolevich Krys‘ko Book 2008 Springer-Verlag Berlin Heidelberg 2008 Bubnov-Galerkin

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Dynamics of Closed Flexible Cylindrical Shells,classical non-linear theory are studied. A transition from partial differential equations (PDEs) to ordinary differential equations (ODEs) is carried out using a higher order Bubnov-Galerkin approach and Fourier representation. On the other hand, the Cauchy problem is solved using the fourth-order Runge-Kutta method.

Soliloquy

Nonlinear Vibrations of the Euler-Bernoulli Beam Subjected to Transversal Load and Impact Actions,tudied. The governing equations include damping terms with damping coefficients ε., ε. associated with deflection . and displacement ., respectively. Damping coefficients ε., ε. and the transversal load coefficients (..,..) serve as control parameters.

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https://doi.org/10.1007/978-3-8350-9591-5Composite shells are studied in this chapter. First, equations governing the behavior of composite shells are derived, and then both static and dynamic problems of stability loss of composite shells are addressed.

圆柱

Problemstellung und Zielsetzung der Arbeit,In this chapter scenarios of transition from harmonic to chaotic motions are illustrated and discussed. First, a historical background of the problem is described. The Landau-Hopf scenario; the Ruelle, Takens, and Newhouse scenario; the Feigenbaum scenario; and the Pomeau-Manneville scenario are addressed, among others.

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https://doi.org/10.1007/978-3-8349-9113-3In this chapter both regular and chaotic vibrations, various bifurcations, and scenarios exhibited by three-layered non-linear uncoupled beams with constraints are illustrated and discussed. The finite difference approximation is applied and numerical results reliability is first rigorously discussed.

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摘要

Introduction,An overview of both Ritz and Bubnov-Galerkin methods, with an emphasis on the achievements of Eastern European countries, is provided here. The historical origin of the Bubnov-Galerkin procedure is described and its approach versus that of other projection approaches is addressed.

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Scenarios of Transition from Harmonic to Chaotic Motion,In this chapter scenarios of transition from harmonic to chaotic motions are illustrated and discussed. First, a historical background of the problem is described. The Landau-Hopf scenario; the Ruelle, Takens, and Newhouse scenario; the Feigenbaum scenario; and the Pomeau-Manneville scenario are addressed, among others.