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

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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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Book 2008n theory and chaos and emphasizes the notion of control and stability of objects and systems the evolution of which is governed by nonlinear ordinary and partial differential equations. Computational methods, in particular the Bubnov-Galerkin method, are thus described in detail. .

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Innovation und Entrepreneurships on problems not yet satisfactorily solved. In the next section various methods devoted to stability investigations are briefly addressed, exhibiting their strong and weak points regarding applications with particular attention to computational advantages of Galerkin’s methods.

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Related literature and previous research,ddresses the spectral analysis of a stress–strain problem of any plate/shell approximated by systems of . degrees of freedom. A harmonic process convergence and spectral analysis of free nonlinear vibrations are illustrated and discussed in Sects. 3.5 and 3.6, respectively.

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Book 2008al mechanical units such as beams, plates and shells or composite systems thereof. ..The approach draws upon the well-established fields of bifurcation theory and chaos and emphasizes the notion of control and stability of objects and systems the evolution of which is governed by nonlinear ordinary

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1860-0832 f either individual or interacting structural mechanical units such as beams, plates and shells or composite systems thereof. ..The approach draws upon the well-established fields of bifurcation theory and chaos and emphasizes the notion of control and stability of objects and systems the evolution

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Construction of data set and variables,, chaos, and quasiperiodicity are also briefly revisited. Sections. 4.6–4.10 refer to both static and dynamic bifurcations and their numerical estimations. Stability loss of homogeneous shells subjected to an action of transversal loads is rigorously studied in Sect. 4.11.

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,Implikationen für Forschung und Praxis,s to chaos are illustrated and discussed. Control of the chaotic state applying synchronous action of harmonic loading torque is proposed. Investigations are carried out using the qualitative theory of differential equations and nonlinear dynamics.

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