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Titlebook: Normal Modes and Localization in Nonlinear Systems; Alexander F. Vakakis Book 2001 Springer Science+Business Media Dordrecht 2001 beam.bou

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Mode Localization in Dynamics and Buckling of Linear Imperfect Continuous Structures,formed into a sequence of algebraic problems in which the spatial variable appears as a parameter. Applications of the method are worked out for beams and strings on elastic soil. All these structures are found to have nearly-defective system matrices, so their characteristic exponents are highly sensitive to imperfections.
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978-90-481-5715-0Springer Science+Business Media Dordrecht 2001
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Dynamics of Relative Phases: Generalised Multibreathers,ct eigenvalues which move at non-zero speed with ε,the linear stability type of the periodic orbit can be read off from the effective Hamiltonian. Our principal application is to networks of oscillators or rotors where many such submanifolds of periodic orbits occur at the uncoupled limit — simply e
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Nonlinear Modal Analysis of Structural Systems Using Multi-Mode Invariant Manifolds,the usual projection onto a set of linear modes, and the invariant manifold approach developed herein. The results show that the method is capable of accurately representing the nonlinear system dynamics with relatively few degrees of freedom over a range of vibration amplitudes.
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