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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Invariant Manifolds, Nonclassical Normal Modes, and Proper Orthogonal Modes in the Dynamics of the ed as a three-dimensional invariant manifold in phase space. This manifold is computed analytically by applying the method of geometric singular perturbations. This manifold is nonlinear and for all energy and angular momentum levels is characterized precisely by three PO (proper orthogonal) modes.

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Normal Vibrations in Near-Conservative Self-Excited and Viscoelastic Nonlinear Systems,lf-excited nonlinear systems close to conservative systems taking into account similar nonlinear normal modes. The analytical construction is presented for some concrete systems. Namely, two linearly connected Van der Pol oscillators with nonlinear elastic characteristics and a simplest twodegrees-o

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Nonlinear Normal Modes of a Parametrically Excited Cantilever Beam,he method of multiple scales to the governing nonlinear nonautonomous integral-partial-differential equation and associated boundary conditions. In the absence of damping, it is shown that the system has nonlinear normal modes, as defined by Rosenberg, even in the presence of the parametric excitati

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Normal Modes and Boundary Layers for a Slender Tensioned Beam on a Nonlinear Foundation,based method is used to obtain NNMs. In conjunction with a matched asymptotic expansion, we analyze, through simple formulas, the local effects that a small bending stiffness has on the dynamics, along with the secular effects caused by a symmetric nonlinearity. Nonlinear mode shapes are computed an

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The Description of Localized Normal Modes in a Chain of Nonlinear Coupled Oscillators Using Complex the dynamic equations. The ideas of the approach are first developed for the case of the system with two degrees of freedom. Special attention is paid to the study of localized normal modes in a chain of weakly coupled nonlinear oscillators. We discuss also certain peculiarities of the localization

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Spatially Localized Models of Extended Systems,n on large one-dimensional domains displays spatiotemporally complex dynamics that are remarkably well-localized in both real and Fourier space, as demonstrated by a (spline) wavelet representation. We show how wavelet projections may be used to construct various localized, relatively low-dimensiona

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Mode Localization in Dynamics and Buckling of Linear Imperfect Continuous Structures,ntal concepts about localization are introduced and similarities between dynamics and buckling localization are highlighted. In particular, it is shown that strong localization of the normal modes is due to turning points in which purely imaginary characteristic exponents assume a non zero real part

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Dynamics of Relative Phases: Generalised Multibreathers,iodic orbits we construct a nearby submanifold and an ‘effective Hamiltonian’ on it such that the difference between the two Hamiltonian vector fields is small. The effective Hamiltonian is independent of one coordinate, the ‘overall phase’, and hence the corresponding action is preserved. Unlike st