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Showing 1 to 12 of 12 for “"nonlinear normal modes"”.
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Analytical amd experimental aspects of nonlinear normal modes and nonlinear mode localization
In this work, several aspects of nonlinear normal modes (NNMs) and free and forced nonlinear mode localization are investigated. In the first phase of the work, new asymptotic methodologies based on the concept of NNM are developed in order to compute synchronous responses for two classes of …
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Parameter Estimation of Structural Systems Possessing One or Two Nonlinear Normal Modes
… that can be described in terms of one or two nonlinear normal modes. We model the dynamics of these modes by second-order ordinary-differential equations based on the principles of mechanics, past experience, and engineering judgment. We perform a number of separate experiments on a two-mass …
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Prediction of Limit Cycle Oscillation in an Aeroelastic System using Nonlinear Normal Modes
There is a need for a nonlinear flutter analysis method capable of predicting limit cycle oscillation in aeroelastic systems. A review is conducted of analysis methods and experiments that have attempted to better understand and model limit cycle oscillation (LCO). The recently developed method of …
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Problems in nonlinear dynamics
Three types of problems in nonlinear dynamics are studied. First, we use a complex-variable invariant-manifold approach to determine the nonlinear normal modes of weakly nonlinear discrete systems with one-to-one and three-to-one internal resonances. Cubic geometric nonlinearities are considered. …
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Theoretical and Experimental Studies of the Nonlinear Dynamics of a Class of Vibroimpact Systems
In the third phase, the nonsimilar nonlinear normal modes of a two degree of freedom vibroimpact problem are obtained analytically, using a Non Smooth Temporal Transformation (NSTT). The modes thus obtained are compared with numerical simulations and their stability is also studied. The bifurcation …
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Nonlinear Dynamics in Metamaterials under Elastic and Plastic Excitation and Spectral Submanifold Parameterization
Nonlinear dynamics have been studied and applied by researchers in many contexts, two of which, elastic-plastic wave propagation in metamaterials and nonlinear normal modes, are examined here. The first topic examined herein addresses the cross-section of plastic wave propagation and elastic …
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Nonlinear Analysis and Control of Aeroelastic Systems
Presence of nonlinearities may lead to limit cycle oscillations (LCOs) in aeroelastic systems. LCOs can result in fatigue in wings leading to catastrophic failures. Existence of LCOs for velocities less than the linear flutter velocity has been observed during flight and wind tunnel tests, making …
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Performance of Nonlinear Mechanical, Resonant-Shunted Piezoelectric, and Electronic Vibration Absorbers for Multi-Degree-of-Freedom Structures
… Limited evaluation of the performance of nonlinear vibration absorbers for nonlinear structures exists in the current literature. The state of the art is extended in this work to vibration absorbers in their three major physical implementations: the mechanical vibration absorber, the …
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A Theoretical and Experimental investigation of Nonlinear Vibrations of Buckled Beams
… methods to determine approximate solutions of nonlinear continuous systems. Recently, it has been proved that finite-degree-of-freedom Galerkin-type discretization procedures applied to some distributed-parameter systems may fail to predict the correct dynamics. By contrast, direct procedures …
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Data-driven system identification of strongly nonlinear modal interactions and model updating of nonlinear dynamical systems
… reduced-order models of the dynamics of nonlinear dynamical systems; the reason is that, typically, nonlinearities introduce new dynamical phenomena that have no counterparts in linear settings. This dissertation focuses on a recently developed, data-driven nonlinear system identification …
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Strongly nonlinear acoustics of one-dimensional granular sonic vacua
This research is concerned with the nonlinear dynamics and acoustics of one dimensional ordered granular media. In particular the considered granular systems are composed of discrete elastic spherical beads that mutually interact through strongly nonlinear Hertzian force interaction law. In this …