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Über dieses Buch

The papers in this volume address advanced nonlinear topics in the general areas of vibration mitigation and system identification, such as, methods of analysis of strongly nonlinear dyanmical systems; techniques and methodologies for interpreting complex, multi-frequency transitions in damped nonlinear responses; new approaches for passive vibration mitigation based on nonlinear targeted energy transfer (TET) and the associated concept of nonlinear energy sink (NES); and an overview and assessment of current nonlinear system identification techniques.



Mitigation Strategies for Systems Subjected to Vibratory, Shock and Seismic Loads

Worldwide, society has made a tremendous investment in constructed infrastructure, such as buildings and bridges. While the fraction of infrastructure vulnerable to large-scale earthquakes tends to belocalized by geography (e.g., the Pacific Rim), there is ample evidence for widespread vulnerability. This strongly suggests the need to develop eective strategies to protect not only new construction but also existing structures likely to be subjected to damaging eathquakes. While various passive, semi-active and active methods for mitigating the eects of earthquakes have been designed for and in some cases applied to large scale structures, none has been shown to be simple, inexpensive, and widely applicable. We now examine the application of TET to the seismic protection of frame structures, in response to this need for a fully passive isolation strategy, lightweight and inexpensive but capable of high performance over a wide range of earthquakes of dierent properties.
Lawrence A. Bergman

Targeted Energy Transfer in Systems with Periodic Excitations

We show that the steady state response of a primary system under harmonic excitation with an attached nonlinear energy sink (NES) exhibits not only common steady — state and weakly modulated responses, but also strongly modulated responses (SMRs), which may be regarded as the extension of the targeted energy transfer (TET) phenomenon to structures under periodic excitation. SMRs are related to relaxation oscillations of the corresponding averaged dynamical flows, and can be regarded as repetitive TET under persisting periodic forcing. The possible application of NESs as strongly nonlinear vibration absorbers is then discussed, and it is shown that the efficiency of the NESs can far exceed that of properly tuned linear absorbers (or tuned mass dampers — TMDs).
O. V. Gendelman, Y. Starosvetsky

Advanced Strategies for Nonlinear System Identification

This chapter contains a review of the past and recent developments in system identifi cation of nonlinear dynamical structures. The objective is to present several approaches that have been proposed in the technical literature, to illustrate them using numerical and experimental applications, to highlight their assets and limitations.
G. Kerschen

CISM Courses and Lectures: Resonant energy exchange in nonlinear oscillatory chains and Limiting Phase Trajectories: from small to large systems

We present an adequate analytical approach to the description of nonlinear vibration with strong energy exchange between weakly coupled oscillators and oscillatory chains. The fundamental notion of the limiting phase trajectory (LPT) corresponding to complete energy exchange is introduced. In certain sense this is an alternative to the nonlinear normal mode (NNM) characterized by complete energy conservation. Well-known approximations based on NNMs turn out to be valid for the case of weak energy exchange, and the proposed approach can be used for the description of nonlinear processes with strong energy exchange between weakly coupled oscillators or oscillatory chains. Such a description is formally similar to that of a vibro-impact process and can be considered as starting approximation when dealing with other processes with intensive energy transfer. At first we propose a simple analytical description of vibrations of nonlinear oscillators. We show that two dynamical transitions occur in the system. First of them corresponds to the bifurcation of anti-phase vibrations of oscillators. And the second one is caused by coincidence of LPT with separatrix dividing two stable stationary states and leads to qualitative change in both phase and temporal behavior of the LPT (in particular, temporal dependence of the amplitude becomes resembling that for vibro-impact vibrations). Next problem under consideration relates to intensive inter modal exchange in the periodic nonlinear systems with finite (n>2) number of degrees of freedom. We consider two limiting cases. If the number of particles is not large enough, the energy exchange between nonlinear normal modes in two-dimensional integral manifolds is considered. When the number of the particles increases the energy exchange between neighbor integral manifolds becomes important that leads to formation of the localized excitations resembling the breathers in the one-dimensional continuum media. Finally, the breathers in the infinite systems of complex (helix) structure are presented.
Leonid I. Manevitch, Valeri V. Smirnov

Signal Processing for Experiments with Nonlinear Energy Sinks

This chapter summarizes several notes on signal processing and numerical computation that have been compiled in the course of performing the experiments reported throughout this volume. While these techniques are certainly not limited to processing data from nonlinear dynamics research, they have proven particularly useful in helping obtain good quantitative agreement between simulations and experiments with the strongly nonlinear models treated herein. Without careful attention to matters such as transducer dynamics, recovering correct time his tory data is especially difficult, and errors that might go unnoticed in the analysis of linear systems can be unacceptable in the nonlinear setting.
D. Michael McFarland

Nonlinear Targeted Energy Transfer and its Application to Vibration Mitigation

We discuss the concept of passive nonlinear targeted energy transfer (TET) and its application to vibration mitigation. By TET we denote the one-way passive transfer of vibration energy from a primary system to an attached lightweight attachment (termed nonlinear energy sink — NES), where this energy is locally confined and dissipated without spreading back to the primary system. Applications of the concept of TET to passive vibration mitigation of discrete and continuous oscillators are discussed.
Alexander F. Vakakis
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