Preliminary Concepts, Methodologies and Techniques

Part of the Solid Mechanics and Its Applications book series (SMIA, volume 156)

As mentioned in the Introduction (Chapter 1), the study of targeted energy transfer (TET) in strongly nonlinear and non-conservative oscillators poses some distinct technical challenges, and dictates the use of concepts, formulations, analytical methodologies and computational techniques from different fields of applied mathematics and engineering, such as dynamical systems and bifurcation theory, theory of asymptotic approximations, numerical signal processing, and experimental dynamics. Therefore, before we initiate our study of the nonlinear dynamics of TET, it is appropriate to provide first some background information related to certain key concepts and methodologies that will be applied in the work that follows.

Specifically, we will briefly discuss the concepts of nonlinear normal mode (NNM) and nonlinear mode localization in discrete and continuous oscillators, and the occurence of nonlinear internal resonances, transient resonance captures (TRCs) and sustained resonance captures (SRCs) in undamped or damped, forced or unforced systems of coupled oscillators. These concepts will provide us with the necessary theoretical framework to base our theoretical study of the dynamics of TET; moreover, using these concepts we will be able to identify, interprete, and place into the right context complex nonlinear dynamical phenomena related to TET.

Keywords

Manifold Attenuation Convolution Sine Dition 

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