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Nonlinear Targeted Energy Transfer in Discrete Linear Oscillators with Single-DOF Nonlinear Energy Sinks

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Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems

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

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In this chapter we initiate our study of passive nonlinear targeted energy transfer — TET (or, so-called nonlinear energy pumping) by considering discrete systems consisting of linear coupled oscillators (refered to from now on as ‘primary systems’) with single-DOF (SDOF) essentially nonlinear attachments. In later chapters we will extend this study to discrete and elastic continuous systems with SDOF or MDOF nonlinear attachments. We aim to show that under certain conditions, the nonlinear attachments are capable of passively absorbing and locally dissipating significant portions of vibration energy of the primary systems to which they are attached. Moreover, this passive targeted energy transfer will be shown to occur over broad frequency ranges, due to the capacity of the nonlinear attachments will be capable to engage in transient resonance (i.e., in transient resonance captures) with linear modes of the primary systems at arbitrary frequency ranges. Then, in essence, these essentially nonlinear attachments will act as nonlinear energy sinks (NESs).

By applying analytic methodologies especially developed for studying strongly nonlinear transient regimes (such as the CX-A method introduced in Section 2.4), performing numerical simulations, and post-processing the results by means of the signal analysis techniques discussed in Section 2.5, we will be able to study, model and understand the dynamical mechanisms governing passive nonlinear TET in the systems under consideration. Moreover, we will formulate appropriate measures for assessing the TET efficiency of different configurations of NESs, which, ultimately, will enable us to establish conditions for optimal TET in the systems considered. At the end of this chapter we will extend the study of TET to infinite-DOF chains with SDOF essentially nonlinear attachments and investigate TET generated by impeding elastic waves to boundary NESs.

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(2008). Nonlinear Targeted Energy Transfer in Discrete Linear Oscillators with Single-DOF Nonlinear Energy Sinks. In: Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems. Solid Mechanics and Its Applications, vol 156. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9130-8_3

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