A modal decomposition approach to topological wave propagation

Tempelman, Joshua R.; Vakakis, Alexander F.; Matlack, Kathryn H.

doi:10.1016/j.jsv.2023.118033

Cited by 3 publications

(2 citation statements)

References 49 publications

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“…As already shown in Eqs. ( 53)- (55), this leads to a participation of only the modes with even or odd wavenumbers, respectively. Without loss of generality we assume in the following that the synchronized sectors are j = 0 and j = N s /2 and apply the Condensation Method to Eq.…”

Section: Appendix a Nonlinear Fourier Coefficientsmentioning

confidence: 99%

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Energy Transfer and Localization in a Forced Cyclic Chain of Oscillators with Vibro-Impact Nonlinear Energy Sinks

Weidemann,

Bergman,

Vakakis

et al. 2024

Preprint

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We theoretically investigate the strongly nonlinear dynamics, inter-modal targeted energy transfer (IMTET) and energy localization in an elastically coupled cyclic chain of oscillators with vibro-impact nonlinear energy sinks (VI-NESs) under symmetric harmonic standing or traveling wave forcing. Each identical sector of the chain consists of a single linear oscillator hosting a VI-NES, which is a small mass that is freely placed inside a cavity of the oscillator. We show that the VI-NESs are able to synchronize to the global response of the structure in the form of 1:1 resonance captures with the oscillators in each sector. In addition, localized states at higher amplitudes can be found where the VI-NESs synchronize to the motion of their host-oscillators in only a subset of all sectors. We derive an analytical model to predict the frequency-amplitude branches of these synchronized solutions and study their (practical) stability numerically. We show that high and practically stable localized amplitudes only arise for sufficiently low excitation wavenumbers and weak inter-sector coupling strengths. However, even the largest practically stable amplitudes show a significant reduction of the vibration level compared to the corresponding linear resonant responses. Hence, a robust high performance of the VI-NESs is observed for all excitation wavenumbers and inter-sector coupling strengths.

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Section: Appendix a Nonlinear Fourier Coefficientsmentioning

confidence: 99%

“…Determining the group velocity as the derivative of the dispersion relation with respect to the wavenumber is a concept arising from the assumption of an infinite periodic structure. Better approximations for the system with a finite number of sectors might be found when applying the approach presented in[55].…”

mentioning

confidence: 99%