TY - JOUR
T1 - Passive nonlinear targeted energy transfer
AU - Vakakis, Alexander F.
N1 - Funding Information:
Data accessibility. This article has no additional data. Competing interests. The author has no competing interests. Funding. The concepts and results reviewed in this work were funded in part by the following Research Grants: DARPA Research Contract HR0011-10-1-0077, ARO MURI grant no. 56150-MS-MUR and NSF Research Grant nos CMMI-1000615 and CMMI-14-638558. Contributors to this work are present and past members, and academic collaborators of the Linear and Nonlinear Dynamics and Vibrations Laboratory (LNDVL) of the University of Illinois at Urbana–Champaign (http://lndvl.mechse.illinois.edu/).
Publisher Copyright:
© 2018 The Author(s).
PY - 2018/8/28
Y1 - 2018/8/28
N2 - Nonlinearity in dynamics and acoustics may be viewed as scattering of energy across frequencies/wavenumbers. This is in contrast with linear systems when no such scattering exists. Motivated by irreversible large-To-small-scale energy transfers in turbulent flows, passive targeted energy transfers (TET) in mechanical and structural systems incorporating intentional strong nonlinearities are considered. Transient or permanent resonance captures are basic mechanisms for inducing TET in such systems, as well as nonlinear energy scattering across scales caused by strongly nonlinear resonance interactions. Certain theoretical concepts are reviewed, and some TET applications are discussed. Specifically, it is shown that the addition of strongly nonlinear local attachments in an otherwise linear dynamical system may induce energy scattering across scales and 'redistribution' of input energy from large to small scales in the linear modal space, in similarity to energy cascades that occur in turbulent flows. Such effects may be intentionally induced in the design stage and may lead to improved performance, e.g. it terms of vibration and shock isolation or energy harvesting. In addition, a simple mechanical analogue in the form of a nonlinear planar chain of particles composed of linear stiffness elements but exhibiting strong nonlinearity due to kinematic and geometric effects is discussed, exhibiting similar energy scattering across scales in its acoustics. These results demonstrate the efficacy of intentional utilization of strong nonlinearity in design to induce predictable and controlled intense multi-scale energy transfers in the dynamics and acoustics of a broad class of systems and structures, thus achieving performance objectives that would be not possible in classical linear settings. This article is part of the theme issue 'Nonlinear energy transfer in dynamical and acoustical systems'.
AB - Nonlinearity in dynamics and acoustics may be viewed as scattering of energy across frequencies/wavenumbers. This is in contrast with linear systems when no such scattering exists. Motivated by irreversible large-To-small-scale energy transfers in turbulent flows, passive targeted energy transfers (TET) in mechanical and structural systems incorporating intentional strong nonlinearities are considered. Transient or permanent resonance captures are basic mechanisms for inducing TET in such systems, as well as nonlinear energy scattering across scales caused by strongly nonlinear resonance interactions. Certain theoretical concepts are reviewed, and some TET applications are discussed. Specifically, it is shown that the addition of strongly nonlinear local attachments in an otherwise linear dynamical system may induce energy scattering across scales and 'redistribution' of input energy from large to small scales in the linear modal space, in similarity to energy cascades that occur in turbulent flows. Such effects may be intentionally induced in the design stage and may lead to improved performance, e.g. it terms of vibration and shock isolation or energy harvesting. In addition, a simple mechanical analogue in the form of a nonlinear planar chain of particles composed of linear stiffness elements but exhibiting strong nonlinearity due to kinematic and geometric effects is discussed, exhibiting similar energy scattering across scales in its acoustics. These results demonstrate the efficacy of intentional utilization of strong nonlinearity in design to induce predictable and controlled intense multi-scale energy transfers in the dynamics and acoustics of a broad class of systems and structures, thus achieving performance objectives that would be not possible in classical linear settings. This article is part of the theme issue 'Nonlinear energy transfer in dynamical and acoustical systems'.
KW - Nonlinear resonance capture
KW - Passive energy transfer
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U2 - 10.1098/rsta.2017.0132
DO - 10.1098/rsta.2017.0132
M3 - Review article
C2 - 30037930
AN - SCOPUS:85051506100
VL - 376
JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
SN - 0962-8428
IS - 2127
M1 - 20170132
ER -