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On the effect of damping on the stabilization of mechanical systems via parametric excitation. / Arkhipova, I.M.; Luongo, A.

In: Zeitschrift für angewandte Mathematik und Physik, Vol. 67, No. 3, 2016.

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Harvard

Arkhipova, IM & Luongo, A 2016, 'On the effect of damping on the stabilization of mechanical systems via parametric excitation', Zeitschrift für angewandte Mathematik und Physik, vol. 67, no. 3. https://doi.org/10.1007/s00033-016-0659-6

APA

Arkhipova, I. M., & Luongo, A. (2016). On the effect of damping on the stabilization of mechanical systems via parametric excitation. Zeitschrift für angewandte Mathematik und Physik, 67(3). https://doi.org/10.1007/s00033-016-0659-6

Vancouver

Arkhipova IM, Luongo A. On the effect of damping on the stabilization of mechanical systems via parametric excitation. Zeitschrift für angewandte Mathematik und Physik. 2016;67(3). https://doi.org/10.1007/s00033-016-0659-6

Author

Arkhipova, I.M. ; Luongo, A. / On the effect of damping on the stabilization of mechanical systems via parametric excitation. In: Zeitschrift für angewandte Mathematik und Physik. 2016 ; Vol. 67, No. 3.

BibTeX

@article{8d87612061524ee09ec19aec26eb9304,
title = "On the effect of damping on the stabilization of mechanical systems via parametric excitation",
abstract = "{\textcopyright} 2016, Springer International Publishing.The effect of damping on the re-stabilization of statically unstable linear Hamiltonian systems, performed via parametric excitation, is studied. A general multi-degree-of-freedom mechanical system is considered, close to a divergence point, at which a mode is incipiently stable and n − 1 modes are (marginally) stable. The asymptotic dynamics of system is studied via the Multiple Scale Method, which supplies amplitude modulation equations ruling the slow flow. Several resonances between the excitation and the natural frequencies, of direct 1:1, 1:2, 2:1, or sum and difference combination types, are studied. The algorithm calls for using integer or fractional asymptotic power expansions and performing nonstandard steps. It is found that a slight damping is able to increase the performances of the control system, but only far from resonance. Results relevant to a sample system are compared with numerical findings based on the Floquet theory.",
author = "I.M. Arkhipova and A. Luongo",
year = "2016",
doi = "10.1007/s00033-016-0659-6",
language = "English",
volume = "67",
journal = "Zeitschrift fur Angewandte Mathematik und Physik",
issn = "0044-2275",
publisher = "Birkh{\"a}user Verlag AG",
number = "3",

}

RIS

TY - JOUR

T1 - On the effect of damping on the stabilization of mechanical systems via parametric excitation

AU - Arkhipova, I.M.

AU - Luongo, A.

PY - 2016

Y1 - 2016

N2 - © 2016, Springer International Publishing.The effect of damping on the re-stabilization of statically unstable linear Hamiltonian systems, performed via parametric excitation, is studied. A general multi-degree-of-freedom mechanical system is considered, close to a divergence point, at which a mode is incipiently stable and n − 1 modes are (marginally) stable. The asymptotic dynamics of system is studied via the Multiple Scale Method, which supplies amplitude modulation equations ruling the slow flow. Several resonances between the excitation and the natural frequencies, of direct 1:1, 1:2, 2:1, or sum and difference combination types, are studied. The algorithm calls for using integer or fractional asymptotic power expansions and performing nonstandard steps. It is found that a slight damping is able to increase the performances of the control system, but only far from resonance. Results relevant to a sample system are compared with numerical findings based on the Floquet theory.

AB - © 2016, Springer International Publishing.The effect of damping on the re-stabilization of statically unstable linear Hamiltonian systems, performed via parametric excitation, is studied. A general multi-degree-of-freedom mechanical system is considered, close to a divergence point, at which a mode is incipiently stable and n − 1 modes are (marginally) stable. The asymptotic dynamics of system is studied via the Multiple Scale Method, which supplies amplitude modulation equations ruling the slow flow. Several resonances between the excitation and the natural frequencies, of direct 1:1, 1:2, 2:1, or sum and difference combination types, are studied. The algorithm calls for using integer or fractional asymptotic power expansions and performing nonstandard steps. It is found that a slight damping is able to increase the performances of the control system, but only far from resonance. Results relevant to a sample system are compared with numerical findings based on the Floquet theory.

U2 - 10.1007/s00033-016-0659-6

DO - 10.1007/s00033-016-0659-6

M3 - Article

VL - 67

JO - Zeitschrift fur Angewandte Mathematik und Physik

JF - Zeitschrift fur Angewandte Mathematik und Physik

SN - 0044-2275

IS - 3

ER -

ID: 7949926