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PreprintCC BY-NC-ND 4.0arXiv

Localized oscillations of an Euler--Bernoulli beam with time-varying parameters on a visco-elastic foundation: asymptotics, adiabatic invariant, and equivalent Hamiltonian system

  • Ekaterina V. Shishkina
  • Serge N. Gavrilov
  • Yulia A. Mochalova
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Abstract

We consider localized oscillations of an Euler--Bernoulli beam on a visco-elastic foundation coupled to a damped discrete oscillator. All system parameters vary slowly and independently in time. For the conservative case, we employ three different analytical approaches: an asymptotic method, a technique based on the adiabatic invariance of the action of a trapped wave, and an analysis of the equivalent Hamiltonian system. All three approaches yield the identical formula for the oscillation amplitude. In the dissipative case, the oscillation amplitude is obtained solely via the asymptotic approach. Finally, we validate our analytical findings against numerical simulations, demonstrating excellent agreement.

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Cite

BibTeXRIS
BibTeX
@misc{shishkina2026localized,
  title = {{Localized oscillations of an Euler--Bernoulli beam with time-varying parameters on a visco-elastic foundation: asymptotics, adiabatic invariant, and equivalent Hamiltonian system}},
  author = {Ekaterina V. Shishkina and Serge N. Gavrilov and Yulia A. Mochalova},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2606.22444},
  eprint = {2606.22444},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.22444},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Localized oscillations of an Euler--Bernoulli beam with time-varying parameters on a visco-elastic foundation: asymptotics, adiabatic invariant, and equivalent Hamiltonian system
AU  - Ekaterina V. Shishkina
AU  - Serge N. Gavrilov
AU  - Yulia A. Mochalova
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2606.22444
UR  - https://arxiv.org/abs/2606.22444
AB  - We consider localized oscillations of an Euler--Bernoulli beam on a visco-elastic foundation coupled to a damped discrete oscillator. All system parameters vary slowly and independently in time. For the conservative case, we employ three different analytical approaches: an asymptotic method, a technique based on the adiabatic invariance of the action of a trapped wave, and an analysis of the equivalent Hamiltonian system. All three approaches yield the identical formula for the oscillation amplitude. In the dissipative case, the oscillation amplitude is obtained solely via the asymptotic approach. Finally, we validate our analytical findings against numerical simulations, demonstrating excellent agreement.
ER  -