Localized oscillations of an Euler--Bernoulli beam with time-varying parameters on a visco-elastic foundation: asymptotics, adiabatic invariant, and equivalent Hamiltonian system
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Institution: Institute of Problems of Mechanical Engineering
Language: English
Subfield: Mechanical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7165631079