9 citations · 24 across the 9 of their papers we have counts for
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Localized oscillation 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
We consider localized oscillation of an Euler--Bernoulli beam on a visco-elastic foundation coupled to a damped discrete oscillator. All parameters of the system independently vary…
On the adiabatic invariance of the action of a trapped wave
Ekaterina V. Shishkina, Serge N. Gavrilov
Recently, it has been shown (Gavrilov et al., Nonlinear Dyn, 112, 2024) that in a linear solid discrete-continuous system with several slowly time-varying parameters, the amplitude…
Energy transport in a free Euler-Bernoulli beam in terms of Schrödinger's wave function
Serge N. Gavrilov, Anton M. Krivtsov, Ekaterina V. Shishkina
The Schrödinger equation is not frequently used in the framework of the classical mechanics, though historically this equation was derived as a simplified equation, which is equiva…