4 papers
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 the Schrödinger plate
Serge N. Gavrilov, Anton M. Krivtsov, Ekaterina V. Shishkina
In this paper, we introduce "the Schrödinger plate." This is an infinite two-dimensional linear micro-polar elastic medium, with out-of-plane degrees of freedom, lying on a linear…
Anti-localization of non-stationary quasi-waves in a strongly nonlinear -FPUT chain
Serge N. Gavrilov, Ekaterina V. Shishkina, Bogdan S. Borisenkov
Recently, a new general wave phenomenon, namely "the anti-localization of non-stationary linear waves", has been introduced and discussed (Shishkina et al., J. Sound. Vib. 553, 202…