9 citations · 24 across the 9 of their papers we have counts for
9 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…
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…
Universal formal asymptotics for localized oscillation of a discrete mass-spring-damper system of time-varying properties, embedded into a one-dimensional medium described by the telegraph equation with variable coefficients
Serge N. Gavrilov, Ilya O. Poroshin, Ekaterina V. Shishkina +1
We consider a quite general problem concerning a linear free oscillation of a discrete mass-spring-damper system. This discrete sub-system is embedded into a one-dimensional contin…
Non-stationary elastic wave scattering and energy transport in a one-dimensional harmonic chain with an isotopic defect
Serge N. Gavrilov, Ekaterina V. Shishkina
The fundamental solution describing non-stationary elastic wave scattering on an isotopic defect in a one-dimensional harmonic chain is obtained in an asymptotic form. The chain is…
The anti-localization of non-stationary linear waves and its relation to the localization. The simplest illustrative problem
Ekaterina V. Shishkina, Serge N. Gavrilov, Yulia A. Mochalova
We introduce a new wave phenomenon, which can be observed in continuum and discrete systems, where a trapped mode exists under certain conditions, namely, the anti-localization of…
Non-stationary oscillation of a string on the Winkler foundation subjected to a discrete mass-spring system non-uniformly moving at a sub-critical speed
Serge N. Gavrilov, Ekaterina V. Shishkina, Ilya O. Poroshin
We consider non-stationary free and forced transverse oscillation of an infinite taut string on the Winkler foundation subjected to a discrete mass-spring system non-uniformly movi…