12 citations · 43 across the 6 of their papers we have counts for
6 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…
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…
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…
Passage through a resonance for a mechanical system, having time-varying parameters and possessing a single trapped mode. The principal term of the resonant solution
Ekaterina V. Shishkina, Serge N. Gavrilov, Yulia A. Mochalova
We consider a forced oscillation and passage through resonance for an infinite-length system, having time-varying parameters and possessing a single trapped mode. The system is a s…
Non-stationary localized oscillations of an infinite Bernoulli-Euler beam lying on the Winkler foundation with a point elastic inhomogeneity of time-varying stiffness
E. V. Shishkina, S. N. Gavrilov, Yu. A. Mochalova
We consider non-stationary localized oscillations of an infinite Bernoulli-Euler beam. The beam lies on the Winkler foundation with a point inhomogeneity (a concentrated spring wit…
Non-stationary localized oscillations of an infinite string, with time-varying tension, lying on the Winkler foundation with a point elastic inhomogeneity
S. N. Gavrilov, E. V. Shishkina, Yu. A. Mochalova
We consider non-stationary oscillations of an infinite string with time-varying tension. The string lies on the Winkler foundation with a point inhomogeneity (a concentrated spring…