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Passage through resonance for a system with time-varying parameters possessing a single trapped mode | | Ekaterina V. Shishkina
; Serge N. Gavrilov
; Yulia A. Mochalova
; | | Date: |
28 Jun 2019 | | Abstract: | We consider a forced oscillations of an infinite-length mechanical system,
with time-varying parameters, possessing a single trapped mode characterized by
frequency $Omega_0(epsilon t)$. The system is a string, lying on the Winkler
foundation, and equipped with a discrete linear mass-spring oscillator of
time-varying stiffness. The discrete oscillator is subjected to harmonic
external force with constant frequency $hatOmega$. In the case of the passage
through the resonance, we obtain the principal term of the asymptotic expansion
describing the motion of the inclusion (e.g. the mass-spring oscillator). To do
this we use the combination of two asymptotic approaches. The first one was
suggested in Gavrilov and Indeitsev (2002) and used in our recent study
Gavrilov et al. (2019b) to describe the free localized oscillation in the
system under consideration. The second one was used in Kevorkian (1971, 1974)
to describe the passage through the resonance in a single degree of freedom
system. The obtained result was verified by independent numerical calculations
based on solution of the corresponding PDE by means of the method of finite
differences. The comparison demonstrates a good mutual agreement. | | Source: | arXiv, 1907.0067 | | Services: | Forum | Review | PDF | Favorites | |
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