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

Abstract

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 string, lying on the Winkler foundation and equipped with a discrete linear mass-spring oscillator of time-varying stiffness. We obtain the principal term of the asymptotic expansion for the resonant solution describing the motion of the inclusion (i.e., the mass-spring oscillator). The obtained result was verified by independent numerical calculations based on solution of the corresponding partial differential equation by means of the method of finite differences. The comparison demonstrates a good agreement in a neighbourhood of the instant of resonance.

arXiv comment28 pages, 3 figures

References in corpus (3)

• Numerical study of the blowup/global existence dichotomy for the focusing cubic nonlinear Klein-Gordon equation
• Non-stationary localized oscillations of an infinite Bernoulli-Euler beam lying on the Winkler foundation with a point elastic inhomogeneity of time-varying stiffness
• Non-stationary localized oscillations of an infinite string, with time-varying tension, lying on the Winkler foundation with a point elastic inhomogeneity

Cited by in corpus (2)

• 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
• 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