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

• Published in: Journal of sound and vibration 2020-09, Vol.481, p.115422, Article 115422
• Main Authors: Shishkina, E.V., Gavrilov, S.N., Mochalova, Yu.A.
• Format: Article
• Language: English
• Subjects: Asymptotic series; Asymptotics; Differential equations; Forced oscillation; Forced vibration; Linear wave localization; Mechanical properties; Mechanical systems; Oscillators; Parameters; Partial differential equations; Passage through resonance; Resonance; Stiffness; Trapped modes
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2020.115422

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. •A string on an elastic bed equipped with a discrete oscillator is considered.•A discrete oscillator has a time-varying stiffness.•A trapped mode can exist in the system.•A forced oscillation and passage through a resonance are under investigation.•Analytic results were verified by independent numerical calculations.