Analysis of transition regions of bi-linear, parametrically driven, two-oscillator model: Resonant excitation in the neighborhood of non-similar NNMs. (October 2022)

• Record Type: Journal Article
• Authors: Kumar, Anish; Starosvetsky, Yuli; Jayaprakash, K.R.
• Is Part Of: International journal of non-linear mechanics. Volume 145(2022)
• Publication Date: 2022-10
• Subjects: Nonlinear normal mode -- Parametric resonance -- Bi-linear oscillator -- Resonant excitation; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2022.104074
• Languages: English
• ISSNs: 0020-7462

Abstract

Abstract: Present study is concerned with the analysis of special family of parametric instability tongues emerging in the dissipative bi-linear model of two oscillators subjected to parametric excitation. The study focuses on analytical approximation and characterization of instability regions corresponding to the resonant, non-similar NNMs. In spite of the complexity of the problem under investigation, we succeeded in devising a novel and efficient analytical approach, which provides an explicit analytical approximation of transition regions corresponding to the special family of most significant sub-harmonic ( m : 1 ) resonance tongues, corresponding to IP and OP NNMs. Analytical study of the model reveals some interesting and unusual properties of instability regions of damped-driven, bi-linear system. Presently devised analytical procedure shows a fairly good correspondence with the direct numerical simulations of the full model.