Kumar, AnishAnishKumarStarosvetsky, YuliYuliStarosvetskyJayaprakash, K. R.K. R.Jayaprakash2025-08-312025-08-312022-10-0110.1016/j.ijnonlinmec.2022.1040742-s2.0-85132551486https://d8.irins.org/handle/IITG2025/25912Present 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.falseBi-linear oscillator | Nonlinear normal mode | Parametric resonance | Resonant excitationArticleOctober 20221104074arJournal1WOS:000811830800001