Strongly Nonlinear Resonance Dynamics of Quasi-One- Dimensional Finite Oscillatory Chains

Abstract eng:
We present an extension of recently developed approach to stationary and non-stationary resonance dynamics of strongly nonlinear two degree of freedom (2DoF) systems to finite strongly nonlinear oscillatory chains (strong nonlinearity implies impossibility to use the linearized equations of motion even as a starting point of dynamic analysis). The proposed extension allows revealing new nonlinear effects in series of widely used mechanical and physical systems. There are in particular: i) breaking the symmetry caused by instability of almost all nonlinear normal modes (NNMs) and appearance of stable elliptic modes (EMs) in the initially un-stretched strings and membranes carrying discrete masses; ii) mobile breathers excitation by localized initial pulse in the un-stretched membrane; iii) efficient inter-cluster energy exchange and transition to energy localization in the un-stretched membrane and in the finite system of weakly coupled pendulums. The applications of revealed strongly nonlinear effects to solution of significant mechanical and physical problems are discussed.

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