The internal resonance of a two degree-of-freedom mechanical system with all typical (quadratic and cubic) geometric nonlinearities is studied, limiting to the case of free dynamics. The Multiple Time Scale method is used to provide an analytical, closed form, approximation of the backbone curves. The cornucopia of different possible behaviours that can been obtained by varying the nonlinear stiffnesses is discussed in depth, illustrating them with some examples and verifying with numerical simulations. Some partially unexpected or relevant behaviours are highlighted, and some hints on how to exploit the proposed results to design nonlinearly tailored systems are given.
1:1 internal resonance in a two d.o.f. complete system: a comprehensive analysis and its possible exploitation for design / Clementi, F.; Lenci, S.; Rega, G.. - In: MECCANICA. - ISSN 0025-6455. - STAMPA. - 55:(2020), pp. 1309-1332. [10.1007/s11012-020-01171-9]