Determining Frequency-Energy Dependencyof Nonlinear Normal Modes and Internal ResonancesUsing a Numerical Independent Approach

Application of linear normal modes to the nonlinear area provides an in-depth investigation of structures. In this paper, a straightforward approach is proposed to investigatenonlinear normal modes (NNMs) thoroughly and focus on all possible solutions and bifurcations, independent of all initial assumptions and prior solutions. In this context, afterdiscretization of the response domain over an appropriate resolution, a periodicity algorithm is suggested to capture the solutions that meet the NNMs criteria. Afterward, thefrequency and energy of the system during accepted responses and degrees of freedom(DOFs)’ relations are derived. Finally, after verifying the proposed approach and acquir-ing new internal resonances, the frequency-energy plots and NNMs of a nonlinear elasticsystem with more substantial nonlinearities and a two-story steel structure with nonlinearmaterial are studied. It is worth noting that the periodicity algorithm and capturing allpossible solutions and bifurcations are among the apparent novelties of the current paper.

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Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).