Strongly nonlinear beats in the dynamics of an elastic system with a strong local stiffness nonlinearity: Analysis and identification

作者: Mehmet Kurt , Melih Eriten , D. Michael McFarland , Lawrence A. Bergman , Alexander F. Vakakis

DOI: 10.1016/J.JSV.2013.11.021

关键词: PhysicsNonlinear systemMathematical analysisCantileverControl theoryHilbert–Huang transformSystem identificationStiffnessNonlinear resonanceNormal modeNonlinear system identification

摘要: Abstract We consider a linear cantilever beam attached to ground through strongly nonlinear stiffness at its free boundary, and study dynamics computationally by the assumed-modes method. The of this system has no component, so it is essentially nonlinearizable. find that strong nonlinearity mostly affects lower-frequency bending modes gives rise beat phenomena. Analysis these beats proves they are caused internal resonance interactions normal (NNMs) system. These resonances not classical type since occur between whose linearized natural frequencies necessarily related rational ratios; rather, due energy-dependence frequency oscillation corresponding NNMs (arising from local nonlinearity) energy ranges where rationally related. Nonlinear effects start different level for each mode. Lower influenced lower energies larger modal displacements than higher thus, certain levels, become related, which results in resonance. studied using reduced order model Then, identification method developed, capable identifying interactions. It based on an adaptive step-by-step application empirical mode decomposition (EMD) measured time series, makes valid multi-frequency beating signals. Our work extends earlier approach developed nearly mono-frequency (monochromatic) extended applied considered with end.

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