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We numerically study a one dimensional, nonlinear lattice model which in thelinear limit is relevant to the study of bending (flexural) waves. In contrastwith the classic one dimensional mass-spring system, the linear dispersionrelation of the considered model has different characteristics in the lowfrequency limit. By introducing disorder in the masses of the latticeparticles, we investigate how different nonlinearities (cubic, quartic andtheir combination) lead to energy delocalization, equipartition and chaoticdynamics. We excite the lattice using single site initial momentum excitationscorresponding to a strongly localized linear mode and increase the initialenergy of excitation. Beyond a certain energy threshold, when the cubicnonlinearity is present, the system is found to reach energy equipartition andtotal delocalization. On the other hand, when only the quartic nonlinearity isactivated, the system remains localized and away from equipartition at leastfor the energies and evolution times considered here. However, for large enoughenergies for all types of nonlinearities we observe chaos. This chaoticbehavior is combined with energy delocalization when cubic nonlinearities arepresent, while the appearance of only quartic nonlinearity leads to energylocalization. Our results reveal a rich dynamical behavior and show differenceswith the relevant Fermi-Pasta-Ulam-Tsingou model. Our findings pave the way forthe study of models relevant to bending (flexural) waves in the presence ofnonlinearity and disorder, anticipating different energy transport behaviors.

Energy spreading, equipartition and chaos in lattices with non-central forces