Dynamic response of lattice structures in linear and nonlinear regime is investigated. In the linear regime, connections between vibration and buckling are revisited in the context of plane wave propagation. The power of wave technique in picking up the correct bifurcation mode and the associated critical load is illustrated. The stability of spatially localised structures arising from homoclinics is examined in the nonlinear regime. Simple analytical results will be presented and illustrated using numerical examples.
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