Wavenumber Lock-in in Buckled Elastic Structures: An Analogue to Parametric Instabilities

Parametric instabilities are a known feature of periodically driven dynamic systems; at particular frequencies and amplitudes of the driving modulation, the system's quasiperiodic response undergoes a frequency lock-in, leading to a periodically unstable response. Here, we demonstrate an analogous phenomenon in a purely static context. We show that the buckling patterns of an elastic beam resting on a modulated Winkler foundation display the same kind of frequency lock-in observed in dynamic systems. Through simulations and experiments, we reveal that compressed elastic strips with modulated height alternate between predictable quasiperiodic and periodic buckling modes. Our findings uncover previously unexplored analogies between structural and dynamic instabilities, highlighting how even simple elastic structures can give rise to rich and intriguing behaviors.