Characterizing the robustness and susceptibility of steady-state dynamics in post-buckled structures to stochastic perturbations

Recent reports exemplify both the potential and the concerns encountered in implementing post-buckled structures in diverse applications. By numerical and experimental methods, characterizations have provided useful insights on the dynamic sensitivities of such bi- or multistable structures subjected to either harmonic or stochastic excitations. Yet, the more realistic scenario of combined harmonic and stochastic loading has been not been closely examined so that such sensitivities might be fully illuminated. To provide a more complete understanding on the robustness and susceptibility of multistable structures to dynamic state transitions, this research establishes new analytical and experimental methods to quantify the likelihood of triggering transitions among dynamic regimes of an archetypal post-buckled structure as a result of combined harmonic and stochastic loading. It is discovered that persistent periodic snap-through dynamics are rapidly disabled by additional noise excitation when the harmonic excitation contribution occurs at frequencies close to the linearized resonance. The extra noise may also drastically compromise the integrity of small-amplitude periodic responses that occur at frequencies around one-half of the linearized resonance. Particular relative proportions of the noise standard deviation and harmonic excitation amplitude are uncovered that most readily compromise the robustness of a given steady-state dynamic regime. The analytical method also complements prior developments focused on stochastic resonance by uncovering the broader perspective of dynamic sensitivities of post-buckled structures under arbitrary combinations of harmonic and random driving loads.