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We analyze the dynamics of a model of a nanobeam under compression. The modelis a two mode truncation of the Euler-Bernoulli beam equation subject tocompressive stress. We consider parameter regimes where the first mode isunstable and the second mode can be either stable or unstable, and theremaining modes (neglected) are always stable. Material parameters usedcorrespond to silicon. The two mode model Hamiltonian is the sum of a(diagonal) kinetic energy term and a potential energy term. The form of thepotential energy function suggests an analogy with isomerisation reactions inchemistry. We therefore study the dynamics of the buckled beam using theconceptual framework established for the theory of isomerisation reactions.When the second mode is stable the potential energy surface has an index onesaddle and when the second mode is unstable the potential energy surface has anindex two saddle and two index one saddles. Symmetry of the system allows us toconstruct a phase space dividing surface between the two "isomers" (buckledstates). The energy range is sufficiently wide that we can treat the effects ofthe index one and index two saddles in a unified fashion. We have computedreactive fluxes, mean gap times and reactant phase space volumes for threestress values at several different energies. In all cases the phase spacevolume swept out by isomerizing trajectories is considerably less than thereactant density of states, proving that the dynamics is highly nonergodic. Theassociated gap time distributions consist of one or more `pulses' oftrajectories. Computation of the reactive flux correlation function shows nosign of a plateau region; rather, the flux exhibits oscillatory decay,indicating that, for the 2-mode model in the physical regime considered, a rateconstant for isomerization does not exist.

Isomerization dynamics of a buckled nanobeam