Many of the strange attractors associated with low dimensional differential equations are known to contain transverse homoclinic orbits. In particular, the Duffing equation with negative linear stiffness, which models the behavior of a buckled beam subject to transverse excitation, possesses such orbits. On the assumption that the chaotic time history of a single variable in such an equation can be represented by the random superposition of deterministic structures, each being a single excursion around a homoclinic orbit, the power spectrum of the variable in question is predicted. Good agreement is demonstrated among our predictions, numerical simulations of Duffing's equation and experimental spectra obtained from a cantilever beam buckled by magnetic forces.
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics
- Mechanics of Materials
- Acoustics and Ultrasonics
- Mechanical Engineering