- Pezeshki, C. and Dowell, E.H., Generation and analysis of Lyapunov exponents for the buckled beam,
Int. J. Non-Linear Mech. (UK), vol. 24 no. 2
pp. 79 - 97 [0020-7462(89)90001-2] .
(last updated on 2007/04/10)
Lyapunov exponents are calculated for the one, two, three and four mode modal projections of the partial differential equation governing the buckled beam. The projection used was taken from a previous paper by Tang and Dowell. Issues such as modal convergence and convergence of the values of the Lyapunov exponents are examined. Finally, the numerical values are compared to experimental values calculated from time series taken from an experimental apparatus also previously used in Tang and Dowell. Power spectra calculated from the experimental time series are also compared with power spectra calculated from theoretical time histories. Conjectures concerning use of the Lyapunov dimension as an estimate of number of required modes are also advanced
buckling;convergence of numerical methods;partial differential equations;