Calculation of Lyapunov exponents in impacted beam on distributed contact

This paper presents the calculation of Lyapunov exponents in a beam subjected to distributed impact. In this case, discontinuity sporadically occurs over the contacted area. The impact area is spatially discretized and the transition condition at impact instance is applied to all impact nodes in the finite element manner. The solution of the continuous vibration in the impacted beam is expressed in the modal expansion form. Then, the spectra of Lyapunov exponents in the periodic and chaotic motion are estimated for the truncated number of modes. Numerical results show that the calculated largest Lyapunov exponent agrees with the bifurcation plot.