Abstract
In this paper the jump phenomena in quasilinear Duffing systems under sinusoidal and narrow band random excitations are examined by numerical simulations. The simulation results for sinusoidal excitations agree very well with analytical solutions obtained by the equivalent linearization method. The results showing the sensitivity of the periodic responses to the initial conditions are believed to be the first published in the literature. The simulation results for narrow band random excitations confirm that multi-level mean square responses can occur for mono-level excitations, but only for very narrow bandwidth excitations. The multi-level random responses are also sensitive to initial conditions. As the bandwidth of the excitation broadens, the multi-level responses merge into a single level one.
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