Random excitation of a yielding cantilever: Approximate analysis versus simulations

Random vibrations of elasto-plastic cantilever beams excited by earthquakes are studied. Distribution of mass and stiffness, as well as plastic zones spreading over the beam, are taken into account. Following a complete elastic-inelastic analogy, strain is splitted into a drift and a linear elastic portion. The linear part is derived under the condition of time-invariant stiffness and is subjected to an effective earthquake excitation. Stochastic response measures of the drift process are calculated using results of the linear analysis corresponding to this effective and updated loading. Analogously, the nonlinear deflection process is considered. Special emphasis is given to the comparison between this approximate probabilistic theory and the results of extensive simulations, using a very efficient cpu-time saving version of the deterministic theory. For practical applications, a nondimensional representation is given using a similarity complex.