Deterministic and stochastic analyses of a nonlinear system with a Biot visco‐elastic element

In the paper the Biot hysteretic model involving an infinite collection of elements whose dynamic characteristics are specified through a probability density‐like function is re‐examined; in the limit case, the Biot model yields a dynamic system with ideal hysteretic damping which is known to be problematic for random vibration analysis. It is shown that bona fide Monte Carlo simulations can be conducted for the Biot model by treating, cautiously, the integrodifferential equation which is involved; this is based on recursive calculations of double integrals encountered in the representation of the system dynamics. The numerical results which pertain to the Monte Carlo studies are further used to assess the accuracy of a statistical linearization procedure adopted in determining the response of the hysteretically damped system to white noise. Published in 2001 by John Wiley & Sons, Ltd.