Stochastic Methods in Nonlinear Structural Dynamics

The uncertainties are inherent in any structural problem. Here attention is focused only on the uncertain nature of the dynamic actions and its consequences on the structural response. In the framework of stochastic dynamics, only three methods are the most used: the Moment Equation Method (MEM), the Stochastic Linearization (SL) and the Monte Carlo Simulation (MCS). The MEM in conjuction with a closure method (CM) allows to obtain the response statistical moments, but it increases in complexity as the problem dimension increases. The SL is easily applied to a large variety of engineering problems. Providing information limited to the first two moments of the system response, unfortunately it suffers of accuracy in the case of strongly nonlinear behavior. MCS is able to give additional information on the structural response, yielding estimates for the probability density function of the nonlinear response, but it is computationally expensive. In this paper some improvements of these three methods are presented, which allow to overcome the aforementioned drawbacks.