Improved stochastic linearization technique for structures with nonlinear viscous dampers

The stochastic linearization technique (SLT), in its conventional force-based Gaussian version (FB-G-SLT), is widely adopted in the literature to handle the nonlinear power-law constitutive behavior of fluid viscous dampers (FVDs), either for evaluating the system response, or within optimal design strategies. In this note, the authors prove that, for the kind of nonlinearity induced by FVDs, this version of FB-G-SLT is not the best choice, especially if the velocity-related response is of major importance in an optimal design process. As an example, the energy dissipated by the devices depends upon the square of the velocity at the ends of the dampers. Among six different formulations of SLT examined in this note, an equal-energy non-Gaussian SLT (EE-NG-SLT) is found to be superior to the FB-G-SLT since it more satisfactorily captures the nonlinear response of the structure as predicted by Monte Carlo simulations. This alternative EE-NG-SLT, without requiring higher computational effort than the FB-G-SLT, is therefore recommended, especially when energy-based (or, in general, velocity-related) objective functions are used in the optimization problem of nonlinear viscous dampers.