A PDEM based new methodology for stochastic dynamic stability control of nonlinear structures with fractional-type viscoelastic dampers

A probability density evolution method (PDEM) based methodology is proposed for the investigation of stochastic dynamic stability control of structures, where the fractional order state feedback control is specifically considered. This study is established based on the probability dissipated system, where the probability density evolution equation for probability dissipated system provides the quantitative basis, say the probability of stability. In such methodology, a newly developed criterion is incorporated to identify the controlled structure is dynamically stable or not. Numerical examples are carried out for the purpose of illustration. The results reveal that the stability-related performance can be significantly improved with application of fractional-type viscoelastic dampers to the structure, which is originally prone to dynamic instability under dynamic excitations.